├── readme ├── actualalbedo1.png ├── browse_image.PNG ├── blackskyalbedo.jpg └── whiteskyalbedo.jpg ├── example-data ├── MCD43A1.006_aid0001.nc └── MCD43A1-Texas-request.json ├── example-output └── MCD43A_calcalbedo.nc ├── f_albedo.R ├── README.md ├── vis_lut.csv ├── sw_lut.csv ├── nir_lut.csv └── main_albedo.R /readme/actualalbedo1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jjmcnelis/mcd43-calculated-albedo/HEAD/readme/actualalbedo1.png -------------------------------------------------------------------------------- /readme/browse_image.PNG: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jjmcnelis/mcd43-calculated-albedo/HEAD/readme/browse_image.PNG -------------------------------------------------------------------------------- /readme/blackskyalbedo.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jjmcnelis/mcd43-calculated-albedo/HEAD/readme/blackskyalbedo.jpg -------------------------------------------------------------------------------- /readme/whiteskyalbedo.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jjmcnelis/mcd43-calculated-albedo/HEAD/readme/whiteskyalbedo.jpg -------------------------------------------------------------------------------- /example-data/MCD43A1.006_aid0001.nc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jjmcnelis/mcd43-calculated-albedo/HEAD/example-data/MCD43A1.006_aid0001.nc -------------------------------------------------------------------------------- /example-output/MCD43A_calcalbedo.nc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jjmcnelis/mcd43-calculated-albedo/HEAD/example-output/MCD43A_calcalbedo.nc -------------------------------------------------------------------------------- /example-data/MCD43A1-Texas-request.json: -------------------------------------------------------------------------------- 1 | {"task_id": "17dcd348-228b-49ec-b888-2be6e03ea605", "status": "processing", "task_type": "area", "task_name": "MCD43A1_Texas", "params": {"dates": [{"yearRange": [2000, 2050], "startDate": "01-01-2001", "endDate": "01-31-2001"}], "layers": [{"layer": "BRDF_Albedo_Band_Mandatory_Quality_nir", "product": "MCD43A1.006"}, {"layer": "BRDF_Albedo_Band_Mandatory_Quality_shortwave", "product": "MCD43A1.006"}, {"layer": "BRDF_Albedo_Band_Mandatory_Quality_vis", "product": "MCD43A1.006"}, {"layer": "BRDF_Albedo_Parameters_nir", "product": "MCD43A1.006"}, {"layer": "BRDF_Albedo_Parameters_shortwave", "product": "MCD43A1.006"}, {"layer": "BRDF_Albedo_Parameters_vis", "product": "MCD43A1.006"}], "output": {"format": {"type": "netcdf4"}, "projection": "geographic"}, "geo": {"type": "FeatureCollection", "fileName": "User-Drawn-Polygon", "features": [{"type": "Feature", "properties": {}, "geometry": {"type": "Polygon", "coordinates": [[[-96.90098369121552, 29.90101846307516], [-96.90098369121552, 30.09657510370016], [-96.68125712871552, 30.09657510370016], [-96.68125712871552, 29.90101846307516], [-96.90098369121552, 29.90101846307516]]]}}]}}, "web_version": "2.5.1", "svc_version": "2.5.1", "api_version": null, "created": "2018-03-18T22:40:55.176000", "updated": "2018-03-18T22:40:55.859000", "user_id": "jjmcnelis@outlook.com", "error": null, "retry_at": null, "expires_on": null, "attempts": 1} 2 | -------------------------------------------------------------------------------- /f_albedo.R: -------------------------------------------------------------------------------- 1 | ##################################################################################### 2 | # These functions are called by the loop function in main_albedo.R 3 | # 4 | #::METHODS:: 5 | # 6 | # https://modis.ornl.gov/documentation.html 7 | # https://www.umb.edu/spectralmass/terra_aqua_modis/modis_brdf_albedo_product_mcd43 8 | # 9 | # Black-sky Albedo = 10 | # Parameters_01 + 11 | # Parameters_02 * (-0.007574 + (-0.070987 * szn^2) + (0.307588 * szn^3)) + 12 | # Parameters_03 * (-1.284909 + (-0.166314 * szn^2) + (0.041840 * szn^3)) 13 | # 14 | # White-sky Albedo = 15 | # Parameters_01 + 16 | # Parameters_02 * (0.189184) + 17 | # Parameters_03 * (-1.377622) 18 | # 19 | # Actual (Blue-sky) Albedo = 20 | # White-sky Albedo * f(optical depth, solar zenith angle, aerosol type, band) + 21 | # Black-sky Albedo * (1 - f(optical depth, solar zenith angle, aerosol type, band)) 22 | # 23 | ##################################################################################### 24 | # Albedo calculation constants 25 | ##################################################################################### 26 | 27 | ## Black sky constants 28 | 29 | # Isotropic constant 30 | g0iso <- 1.0 31 | g1iso <- 0.0 32 | g2iso <- 0.0 33 | 34 | # RossThick constant 35 | g0vol <- -0.007574 36 | g1vol <- -0.070987 37 | g2vol <- 0.307588 38 | 39 | # LiSparseR constant 40 | g0geo <- -1.284909 41 | g1geo <- -0.166314 42 | g2geo <- 0.041840 43 | 44 | ## White sky constants 45 | 46 | gIso <- 1.0 # Isotropic 47 | gVol <- 0.189184 # RossThick 48 | gGeo <- -1.377622 # LiSparseR 49 | 50 | ##################################################################################### 51 | # Albedo functions 52 | ##################################################################################### 53 | 54 | # Convert SZN degrees to radians 55 | Deg2Rad = 3.1415926535/180 56 | SF = 1 # Scale factor (0.001) already applied to values by ncdf4. Set to 1. 57 | 58 | # Black-sky albedo formula 59 | BlackSA <- function(p1arr, p2arr, p3arr, szn){ 60 | sznrad = szn*Deg2Rad 61 | return((p1arr*SF)+(p2arr*SF)*(g0vol+(g1vol*sznrad^2)+(g2vol*sznrad^3))+(p3arr*SF)*(g0geo+(g1geo*sznrad^2)+(g2geo*sznrad^3))) 62 | } 63 | 64 | # White-sky albedo formula 65 | WhiteSA <- function(p1arr, p2arr, p3arr){ 66 | return((p1arr*SF)*gIso+(p2arr*SF)*gVol+(p3arr*SF)*+gGeo) 67 | } 68 | 69 | # Actual albedo formula 70 | ActualSA <- function(WSA, BSA, LUTVal){ 71 | return((WSA*LUTVal)+(BSA*(1-LUTVal))) 72 | } 73 | 74 | ##################################################################################### 75 | # Lookup tables 76 | ##################################################################################### 77 | 78 | LUT <- function(band, szn, sod){ 79 | if(band == 'vis'){ 80 | return(vislut[paste('X', sprintf('%.2f', sod), sep = ''),round(abs(szn), digits = 0)+1]) 81 | } 82 | if(band == 'nir'){ 83 | return(nirlut[paste('X', sprintf('%.2f', sod), sep = ''),round(abs(szn), digits = 0)+1]) 84 | } 85 | if(band == 'shortwave'){ 86 | return(swlut[paste('X', sprintf('%.2f', sod), sep = ''),round(abs(szn), digits = 0)+1]) 87 | } 88 | } 89 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Calculate black-sky, white-sky, and actual albedo (MCD43A) from MCD43A1 BRDF Parameters using R 2 | 3 | R script for calculating black-sky, white-sky, and actual albedo from MODIS MCD43A1 BRDF parameters product with custom solar zenith angle and solar optical depth inputs. Input and output in NetCDF format. 4 | 5 | ![Broken Image Link --- browse image](https://github.com/jjmcnelis/mcd43-calculated-albedo/blob/master/readme/browse_image.PNG?raw=true) 6 | 7 | ### Why? 8 | 9 | While some users are content to use the MODIS black-sky albedo at local solar noon and the white-sky albedo measures as provided in [**MCD43A3**](https://lpdaac.usgs.gov/dataset_discovery/modis/modis_products_table/mcd43a3_v006), most researchers want to make use of the BRDF model parameters ([**MCD43A1**](https://lpdaac.usgs.gov/dataset_discovery/modis/modis_products_table/mcd43a1_v006)) to obtain black-sky albedos at other solar illumination angles or to combine the black-sky and white-sky albedos as a function of optical depth to calculate "actual" or blue-sky albedos for validation studies. 10 | 11 | [**MCD43A**](https://modis.ornl.gov/documentation.html#MCD43) is the unofficial MODIS product code for **black-sky**, **white-sky**, and **actual (blue-sky) albedo** calculated using the BRDF model parameters and user-specified **solar optical depth** and **solar zenith angle**. The MCD43A Calculated Albedo Product is available through the [MODIS Global Subsetting and Visualization Tool](https://modis.ornl.gov/cgi-bin/MODIS/global/subset.pl) maintained by the [ORNL DAAC](https://daac.ornl.gov). Alternatively, it can be calculated from MODIS HDF files using the binaries available at the [product page](https://www.umb.edu/spectralmass/terra_aqua_modis) maintained by the PI of MCD43, Dr. Crystal Schaaf. 12 | 13 | In MODIS Collection 5, MCD43 was generated in 16-day composite time intervals. In Collection 6 (C6), MCD43 is a daily product; thus, the data volume is prohibitively large. The large data volume for MCD43 in C6 was the motivation for writing these scripts. 14 | 15 | [See below for more information about MCD43A Calculated Albedo.](https://github.com/jjmcnelis/mcd43-calculated-albedo#mcd43a-calculated-albedo) 16 | 17 | For more information about MODIS, visit the LP DAAC's [MODIS Overview](https://lpdaac.usgs.gov/dataset_discovery/modis) page. 18 | 19 | ### How? 20 | 21 | #### Input data from AppEEARS 22 | 23 | The albedo formulas are implemented in R. They take as input a subset of the MCD43A1 product in NetCDF format generated through [AppEEARS](https://lpdaac.usgs.gov/tools/data_access/appeears). AppEEARS is a data delivery tool maintained by the LP DAAC offering spatial and temporal subsets of MODIS data and other data products. You will need to sign up for a NASA Earthdata account to use AppEEARS. 24 | 25 | To request a compatible subset, choose **Area Sample** from the ***Extract*** button in AppEEARS. Click **Start a new request**. 26 | 1. Provide a name for your sample. 27 | 2. Choose a spatial extent by either uploading an ESRI Shapefile or GeoJSON, or by drawing a box/polygon on the map. 28 | 3. Choose a temporal extent for the subset. 29 | 4. Search for MCD43A1 under ***Select the layers to include in the sample*** and choose the C6 product: **MCD43A1.006** 30 | 5. Select the following layers: 31 | * **BRDF_Albedo_Parameters_vis** 32 | * **BRDF_Albedo_Parameters_nir** 33 | * **BRDF_Albedo_Parameters_shortwave** 34 | * **BRDF_Albedo_Band Mandatory_Quality_vis** 35 | * **BRDF_Albedo_Band Mandatory_Quality_nir** 36 | * **BRDF_Albedo_Band Mandatory_Quality_shortwave** 37 | 6. For ***File Format***, choose **NetCDF**. 38 | 7. For ***Projection***, choose **Geographic**. 39 | 40 | You will receive an email upon order completion. 41 | 42 | An example input file is provided: [*./example-data/MCD43A1.006_aid0001.nc*](https://github.com/jjmcnelis/mcd43-calculated-albedo/blob/master/example-data/MCD43A1.006_aid0001.nc). 43 | 44 | You can submit an identical AppEEARS request by uploading the supplied GeoJSON: [*./example-data/MCD43A1-Texas-request.json*](https://github.com/jjmcnelis/mcd43-calculated-albedo/blob/master/example-data/MCD43A1-Texas-request.json). 45 | 46 | **Requirements** 47 | * [ncdf4](https://cran.r-project.org/web/packages/ncdf4/index.html) 48 | * [raster](https://cran.r-project.org/web/packages/raster/index.html) 49 | * [RAtmosphere](https://cran.r-project.org/web/packages/RAtmosphere/index.html) 50 | 51 | #### Usage 52 | 53 | The primary script (*main_albedo.R*) calls the functions defined in *f_albedo.R*. Open *main_albedo.R* and make a few edits to the settings in the first section: 54 | ``` 55 | # Set your working directory 56 | # Contains R scripts, lookup tables (vis_lut.csv, nir_lut, sw_lut.csv), and input NetCDF 57 | wkd <- '<>' 58 | setwd(wkd) 59 | 60 | # Set path and filename for input NetCDF. Default output from AppEEARS should be MCD43A1.006_aid0001.nc 61 | nc_in = paste(wkd, 'example-data/', 'MCD43A1.006_aid0001.nc', sep = '') 62 | 63 | # Set solar optical depth (value between 0.00 and 0.98 x0.02 with 2-digit precision) 64 | SolOptDepth <- 0.20 65 | # Set solar zenith angle (0.0-89.0 degrees, or "local" for local solar noon) 66 | SolZenAngle <- 'local' 67 | 68 | # Set path to output NetCDF 69 | out_dir <- paste(wkd, 'example-output/', sep = '') 70 | out_filename <- '' 71 | suppressWarnings(dir.create(out_dir)) 72 | ``` 73 | 74 | Execute the script via command line: 75 | ``` 76 | > Rscript main_albedo.R 77 | 78 | In Windows, you may need to point to your Rscript executable: 79 | > C:\Path\to\R\directory\Rscript.exe main_albedo.R 80 | ``` 81 | Output will be a NetCDF with the following data variables: 82 | * **visible_black_sky_albedo** 83 | * **visible_white_sky_albedo** 84 | * **visible_actual_albedo** 85 | * **nir_black_sky_albedo** 86 | * **nir_white_sky_albedo** 87 | * **nir_actual_albedo** 88 | * **shortwave_black_sky_albedo** 89 | * **shortwave_white_sky_albedo** 90 | * **shortwave_actual_albedo** 91 | 92 | An example output file is provided: [*./example-output/MCD43A_calcalbedo.nc*](https://github.com/jjmcnelis/mcd43-calculated-albedo/blob/master/example-output/MCD43A_calcalbedo.nc). 93 | 94 | ## MCD43A Calculated Albedo 95 | 96 | The primary resource for information about MCD43 products is the [product page](https://www.umb.edu/spectralmass/terra_aqua_modis/v006) maintained by Dr. Schaaf's group at UMass Boston. As the only institution offering on-demand delivery of MCD43A Calculated Albedo, the ORNL DAAC has a [web page](https://modis.ornl.gov/documentation.html#MCD43) with a more concise explanation of its derivation. 97 | 98 | Albedo is defined as the ratio of upwelling to downwelling radiative flux at the surface. Downwelling flux may be written as the sum of a direct component and a diffuse component. Black-sky albedo (directional hemispherical reflectance) is defined as albedo in the absence of a diffuse component and is a function of solar zenith angle. White-sky albedo (bihemispherical reflectance) is defined as albedo in the absence of a direct component when the diffuse component is isotropic. Black-sky albedo and white-sky albedo mark the extreme cases of completely direct and completely diffuse illumination. Actual albedo is a value which is interpolated between these two as a function of the fraction of diffuse skylight which is itself a function of the aerosol optical depth (Lewis and Barnsley 1994; Román et al. 2010; Schaaf et al. 2002). 99 | 100 | The MCD43A1 BRDF/Albedo Model Parameters Product (MODIS/Terra BRDF/Albedo Model_1 Daily L3 Global 500m SIN Grid) supplies the weighting parameters associated with the RossThickLiSparseReciprocal BRDF model that best describes the anisotropy of each pixel. These three parameters ( fiso , fvol , fgeo ) are provided for each of the MODIS spectral bands as well as for three broad bands (0.3-0.7µm, 0.7-5.0µm, and 0.3-5.0µm). These parameters can be used in a forward version of the model to reconstruct the surface anisotropic effects and thus correct directional reflectances to a common view geometry (this is the procedure that is used to produce MCD43A4 Nadir BRDF-Adjusted Reflectances - NBAR) or to compute the integrated black-sky (at some solar zenith angle) and white-sky albedos (as are done for MCD43A3). Alternately, the parameters can be used with a simple polynomial to easily estimate the black-sky albedo with good accuracy for any desired solar zenith angle. The polynomial is as follows: 101 | 102 | ![Broken Image Link --- black sky albedo](https://github.com/jjmcnelis/mcd43-calculated-albedo/blob/master/readme/blackskyalbedo.jpg?raw=true) 103 | 104 | The appropriate constants are: 105 | 106 | | Term | Isotropic (iso) | RossThick (vol) | LiSparseR (geo) | 107 | |--------|-----------------|-----------------|-----------------| 108 | | *g0* | 1.0 | -0.007574 | -1.284909 | 109 | | *g1* | 0.0 | -0.070987 | -0.166314 | 110 | | *g2* | 0.0 | 0.307588 | 0.041840 | 111 | 112 | Similarly, the white-sky albedo can be computed by using the equation: 113 | 114 | ![Broken Image Link --- white sky albedo](https://github.com/jjmcnelis/mcd43-calculated-albedo/blob/master/readme/whiteskyalbedo.jpg?raw=true) 115 | 116 | and the estimates of the white-sky kernel integrals are: 117 | 118 | | Term | Isotropic (iso) | RossThick (vol) | LiSparseR (geo) | 119 | |--------------------------|-----------------|-----------------|-----------------| 120 | | White-sky integral *g* | 1.0 | 0.189184 | -1.377622 | 121 | 122 | Actual (blue-sky) albedo is interpolated between black- and white-sky albedo as a function of the fraction of diffuse skylight which is itself a function of the aerosol optical depth: 123 | 124 | ![Broken Image Link --- actual albedo](https://github.com/jjmcnelis/mcd43-calculated-albedo/blob/master/readme/actualalbedo1.png?raw=true) 125 | 126 | Lewis, P., and M. J. Barnsley, Influence of the sky radiance distribution on various formulations of the earth surface albedo, in Proc. Conf. Phys. Meas. Sign. Remote Sens., Val d'Isere, France, pp. 707-715, 1994. 127 | 128 | Román, M. O., C. B. Schaaf, P. Lewis, F. Gao, G. P. Anderson, J. L. Privette, A. H. Strahler, C. E. Woodcock, M. Barnsley, Assessing the coupling between surface albedo derived from MODIS and the fraction of diffuse skylight over spatially-characterized landscapes, Remote Sensing of Environment, 114, 738-760,2010. 129 | 130 | Schaaf, C. B., F. Gao, A. H. Strahler, W. Lucht, X. Li, T. Tsang, N. C. Strugnell, X. Zhang, Y. Jin, J.-P. Muller, P. Lewis, M. Barnsley, P. Hobson, M. Disney, G. Roberts, M. Dunderdale, C. Doll, R. d'Entremont, B. Hu, S. Liang, and J. L. Privette, First Operational BRDF, Albedo and Nadir Reflectance Products from MODIS, Remote Sens. Environ., 83, 135-148, 2002. 131 | -------------------------------------------------------------------------------- /vis_lut.csv: -------------------------------------------------------------------------------- 1 | ,0.00,0.02,0.04,0.06,0.08,0.10,0.12,0.14,0.16,0.18,0.20,0.22,0.24,0.26,0.28,0.30,0.32,0.34,0.36,0.38,0.40,0.42,0.44,0.46,0.48,0.50,0.52,0.54,0.56,0.58,0.60,0.62,0.64,0.66,0.68,0.70,0.72,0.74,0.76,0.78,0.80,0.82,0.84,0.86,0.88,0.90,0.92,0.94,0.96,0.98 2 | 0,0.072,0.087,0.102,0.117,0.131,0.145,0.159,0.172,0.185,0.198,0.211,0.224,0.236,0.248,0.26,0.271,0.283,0.294,0.305,0.316,0.326,0.337,0.347,0.357,0.367,0.377,0.386,0.396,0.405,0.414,0.423,0.432,0.44,0.449,0.457,0.465,0.473,0.481,0.489,0.496,0.504,0.511,0.518,0.526,0.533,0.539,0.546,0.553,0.559,0.566 3 | 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4,0.072,0.087,0.102,0.117,0.131,0.145,0.159,0.172,0.186,0.199,0.212,0.224,0.236,0.248,0.26,0.272,0.283,0.295,0.306,0.316,0.327,0.337,0.348,0.358,0.368,0.377,0.387,0.396,0.406,0.415,0.424,0.432,0.441,0.449,0.458,0.466,0.474,0.482,0.489,0.497,0.505,0.512,0.519,0.526,0.533,0.54,0.547,0.554,0.56,0.567 7 | 5,0.072,0.087,0.102,0.117,0.131,0.145,0.159,0.173,0.186,0.199,0.212,0.224,0.237,0.249,0.261,0.272,0.284,0.295,0.306,0.317,0.327,0.338,0.348,0.358,0.368,0.378,0.387,0.397,0.406,0.415,0.424,0.433,0.441,0.45,0.458,0.466,0.474,0.482,0.49,0.497,0.505,0.512,0.52,0.527,0.534,0.541,0.547,0.554,0.561,0.567 8 | 6,0.072,0.088,0.102,0.117,0.131,0.146,0.159,0.173,0.186,0.199,0.212,0.225,0.237,0.249,0.261,0.273,0.284,0.295,0.306,0.317,0.328,0.338,0.348,0.359,0.368,0.378,0.388,0.397,0.406,0.415,0.424,0.433,0.442,0.45,0.458,0.467,0.475,0.483,0.49,0.498,0.505,0.513,0.52,0.527,0.534,0.541,0.548,0.555,0.561,0.568 9 | 7,0.073,0.088,0.103,0.117,0.132,0.146,0.16,0.173,0.186,0.2,0.212,0.225,0.237,0.249,0.261,0.273,0.284,0.296,0.307,0.318,0.328,0.339,0.349,0.359,0.369,0.379,0.388,0.398,0.407,0.416,0.425,0.434,0.442,0.451,0.459,0.467,0.475,0.483,0.491,0.499,0.506,0.513,0.521,0.528,0.535,0.542,0.549,0.555,0.562,0.568 10 | 8,0.073,0.088,0.103,0.118,0.132,0.146,0.16,0.173,0.187,0.2,0.213,0.225,0.238,0.25,0.262,0.273,0.285,0.296,0.307,0.318,0.329,0.339,0.349,0.36,0.37,0.379,0.389,0.398,0.407,0.417,0.426,0.434,0.443,0.451,0.46,0.468,0.476,0.484,0.492,0.499,0.507,0.514,0.521,0.529,0.536,0.542,0.549,0.556,0.562,0.569 11 | 9,0.073,0.088,0.103,0.118,0.132,0.146,0.16,0.174,0.187,0.2,0.213,0.226,0.238,0.25,0.262,0.274,0.285,0.297,0.308,0.319,0.329,0.34,0.35,0.36,0.37,0.38,0.39,0.399,0.408,0.417,0.426,0.435,0.444,0.452,0.46,0.469,0.477,0.485,0.492,0.5,0.508,0.515,0.522,0.529,0.536,0.543,0.55,0.557,0.563,0.57 12 | 10,0.073,0.088,0.103,0.118,0.133,0.147,0.161,0.174,0.188,0.201,0.214,0.226,0.239,0.251,0.263,0.274,0.286,0.297,0.308,0.319,0.33,0.34,0.351,0.361,0.371,0.381,0.39,0.4,0.409,0.418,0.427,0.436,0.444,0.453,0.461,0.469,0.478,0.485,0.493,0.501,0.508,0.516,0.523,0.53,0.537,0.544,0.551,0.558,0.564,0.571 13 | 11,0.073,0.089,0.104,0.118,0.133,0.147,0.161,0.175,0.188,0.201,0.214,0.227,0.239,0.251,0.263,0.275,0.287,0.298,0.309,0.32,0.331,0.341,0.352,0.362,0.372,0.381,0.391,0.401,0.41,0.419,0.428,0.437,0.445,0.454,0.462,0.47,0.478,0.486,0.494,0.502,0.509,0.517,0.524,0.531,0.538,0.545,0.552,0.559,0.565,0.572 14 | 12,0.073,0.089,0.104,0.119,0.133,0.147,0.161,0.175,0.189,0.202,0.215,0.227,0.24,0.252,0.264,0.276,0.287,0.299,0.31,0.321,0.332,0.342,0.352,0.363,0.373,0.382,0.392,0.401,0.411,0.42,0.429,0.438,0.446,0.455,0.463,0.471,0.479,0.487,0.495,0.503,0.51,0.518,0.525,0.532,0.539,0.546,0.553,0.56,0.566,0.573 15 | 13,0.074,0.089,0.104,0.119,0.134,0.148,0.162,0.176,0.189,0.202,0.215,0.228,0.241,0.253,0.265,0.277,0.288,0.3,0.311,0.322,0.332,0.343,0.353,0.364,0.374,0.383,0.393,0.402,0.412,0.421,0.43,0.439,0.447,0.456,0.464,0.473,0.481,0.489,0.496,0.504,0.512,0.519,0.526,0.533,0.541,0.547,0.554,0.561,0.568,0.574 16 | 14,0.074,0.089,0.105,0.12,0.134,0.148,0.162,0.176,0.19,0.203,0.216,0.229,0.241,0.254,0.266,0.277,0.289,0.3,0.312,0.323,0.333,0.344,0.354,0.365,0.375,0.384,0.394,0.404,0.413,0.422,0.431,0.44,0.449,0.457,0.466,0.474,0.482,0.49,0.498,0.505,0.513,0.52,0.528,0.535,0.542,0.549,0.556,0.562,0.569,0.575 17 | 15,0.074,0.09,0.105,0.12,0.135,0.149,0.163,0.177,0.19,0.204,0.217,0.23,0.242,0.254,0.267,0.278,0.29,0.301,0.313,0.324,0.334,0.345,0.355,0.366,0.376,0.386,0.395,0.405,0.414,0.423,0.432,0.441,0.45,0.458,0.467,0.475,0.483,0.491,0.499,0.507,0.514,0.522,0.529,0.536,0.543,0.55,0.557,0.564,0.57,0.577 18 | 16,0.075,0.09,0.105,0.12,0.135,0.15,0.164,0.178,0.191,0.205,0.218,0.23,0.243,0.255,0.267,0.279,0.291,0.302,0.314,0.325,0.336,0.346,0.357,0.367,0.377,0.387,0.397,0.406,0.415,0.425,0.434,0.443,0.451,0.46,0.468,0.476,0.485,0.493,0.5,0.508,0.516,0.523,0.53,0.538,0.545,0.552,0.558,0.565,0.572,0.578 19 | 17,0.075,0.091,0.106,0.121,0.136,0.15,0.164,0.178,0.192,0.205,0.218,0.231,0.244,0.256,0.268,0.28,0.292,0.304,0.315,0.326,0.337,0.347,0.358,0.368,0.378,0.388,0.398,0.407,0.417,0.426,0.435,0.444,0.453,0.461,0.47,0.478,0.486,0.494,0.502,0.51,0.517,0.525,0.532,0.539,0.546,0.553,0.56,0.567,0.573,0.58 20 | 18,0.075,0.091,0.106,0.122,0.136,0.151,0.165,0.179,0.193,0.206,0.219,0.232,0.245,0.257,0.27,0.282,0.293,0.305,0.316,0.327,0.338,0.349,0.359,0.37,0.38,0.39,0.399,0.409,0.418,0.428,0.437,0.446,0.454,0.463,0.471,0.48,0.488,0.496,0.504,0.511,0.519,0.526,0.534,0.541,0.548,0.555,0.562,0.569,0.575,0.582 21 | 19,0.076,0.091,0.107,0.122,0.137,0.152,0.166,0.18,0.194,0.207,0.22,0.233,0.246,0.258,0.271,0.283,0.294,0.306,0.317,0.329,0.339,0.35,0.361,0.371,0.381,0.391,0.401,0.41,0.42,0.429,0.438,0.447,0.456,0.465,0.473,0.481,0.489,0.497,0.505,0.513,0.521,0.528,0.536,0.543,0.55,0.557,0.564,0.57,0.577,0.584 22 | 20,0.076,0.092,0.107,0.123,0.138,0.152,0.167,0.181,0.195,0.208,0.221,0.234,0.247,0.26,0.272,0.284,0.296,0.307,0.319,0.33,0.341,0.352,0.362,0.373,0.383,0.393,0.402,0.412,0.422,0.431,0.44,0.449,0.458,0.466,0.475,0.483,0.491,0.499,0.507,0.515,0.523,0.53,0.537,0.545,0.552,0.559,0.566,0.572,0.579,0.585 23 | 21,0.076,0.092,0.108,0.123,0.138,0.153,0.168,0.182,0.196,0.209,0.222,0.236,0.248,0.261,0.273,0.285,0.297,0.309,0.32,0.331,0.342,0.353,0.364,0.374,0.384,0.394,0.404,0.414,0.423,0.433,0.442,0.451,0.46,0.468,0.477,0.485,0.493,0.501,0.509,0.517,0.525,0.532,0.539,0.547,0.554,0.561,0.568,0.574,0.581,0.588 24 | 22,0.077,0.093,0.109,0.124,0.139,0.154,0.168,0.183,0.197,0.21,0.224,0.237,0.25,0.262,0.275,0.287,0.299,0.31,0.322,0.333,0.344,0.355,0.365,0.376,0.386,0.396,0.406,0.416,0.425,0.435,0.444,0.453,0.461,0.47,0.479,0.487,0.495,0.503,0.511,0.519,0.527,0.534,0.542,0.549,0.556,0.563,0.57,0.577,0.583,0.59 25 | 23,0.077,0.094,0.109,0.125,0.14,0.155,0.169,0.184,0.198,0.211,0.225,0.238,0.251,0.264,0.276,0.288,0.3,0.312,0.323,0.335,0.346,0.357,0.367,0.378,0.388,0.398,0.408,0.418,0.427,0.437,0.446,0.455,0.464,0.472,0.481,0.489,0.497,0.505,0.513,0.521,0.529,0.536,0.544,0.551,0.558,0.565,0.572,0.579,0.586,0.592 26 | 24,0.078,0.094,0.11,0.126,0.141,0.156,0.17,0.185,0.199,0.213,0.226,0.239,0.252,0.265,0.278,0.29,0.302,0.314,0.325,0.336,0.348,0.358,0.369,0.38,0.39,0.4,0.41,0.42,0.429,0.439,0.448,0.457,0.466,0.474,0.483,0.491,0.5,0.508,0.516,0.524,0.531,0.539,0.546,0.553,0.561,0.568,0.574,0.581,0.588,0.594 27 | 25,0.078,0.095,0.111,0.126,0.142,0.157,0.172,0.186,0.2,0.214,0.228,0.241,0.254,0.267,0.279,0.291,0.304,0.315,0.327,0.338,0.349,0.36,0.371,0.382,0.392,0.402,0.412,0.422,0.431,0.441,0.45,0.459,0.468,0.477,0.485,0.494,0.502,0.51,0.518,0.526,0.534,0.541,0.549,0.556,0.563,0.57,0.577,0.584,0.59,0.597 28 | 26,0.079,0.095,0.112,0.127,0.143,0.158,0.173,0.187,0.201,0.215,0.229,0.242,0.255,0.268,0.281,0.293,0.305,0.317,0.329,0.34,0.351,0.362,0.373,0.384,0.394,0.404,0.414,0.424,0.434,0.443,0.452,0.462,0.47,0.479,0.488,0.496,0.505,0.513,0.521,0.529,0.536,0.544,0.551,0.559,0.566,0.573,0.58,0.586,0.593,0.6 29 | 27,0.08,0.096,0.112,0.128,0.144,0.159,0.174,0.188,0.203,0.217,0.23,0.244,0.257,0.27,0.283,0.295,0.307,0.319,0.331,0.342,0.354,0.365,0.375,0.386,0.396,0.407,0.417,0.427,0.436,0.446,0.455,0.464,0.473,0.482,0.49,0.499,0.507,0.515,0.523,0.531,0.539,0.547,0.554,0.561,0.568,0.576,0.582,0.589,0.596,0.602 30 | 28,0.08,0.097,0.113,0.129,0.145,0.16,0.175,0.19,0.204,0.218,0.232,0.246,0.259,0.272,0.285,0.297,0.309,0.321,0.333,0.344,0.356,0.367,0.378,0.388,0.399,0.409,0.419,0.429,0.439,0.448,0.458,0.467,0.476,0.484,0.493,0.502,0.51,0.518,0.526,0.534,0.542,0.549,0.557,0.564,0.571,0.578,0.585,0.592,0.599,0.605 31 | 29,0.081,0.098,0.114,0.13,0.146,0.161,0.176,0.191,0.206,0.22,0.234,0.247,0.261,0.274,0.286,0.299,0.311,0.323,0.335,0.347,0.358,0.369,0.38,0.391,0.401,0.412,0.422,0.432,0.441,0.451,0.46,0.469,0.478,0.487,0.496,0.504,0.513,0.521,0.529,0.537,0.545,0.552,0.56,0.567,0.574,0.581,0.588,0.595,0.602,0.608 32 | 30,0.082,0.099,0.115,0.131,0.147,0.163,0.178,0.193,0.207,0.221,0.235,0.249,0.263,0.276,0.289,0.301,0.313,0.326,0.337,0.349,0.361,0.372,0.383,0.393,0.404,0.414,0.424,0.434,0.444,0.454,0.463,0.472,0.481,0.49,0.499,0.507,0.516,0.524,0.532,0.54,0.548,0.555,0.563,0.57,0.577,0.585,0.592,0.598,0.605,0.612 33 | 31,0.082,0.099,0.116,0.132,0.148,0.164,0.179,0.194,0.209,0.223,0.237,0.251,0.265,0.278,0.291,0.303,0.316,0.328,0.34,0.352,0.363,0.374,0.385,0.396,0.407,0.417,0.427,0.437,0.447,0.457,0.466,0.475,0.484,0.493,0.502,0.511,0.519,0.527,0.535,0.543,0.551,0.559,0.566,0.574,0.581,0.588,0.595,0.602,0.608,0.615 34 | 32,0.083,0.1,0.117,0.134,0.15,0.165,0.181,0.196,0.211,0.225,0.239,0.253,0.267,0.28,0.293,0.306,0.318,0.33,0.342,0.354,0.366,0.377,0.388,0.399,0.41,0.42,0.43,0.44,0.45,0.46,0.469,0.478,0.488,0.496,0.505,0.514,0.522,0.531,0.539,0.547,0.554,0.562,0.57,0.577,0.584,0.591,0.598,0.605,0.612,0.618 35 | 33,0.084,0.101,0.118,0.135,0.151,0.167,0.182,0.198,0.212,0.227,0.241,0.255,0.269,0.282,0.295,0.308,0.321,0.333,0.345,0.357,0.368,0.38,0.391,0.402,0.413,0.423,0.433,0.443,0.453,0.463,0.472,0.482,0.491,0.5,0.509,0.517,0.526,0.534,0.542,0.55,0.558,0.566,0.573,0.581,0.588,0.595,0.602,0.609,0.615,0.622 36 | 34,0.085,0.102,0.119,0.136,0.152,0.168,0.184,0.199,0.214,0.229,0.243,0.257,0.271,0.285,0.298,0.311,0.323,0.336,0.348,0.36,0.371,0.383,0.394,0.405,0.416,0.426,0.437,0.447,0.457,0.466,0.476,0.485,0.494,0.503,0.512,0.521,0.529,0.538,0.546,0.554,0.562,0.569,0.577,0.584,0.592,0.599,0.606,0.613,0.619,0.626 37 | 35,0.086,0.103,0.121,0.137,0.154,0.17,0.186,0.201,0.216,0.231,0.246,0.26,0.274,0.287,0.3,0.313,0.326,0.339,0.351,0.363,0.374,0.386,0.397,0.408,0.419,0.43,0.44,0.45,0.46,0.47,0.479,0.489,0.498,0.507,0.516,0.524,0.533,0.541,0.549,0.558,0.565,0.573,0.581,0.588,0.595,0.603,0.61,0.616,0.623,0.63 38 | 36,0.087,0.104,0.122,0.139,0.155,0.172,0.188,0.203,0.218,0.233,0.248,0.262,0.276,0.29,0.303,0.316,0.329,0.341,0.354,0.366,0.378,0.389,0.4,0.412,0.422,0.433,0.443,0.454,0.464,0.473,0.483,0.492,0.502,0.511,0.52,0.528,0.537,0.545,0.553,0.561,0.569,0.577,0.585,0.592,0.599,0.607,0.614,0.621,0.627,0.634 39 | 37,0.088,0.106,0.123,0.14,0.157,0.173,0.19,0.205,0.221,0.236,0.25,0.265,0.279,0.292,0.306,0.319,0.332,0.345,0.357,0.369,0.381,0.393,0.404,0.415,0.426,0.437,0.447,0.457,0.467,0.477,0.487,0.496,0.506,0.515,0.524,0.532,0.541,0.549,0.558,0.566,0.574,0.581,0.589,0.596,0.604,0.611,0.618,0.625,0.632,0.638 40 | 38,0.089,0.107,0.125,0.142,0.159,0.175,0.192,0.207,0.223,0.238,0.253,0.267,0.281,0.295,0.309,0.322,0.335,0.348,0.36,0.372,0.384,0.396,0.407,0.419,0.43,0.44,0.451,0.461,0.471,0.481,0.491,0.5,0.51,0.519,0.528,0.537,0.545,0.554,0.562,0.57,0.578,0.586,0.593,0.601,0.608,0.615,0.622,0.629,0.636,0.643 41 | 39,0.09,0.108,0.126,0.144,0.161,0.177,0.194,0.21,0.225,0.24,0.255,0.27,0.284,0.298,0.312,0.325,0.338,0.351,0.364,0.376,0.388,0.4,0.411,0.423,0.434,0.444,0.455,0.465,0.475,0.485,0.495,0.505,0.514,0.523,0.532,0.541,0.55,0.558,0.566,0.574,0.582,0.59,0.598,0.605,0.613,0.62,0.627,0.634,0.64,0.647 42 | 40,0.091,0.109,0.128,0.145,0.162,0.179,0.196,0.212,0.228,0.243,0.258,0.273,0.287,0.301,0.315,0.329,0.342,0.355,0.367,0.38,0.392,0.404,0.415,0.426,0.438,0.448,0.459,0.47,0.48,0.49,0.499,0.509,0.518,0.528,0.537,0.545,0.554,0.563,0.571,0.579,0.587,0.595,0.602,0.61,0.617,0.625,0.632,0.638,0.645,0.652 43 | 41,0.092,0.111,0.129,0.147,0.164,0.182,0.198,0.214,0.23,0.246,0.261,0.276,0.29,0.305,0.319,0.332,0.345,0.358,0.371,0.384,0.396,0.408,0.419,0.431,0.442,0.453,0.463,0.474,0.484,0.494,0.504,0.514,0.523,0.532,0.541,0.55,0.559,0.567,0.576,0.584,0.592,0.6,0.607,0.615,0.622,0.629,0.636,0.643,0.65,0.657 44 | 42,0.093,0.112,0.131,0.149,0.167,0.184,0.201,0.217,0.233,0.249,0.264,0.279,0.294,0.308,0.322,0.336,0.349,0.362,0.375,0.388,0.4,0.412,0.424,0.435,0.446,0.457,0.468,0.479,0.489,0.499,0.509,0.518,0.528,0.537,0.546,0.555,0.564,0.572,0.581,0.589,0.597,0.605,0.612,0.62,0.627,0.635,0.642,0.649,0.655,0.662 45 | 43,0.095,0.114,0.133,0.151,0.169,0.186,0.203,0.22,0.236,0.252,0.267,0.282,0.297,0.312,0.326,0.34,0.353,0.366,0.379,0.392,0.404,0.416,0.428,0.44,0.451,0.462,0.473,0.483,0.494,0.504,0.514,0.523,0.533,0.542,0.551,0.56,0.569,0.578,0.586,0.594,0.602,0.61,0.618,0.625,0.633,0.64,0.647,0.654,0.661,0.667 46 | 44,0.096,0.116,0.134,0.153,0.171,0.189,0.206,0.223,0.239,0.255,0.271,0.286,0.301,0.315,0.33,0.344,0.357,0.37,0.383,0.396,0.409,0.421,0.433,0.444,0.456,0.467,0.478,0.488,0.499,0.509,0.519,0.529,0.538,0.548,0.557,0.566,0.574,0.583,0.591,0.6,0.608,0.616,0.623,0.631,0.638,0.645,0.652,0.659,0.666,0.673 47 | 45,0.098,0.117,0.136,0.155,0.173,0.191,0.209,0.226,0.242,0.258,0.274,0.29,0.305,0.319,0.334,0.348,0.361,0.375,0.388,0.401,0.413,0.426,0.438,0.449,0.461,0.472,0.483,0.494,0.504,0.514,0.524,0.534,0.544,0.553,0.562,0.571,0.58,0.589,0.597,0.605,0.613,0.621,0.629,0.637,0.644,0.651,0.658,0.665,0.672,0.679 48 | 46,0.099,0.119,0.139,0.157,0.176,0.194,0.212,0.229,0.245,0.262,0.278,0.293,0.309,0.323,0.338,0.352,0.366,0.379,0.393,0.406,0.418,0.431,0.443,0.454,0.466,0.477,0.488,0.499,0.51,0.52,0.53,0.54,0.549,0.559,0.568,0.577,0.586,0.594,0.603,0.611,0.619,0.627,0.635,0.642,0.65,0.657,0.664,0.671,0.678,0.685 49 | 47,0.101,0.121,0.141,0.16,0.179,0.197,0.215,0.232,0.249,0.265,0.282,0.297,0.313,0.328,0.342,0.357,0.371,0.384,0.398,0.411,0.423,0.436,0.448,0.46,0.471,0.483,0.494,0.505,0.515,0.526,0.536,0.546,0.555,0.565,0.574,0.583,0.592,0.601,0.609,0.617,0.625,0.633,0.641,0.649,0.656,0.663,0.67,0.677,0.684,0.691 50 | 48,0.103,0.123,0.143,0.162,0.181,0.2,0.218,0.235,0.253,0.269,0.286,0.301,0.317,0.332,0.347,0.361,0.376,0.389,0.403,0.416,0.429,0.441,0.453,0.465,0.477,0.489,0.5,0.511,0.521,0.532,0.542,0.552,0.562,0.571,0.58,0.589,0.598,0.607,0.615,0.624,0.632,0.64,0.647,0.655,0.662,0.67,0.677,0.684,0.691,0.697 51 | 49,0.104,0.125,0.145,0.165,0.184,0.203,0.221,0.239,0.256,0.273,0.29,0.306,0.322,0.337,0.352,0.366,0.381,0.395,0.408,0.421,0.434,0.447,0.459,0.471,0.483,0.495,0.506,0.517,0.528,0.538,0.548,0.558,0.568,0.577,0.587,0.596,0.605,0.614,0.622,0.63,0.638,0.646,0.654,0.662,0.669,0.676,0.683,0.69,0.697,0.704 52 | 50,0.106,0.127,0.148,0.168,0.187,0.206,0.225,0.243,0.26,0.278,0.294,0.31,0.326,0.342,0.357,0.372,0.386,0.4,0.414,0.427,0.44,0.453,0.465,0.478,0.489,0.501,0.512,0.523,0.534,0.545,0.555,0.565,0.575,0.584,0.594,0.603,0.612,0.62,0.629,0.637,0.645,0.653,0.661,0.669,0.676,0.683,0.69,0.697,0.704,0.711 53 | 51,0.108,0.13,0.151,0.171,0.191,0.21,0.229,0.247,0.265,0.282,0.299,0.315,0.331,0.347,0.362,0.377,0.392,0.406,0.42,0.433,0.446,0.459,0.472,0.484,0.496,0.508,0.519,0.53,0.541,0.551,0.562,0.572,0.582,0.591,0.601,0.61,0.619,0.628,0.636,0.644,0.653,0.66,0.668,0.676,0.683,0.69,0.698,0.704,0.711,0.718 54 | 52,0.111,0.132,0.153,0.174,0.194,0.214,0.233,0.251,0.269,0.287,0.304,0.32,0.337,0.353,0.368,0.383,0.398,0.412,0.426,0.44,0.453,0.466,0.478,0.491,0.503,0.515,0.526,0.537,0.548,0.559,0.569,0.579,0.589,0.599,0.608,0.617,0.626,0.635,0.644,0.652,0.66,0.668,0.676,0.683,0.691,0.698,0.705,0.712,0.719,0.725 55 | 53,0.113,0.135,0.156,0.177,0.198,0.217,0.237,0.256,0.274,0.292,0.309,0.326,0.342,0.358,0.374,0.389,0.404,0.418,0.432,0.446,0.46,0.473,0.485,0.498,0.51,0.522,0.533,0.545,0.555,0.566,0.577,0.587,0.597,0.606,0.616,0.625,0.634,0.643,0.651,0.66,0.668,0.676,0.683,0.691,0.698,0.706,0.713,0.72,0.726,0.733 56 | 54,0.115,0.138,0.16,0.181,0.201,0.222,0.241,0.26,0.279,0.297,0.314,0.331,0.348,0.364,0.38,0.395,0.41,0.425,0.439,0.453,0.467,0.48,0.493,0.505,0.517,0.529,0.541,0.552,0.563,0.574,0.584,0.595,0.605,0.614,0.624,0.633,0.642,0.651,0.659,0.668,0.676,0.684,0.692,0.699,0.706,0.714,0.721,0.727,0.734,0.741 57 | 55,0.118,0.141,0.163,0.185,0.206,0.226,0.246,0.265,0.284,0.302,0.32,0.337,0.354,0.371,0.387,0.402,0.417,0.432,0.447,0.461,0.474,0.487,0.5,0.513,0.525,0.537,0.549,0.56,0.571,0.582,0.593,0.603,0.613,0.623,0.632,0.641,0.65,0.659,0.668,0.676,0.684,0.692,0.7,0.707,0.715,0.722,0.729,0.736,0.742,0.749 58 | 56,0.121,0.144,0.166,0.188,0.21,0.231,0.251,0.27,0.289,0.308,0.326,0.344,0.361,0.377,0.394,0.409,0.425,0.44,0.454,0.468,0.482,0.495,0.508,0.521,0.534,0.546,0.557,0.569,0.58,0.591,0.601,0.612,0.622,0.631,0.641,0.65,0.659,0.668,0.677,0.685,0.693,0.701,0.709,0.716,0.723,0.731,0.737,0.744,0.751,0.757 59 | 57,0.123,0.147,0.17,0.193,0.214,0.235,0.256,0.276,0.295,0.314,0.332,0.35,0.368,0.384,0.401,0.417,0.432,0.447,0.462,0.476,0.49,0.504,0.517,0.53,0.542,0.554,0.566,0.578,0.589,0.6,0.61,0.621,0.631,0.641,0.65,0.659,0.668,0.677,0.686,0.694,0.702,0.71,0.718,0.725,0.732,0.739,0.746,0.753,0.76,0.766 60 | 58,0.127,0.151,0.174,0.197,0.219,0.241,0.262,0.282,0.301,0.321,0.339,0.357,0.375,0.392,0.409,0.425,0.44,0.456,0.47,0.485,0.499,0.513,0.526,0.539,0.551,0.564,0.575,0.587,0.598,0.609,0.62,0.63,0.64,0.65,0.66,0.669,0.678,0.687,0.695,0.703,0.711,0.719,0.727,0.734,0.742,0.749,0.756,0.762,0.769,0.775 61 | 59,0.13,0.155,0.179,0.202,0.224,0.246,0.267,0.288,0.308,0.327,0.346,0.365,0.383,0.4,0.417,0.433,0.449,0.464,0.479,0.494,0.508,0.522,0.535,0.548,0.561,0.573,0.585,0.597,0.608,0.619,0.63,0.64,0.65,0.66,0.669,0.679,0.688,0.696,0.705,0.713,0.721,0.729,0.737,0.744,0.751,0.758,0.765,0.772,0.778,0.784 62 | 60,0.133,0.159,0.183,0.207,0.23,0.252,0.274,0.295,0.315,0.335,0.354,0.373,0.391,0.408,0.425,0.442,0.458,0.473,0.489,0.503,0.518,0.532,0.545,0.558,0.571,0.583,0.595,0.607,0.618,0.629,0.64,0.65,0.66,0.67,0.68,0.689,0.698,0.707,0.715,0.723,0.731,0.739,0.747,0.754,0.761,0.768,0.775,0.781,0.788,0.794 63 | 61,0.137,0.163,0.188,0.212,0.236,0.258,0.28,0.302,0.322,0.343,0.362,0.381,0.399,0.417,0.434,0.451,0.467,0.483,0.499,0.513,0.528,0.542,0.555,0.569,0.581,0.594,0.606,0.618,0.629,0.64,0.651,0.661,0.671,0.681,0.691,0.7,0.709,0.717,0.726,0.734,0.742,0.75,0.757,0.764,0.771,0.778,0.785,0.791,0.798,0.804 64 | 62,0.141,0.168,0.193,0.218,0.242,0.265,0.287,0.309,0.33,0.351,0.371,0.39,0.408,0.426,0.444,0.461,0.477,0.493,0.509,0.524,0.539,0.553,0.566,0.58,0.593,0.605,0.617,0.629,0.64,0.651,0.662,0.673,0.683,0.692,0.702,0.711,0.72,0.729,0.737,0.745,0.753,0.761,0.768,0.775,0.782,0.789,0.795,0.802,0.808,0.814 65 | 63,0.146,0.173,0.199,0.224,0.248,0.272,0.295,0.317,0.339,0.36,0.38,0.399,0.418,0.436,0.454,0.471,0.488,0.504,0.52,0.535,0.55,0.564,0.578,0.591,0.604,0.617,0.629,0.641,0.652,0.663,0.674,0.684,0.694,0.704,0.714,0.723,0.732,0.74,0.748,0.756,0.764,0.772,0.779,0.786,0.793,0.8,0.806,0.812,0.818,0.824 66 | 64,0.15,0.178,0.205,0.231,0.256,0.28,0.303,0.326,0.348,0.369,0.389,0.409,0.429,0.447,0.465,0.483,0.5,0.516,0.532,0.547,0.562,0.576,0.59,0.604,0.617,0.629,0.641,0.653,0.665,0.676,0.686,0.697,0.707,0.716,0.726,0.735,0.744,0.752,0.76,0.768,0.776,0.783,0.791,0.798,0.804,0.811,0.817,0.823,0.829,0.835 67 | 65,0.155,0.184,0.211,0.238,0.263,0.288,0.312,0.335,0.357,0.379,0.4,0.42,0.44,0.458,0.477,0.494,0.512,0.528,0.544,0.56,0.575,0.589,0.603,0.616,0.63,0.642,0.654,0.666,0.678,0.689,0.699,0.71,0.72,0.729,0.739,0.748,0.756,0.765,0.773,0.781,0.788,0.795,0.802,0.809,0.816,0.822,0.828,0.834,0.84,0.846 68 | 66,0.161,0.19,0.218,0.245,0.271,0.297,0.321,0.345,0.368,0.39,0.411,0.432,0.451,0.471,0.489,0.507,0.524,0.541,0.557,0.573,0.588,0.602,0.617,0.63,0.643,0.656,0.668,0.68,0.691,0.702,0.713,0.723,0.733,0.743,0.752,0.761,0.769,0.777,0.785,0.793,0.801,0.808,0.815,0.821,0.828,0.834,0.84,0.846,0.851,0.857 69 | 67,0.167,0.197,0.226,0.254,0.28,0.306,0.331,0.355,0.379,0.401,0.423,0.444,0.464,0.484,0.502,0.521,0.538,0.555,0.571,0.587,0.602,0.617,0.631,0.644,0.658,0.67,0.682,0.694,0.706,0.717,0.727,0.737,0.747,0.756,0.766,0.774,0.783,0.791,0.799,0.806,0.813,0.82,0.827,0.834,0.84,0.846,0.852,0.857,0.863,0.868 70 | 68,0.173,0.204,0.234,0.262,0.29,0.317,0.342,0.367,0.391,0.414,0.436,0.457,0.478,0.497,0.516,0.535,0.553,0.57,0.586,0.602,0.617,0.632,0.646,0.66,0.673,0.685,0.698,0.709,0.721,0.731,0.742,0.752,0.762,0.771,0.78,0.788,0.797,0.805,0.812,0.82,0.827,0.833,0.84,0.846,0.852,0.858,0.864,0.869,0.874,0.879 71 | 69,0.18,0.212,0.243,0.272,0.301,0.328,0.354,0.379,0.404,0.427,0.45,0.471,0.492,0.512,0.532,0.55,0.568,0.585,0.602,0.618,0.633,0.648,0.662,0.676,0.689,0.701,0.713,0.725,0.736,0.747,0.757,0.767,0.777,0.786,0.795,0.803,0.811,0.819,0.826,0.833,0.84,0.847,0.853,0.859,0.865,0.871,0.876,0.881,0.886,0.891 72 | 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19,0.071,0.083,0.094,0.105,0.116,0.127,0.137,0.147,0.158,0.168,0.177,0.187,0.196,0.205,0.214,0.223,0.232,0.241,0.249,0.258,0.266,0.274,0.282,0.289,0.297,0.305,0.312,0.319,0.327,0.334,0.341,0.347,0.354,0.361,0.367,0.374,0.38,0.386,0.392,0.398,0.404,0.41,0.416,0.422,0.427,0.433,0.438,0.444,0.449,0.454 22 | 20,0.071,0.083,0.094,0.106,0.117,0.127,0.138,0.148,0.158,0.168,0.178,0.188,0.197,0.206,0.215,0.224,0.233,0.242,0.25,0.259,0.267,0.275,0.283,0.291,0.298,0.306,0.313,0.321,0.328,0.335,0.342,0.349,0.355,0.362,0.369,0.375,0.381,0.388,0.394,0.4,0.406,0.412,0.418,0.423,0.429,0.434,0.44,0.445,0.451,0.456 23 | 21,0.072,0.083,0.095,0.106,0.117,0.128,0.138,0.149,0.159,0.169,0.179,0.188,0.198,0.207,0.216,0.225,0.234,0.243,0.251,0.26,0.268,0.276,0.284,0.292,0.299,0.307,0.314,0.322,0.329,0.336,0.343,0.35,0.357,0.363,0.37,0.376,0.383,0.389,0.395,0.401,0.407,0.413,0.419,0.425,0.43,0.436,0.441,0.447,0.452,0.457 24 | 22,0.072,0.084,0.095,0.107,0.118,0.128,0.139,0.149,0.16,0.17,0.18,0.189,0.199,0.208,0.217,0.226,0.235,0.244,0.252,0.261,0.269,0.277,0.285,0.293,0.301,0.308,0.316,0.323,0.33,0.337,0.344,0.351,0.358,0.365,0.371,0.378,0.384,0.391,0.397,0.403,0.409,0.415,0.421,0.426,0.432,0.438,0.443,0.448,0.454,0.459 25 | 23,0.072,0.084,0.096,0.107,0.118,0.129,0.14,0.15,0.16,0.171,0.18,0.19,0.2,0.209,0.218,0.227,0.236,0.245,0.254,0.262,0.27,0.278,0.286,0.294,0.302,0.31,0.317,0.325,0.332,0.339,0.346,0.353,0.36,0.366,0.373,0.379,0.386,0.392,0.398,0.405,0.411,0.416,0.422,0.428,0.434,0.439,0.445,0.45,0.456,0.461 26 | 24,0.073,0.085,0.096,0.108,0.119,0.13,0.14,0.151,0.161,0.171,0.181,0.191,0.201,0.21,0.219,0.228,0.237,0.246,0.255,0.263,0.272,0.28,0.288,0.296,0.303,0.311,0.319,0.326,0.333,0.34,0.348,0.354,0.361,0.368,0.375,0.381,0.388,0.394,0.4,0.406,0.412,0.418,0.424,0.43,0.435,0.441,0.447,0.452,0.457,0.463 27 | 25,0.073,0.085,0.097,0.108,0.119,0.13,0.141,0.152,0.162,0.172,0.182,0.192,0.202,0.211,0.22,0.23,0.239,0.247,0.256,0.265,0.273,0.281,0.289,0.297,0.305,0.313,0.32,0.328,0.335,0.342,0.349,0.356,0.363,0.37,0.376,0.383,0.389,0.396,0.402,0.408,0.414,0.42,0.426,0.432,0.437,0.443,0.449,0.454,0.459,0.465 28 | 26,0.074,0.086,0.097,0.109,0.12,0.131,0.142,0.153,0.163,0.173,0.183,0.193,0.203,0.212,0.222,0.231,0.24,0.249,0.257,0.266,0.274,0.283,0.291,0.299,0.306,0.314,0.322,0.329,0.337,0.344,0.351,0.358,0.365,0.371,0.378,0.385,0.391,0.397,0.404,0.41,0.416,0.422,0.428,0.434,0.439,0.445,0.45,0.456,0.461,0.467 29 | 27,0.074,0.086,0.098,0.109,0.121,0.132,0.143,0.154,0.164,0.174,0.184,0.194,0.204,0.214,0.223,0.232,0.241,0.25,0.259,0.267,0.276,0.284,0.292,0.3,0.308,0.316,0.323,0.331,0.338,0.346,0.353,0.36,0.367,0.373,0.38,0.387,0.393,0.399,0.406,0.412,0.418,0.424,0.43,0.436,0.441,0.447,0.453,0.458,0.463,0.469 30 | 28,0.074,0.087,0.099,0.11,0.122,0.133,0.144,0.154,0.165,0.175,0.186,0.195,0.205,0.215,0.224,0.234,0.243,0.252,0.26,0.269,0.277,0.286,0.294,0.302,0.31,0.318,0.325,0.333,0.34,0.347,0.355,0.362,0.368,0.375,0.382,0.389,0.395,0.401,0.408,0.414,0.42,0.426,0.432,0.438,0.444,0.449,0.455,0.46,0.466,0.471 31 | 29,0.075,0.087,0.099,0.111,0.122,0.134,0.145,0.155,0.166,0.177,0.187,0.197,0.207,0.216,0.226,0.235,0.244,0.253,0.262,0.271,0.279,0.287,0.296,0.304,0.312,0.319,0.327,0.335,0.342,0.349,0.357,0.364,0.371,0.377,0.384,0.391,0.397,0.404,0.41,0.416,0.422,0.428,0.434,0.44,0.446,0.451,0.457,0.463,0.468,0.473 32 | 30,0.075,0.088,0.1,0.112,0.123,0.135,0.146,0.157,0.167,0.178,0.188,0.198,0.208,0.218,0.227,0.236,0.246,0.255,0.264,0.272,0.281,0.289,0.297,0.306,0.313,0.321,0.329,0.337,0.344,0.351,0.359,0.366,0.373,0.379,0.386,0.393,0.399,0.406,0.412,0.418,0.425,0.431,0.437,0.442,0.448,0.454,0.459,0.465,0.47,0.476 33 | 31,0.076,0.088,0.101,0.112,0.124,0.136,0.147,0.158,0.168,0.179,0.189,0.199,0.209,0.219,0.229,0.238,0.247,0.256,0.265,0.274,0.283,0.291,0.299,0.307,0.315,0.323,0.331,0.339,0.346,0.354,0.361,0.368,0.375,0.382,0.389,0.395,0.402,0.408,0.415,0.421,0.427,0.433,0.439,0.445,0.451,0.456,0.462,0.467,0.473,0.478 34 | 32,0.077,0.089,0.101,0.113,0.125,0.136,0.148,0.159,0.17,0.18,0.191,0.201,0.211,0.221,0.23,0.24,0.249,0.258,0.267,0.276,0.284,0.293,0.301,0.309,0.317,0.325,0.333,0.341,0.348,0.356,0.363,0.37,0.377,0.384,0.391,0.398,0.404,0.411,0.417,0.423,0.429,0.436,0.442,0.447,0.453,0.459,0.465,0.47,0.476,0.481 35 | 33,0.077,0.09,0.102,0.114,0.126,0.138,0.149,0.16,0.171,0.182,0.192,0.202,0.212,0.222,0.232,0.241,0.251,0.26,0.269,0.278,0.286,0.295,0.303,0.312,0.32,0.328,0.335,0.343,0.351,0.358,0.365,0.373,0.38,0.387,0.393,0.4,0.407,0.413,0.42,0.426,0.432,0.438,0.444,0.45,0.456,0.462,0.467,0.473,0.478,0.484 36 | 34,0.078,0.09,0.103,0.115,0.127,0.139,0.15,0.161,0.172,0.183,0.193,0.204,0.214,0.224,0.234,0.243,0.253,0.262,0.271,0.28,0.288,0.297,0.305,0.314,0.322,0.33,0.338,0.345,0.353,0.36,0.368,0.375,0.382,0.389,0.396,0.403,0.409,0.416,0.422,0.429,0.435,0.441,0.447,0.453,0.459,0.464,0.47,0.476,0.481,0.487 37 | 35,0.078,0.091,0.104,0.116,0.128,0.14,0.151,0.163,0.174,0.184,0.195,0.205,0.216,0.226,0.235,0.245,0.255,0.264,0.273,0.282,0.291,0.299,0.308,0.316,0.324,0.332,0.34,0.348,0.356,0.363,0.37,0.378,0.385,0.392,0.399,0.405,0.412,0.419,0.425,0.431,0.438,0.444,0.45,0.456,0.462,0.467,0.473,0.479,0.484,0.49 38 | 36,0.079,0.092,0.105,0.117,0.129,0.141,0.153,0.164,0.175,0.186,0.197,0.207,0.217,0.227,0.237,0.247,0.257,0.266,0.275,0.284,0.293,0.302,0.31,0.318,0.327,0.335,0.343,0.35,0.358,0.366,0.373,0.38,0.387,0.395,0.401,0.408,0.415,0.421,0.428,0.434,0.441,0.447,0.453,0.459,0.465,0.47,0.476,0.482,0.487,0.493 39 | 37,0.08,0.093,0.106,0.118,0.13,0.142,0.154,0.165,0.177,0.188,0.198,0.209,0.219,0.229,0.239,0.249,0.259,0.268,0.277,0.286,0.295,0.304,0.313,0.321,0.329,0.337,0.345,0.353,0.361,0.368,0.376,0.383,0.39,0.397,0.404,0.411,0.418,0.425,0.431,0.437,0.444,0.45,0.456,0.462,0.468,0.474,0.479,0.485,0.49,0.496 40 | 38,0.081,0.094,0.107,0.119,0.131,0.144,0.155,0.167,0.178,0.189,0.2,0.211,0.221,0.231,0.241,0.251,0.261,0.27,0.28,0.289,0.298,0.307,0.315,0.324,0.332,0.34,0.348,0.356,0.364,0.371,0.379,0.386,0.393,0.4,0.407,0.414,0.421,0.428,0.434,0.441,0.447,0.453,0.459,0.465,0.471,0.477,0.483,0.488,0.494,0.499 41 | 39,0.081,0.095,0.108,0.12,0.133,0.145,0.157,0.169,0.18,0.191,0.202,0.213,0.223,0.234,0.244,0.254,0.263,0.273,0.282,0.291,0.3,0.309,0.318,0.326,0.335,0.343,0.351,0.359,0.367,0.374,0.382,0.389,0.396,0.404,0.411,0.417,0.424,0.431,0.437,0.444,0.45,0.456,0.463,0.469,0.475,0.48,0.486,0.492,0.497,0.503 42 | 40,0.082,0.096,0.109,0.122,0.134,0.146,0.158,0.17,0.182,0.193,0.204,0.215,0.225,0.236,0.246,0.256,0.266,0.275,0.285,0.294,0.303,0.312,0.321,0.329,0.338,0.346,0.354,0.362,0.37,0.377,0.385,0.392,0.4,0.407,0.414,0.421,0.428,0.434,0.441,0.447,0.454,0.46,0.466,0.472,0.478,0.484,0.49,0.495,0.501,0.506 43 | 41,0.083,0.097,0.11,0.123,0.136,0.148,0.16,0.172,0.183,0.195,0.206,0.217,0.228,0.238,0.248,0.258,0.268,0.278,0.287,0.297,0.306,0.315,0.323,0.332,0.341,0.349,0.357,0.365,0.373,0.381,0.388,0.396,0.403,0.41,0.417,0.424,0.431,0.438,0.444,0.451,0.457,0.464,0.47,0.476,0.482,0.488,0.494,0.499,0.505,0.51 44 | 42,0.084,0.098,0.111,0.124,0.137,0.149,0.162,0.174,0.185,0.197,0.208,0.219,0.23,0.24,0.251,0.261,0.271,0.281,0.29,0.299,0.309,0.318,0.327,0.335,0.344,0.352,0.36,0.368,0.376,0.384,0.392,0.399,0.407,0.414,0.421,0.428,0.435,0.442,0.448,0.455,0.461,0.467,0.474,0.48,0.486,0.492,0.497,0.503,0.509,0.514 45 | 43,0.085,0.099,0.112,0.126,0.138,0.151,0.163,0.176,0.187,0.199,0.21,0.221,0.232,0.243,0.253,0.264,0.274,0.283,0.293,0.302,0.312,0.321,0.33,0.338,0.347,0.355,0.364,0.372,0.38,0.388,0.395,0.403,0.41,0.418,0.425,0.432,0.439,0.445,0.452,0.459,0.465,0.471,0.478,0.484,0.49,0.496,0.501,0.507,0.513,0.518 46 | 44,0.086,0.1,0.114,0.127,0.14,0.153,0.165,0.178,0.189,0.201,0.213,0.224,0.235,0.245,0.256,0.266,0.276,0.286,0.296,0.306,0.315,0.324,0.333,0.342,0.35,0.359,0.367,0.375,0.383,0.391,0.399,0.407,0.414,0.421,0.429,0.436,0.443,0.449,0.456,0.463,0.469,0.475,0.482,0.488,0.494,0.5,0.506,0.511,0.517,0.523 47 | 45,0.087,0.101,0.115,0.129,0.142,0.155,0.167,0.18,0.192,0.203,0.215,0.226,0.237,0.248,0.259,0.269,0.279,0.289,0.299,0.309,0.318,0.327,0.336,0.345,0.354,0.363,0.371,0.379,0.387,0.395,0.403,0.411,0.418,0.425,0.433,0.44,0.447,0.454,0.46,0.467,0.473,0.48,0.486,0.492,0.498,0.504,0.51,0.516,0.522,0.527 48 | 46,0.088,0.102,0.116,0.13,0.143,0.157,0.169,0.182,0.194,0.206,0.217,0.229,0.24,0.251,0.262,0.272,0.283,0.293,0.302,0.312,0.322,0.331,0.34,0.349,0.358,0.366,0.375,0.383,0.391,0.399,0.407,0.415,0.422,0.43,0.437,0.444,0.451,0.458,0.465,0.471,0.478,0.484,0.491,0.497,0.503,0.509,0.515,0.52,0.526,0.532 49 | 47,0.089,0.104,0.118,0.132,0.145,0.158,0.171,0.184,0.196,0.208,0.22,0.232,0.243,0.254,0.265,0.275,0.286,0.296,0.306,0.316,0.325,0.335,0.344,0.353,0.362,0.37,0.379,0.387,0.395,0.403,0.411,0.419,0.427,0.434,0.441,0.448,0.455,0.462,0.469,0.476,0.482,0.489,0.495,0.501,0.508,0.514,0.519,0.525,0.531,0.536 50 | 48,0.09,0.105,0.12,0.134,0.147,0.161,0.174,0.186,0.199,0.211,0.223,0.235,0.246,0.257,0.268,0.279,0.289,0.299,0.31,0.319,0.329,0.338,0.348,0.357,0.366,0.374,0.383,0.391,0.4,0.408,0.416,0.423,0.431,0.439,0.446,0.453,0.46,0.467,0.474,0.481,0.487,0.494,0.5,0.507,0.513,0.519,0.525,0.53,0.536,0.542 51 | 49,0.092,0.107,0.121,0.136,0.149,0.163,0.176,0.189,0.202,0.214,0.226,0.238,0.249,0.261,0.272,0.282,0.293,0.303,0.314,0.323,0.333,0.343,0.352,0.361,0.37,0.379,0.388,0.396,0.404,0.413,0.42,0.428,0.436,0.444,0.451,0.458,0.465,0.472,0.479,0.486,0.492,0.499,0.505,0.512,0.518,0.524,0.53,0.536,0.541,0.547 52 | 50,0.093,0.109,0.123,0.138,0.152,0.165,0.179,0.192,0.205,0.217,0.229,0.241,0.253,0.264,0.275,0.286,0.297,0.307,0.318,0.328,0.337,0.347,0.357,0.366,0.375,0.384,0.392,0.401,0.409,0.417,0.425,0.433,0.441,0.449,0.456,0.463,0.471,0.478,0.484,0.491,0.498,0.504,0.511,0.517,0.523,0.529,0.535,0.541,0.547,0.552 53 | 51,0.095,0.11,0.125,0.14,0.154,0.168,0.182,0.195,0.208,0.22,0.233,0.245,0.256,0.268,0.279,0.29,0.301,0.312,0.322,0.332,0.342,0.352,0.361,0.371,0.38,0.389,0.397,0.406,0.414,0.423,0.431,0.439,0.446,0.454,0.461,0.469,0.476,0.483,0.49,0.497,0.503,0.51,0.516,0.523,0.529,0.535,0.541,0.547,0.553,0.558 54 | 52,0.096,0.112,0.127,0.142,0.156,0.17,0.184,0.198,0.211,0.223,0.236,0.248,0.26,0.272,0.283,0.294,0.305,0.316,0.326,0.337,0.347,0.356,0.366,0.375,0.385,0.394,0.402,0.411,0.419,0.428,0.436,0.444,0.452,0.459,0.467,0.474,0.482,0.489,0.496,0.502,0.509,0.516,0.522,0.528,0.535,0.541,0.547,0.553,0.558,0.564 55 | 53,0.098,0.114,0.129,0.144,0.159,0.173,0.187,0.201,0.214,0.227,0.239,0.252,0.264,0.276,0.287,0.298,0.309,0.32,0.331,0.341,0.351,0.361,0.371,0.38,0.39,0.399,0.408,0.416,0.425,0.433,0.441,0.449,0.457,0.465,0.473,0.48,0.487,0.494,0.501,0.508,0.515,0.522,0.528,0.534,0.541,0.547,0.553,0.559,0.565,0.57 56 | 54,0.1,0.116,0.132,0.147,0.162,0.176,0.19,0.204,0.217,0.23,0.243,0.256,0.268,0.28,0.292,0.303,0.314,0.325,0.336,0.346,0.356,0.366,0.376,0.386,0.395,0.404,0.413,0.422,0.431,0.439,0.448,0.456,0.464,0.471,0.479,0.486,0.494,0.501,0.508,0.515,0.522,0.528,0.535,0.541,0.547,0.553,0.559,0.565,0.571,0.577 57 | 55,0.102,0.118,0.134,0.15,0.165,0.179,0.194,0.208,0.221,0.235,0.247,0.26,0.273,0.285,0.296,0.308,0.319,0.33,0.341,0.352,0.362,0.372,0.382,0.391,0.401,0.41,0.419,0.428,0.437,0.445,0.454,0.462,0.47,0.478,0.485,0.493,0.5,0.507,0.514,0.521,0.528,0.535,0.541,0.548,0.554,0.56,0.566,0.572,0.578,0.583 58 | 56,0.104,0.121,0.137,0.153,0.168,0.183,0.198,0.212,0.225,0.239,0.252,0.265,0.277,0.29,0.302,0.313,0.325,0.336,0.347,0.357,0.368,0.378,0.388,0.398,0.407,0.417,0.426,0.435,0.443,0.452,0.46,0.469,0.477,0.484,0.492,0.5,0.507,0.514,0.521,0.528,0.535,0.542,0.548,0.555,0.561,0.567,0.573,0.579,0.585,0.591 59 | 57,0.106,0.123,0.14,0.156,0.171,0.186,0.201,0.215,0.229,0.243,0.256,0.269,0.282,0.295,0.307,0.318,0.33,0.341,0.352,0.363,0.374,0.384,0.394,0.404,0.413,0.423,0.432,0.441,0.45,0.459,0.467,0.476,0.484,0.492,0.499,0.507,0.514,0.522,0.529,0.536,0.543,0.549,0.556,0.562,0.569,0.575,0.581,0.587,0.593,0.598 60 | 58,0.109,0.126,0.143,0.159,0.175,0.19,0.205,0.22,0.234,0.248,0.261,0.275,0.288,0.3,0.312,0.324,0.336,0.347,0.359,0.37,0.38,0.391,0.401,0.411,0.42,0.43,0.439,0.448,0.457,0.466,0.474,0.483,0.491,0.499,0.507,0.514,0.522,0.529,0.536,0.543,0.55,0.557,0.563,0.57,0.576,0.582,0.588,0.594,0.6,0.606 61 | 59,0.111,0.128,0.145,0.162,0.178,0.194,0.209,0.224,0.238,0.252,0.266,0.28,0.293,0.305,0.318,0.33,0.342,0.353,0.365,0.376,0.387,0.397,0.407,0.417,0.427,0.437,0.446,0.455,0.464,0.473,0.482,0.49,0.498,0.506,0.514,0.522,0.529,0.536,0.544,0.551,0.558,0.564,0.571,0.577,0.584,0.59,0.596,0.602,0.608,0.613 62 | 60,0.113,0.131,0.148,0.165,0.182,0.198,0.213,0.228,0.243,0.257,0.271,0.285,0.298,0.311,0.324,0.336,0.348,0.36,0.371,0.382,0.393,0.404,0.414,0.424,0.434,0.444,0.453,0.463,0.472,0.481,0.489,0.498,0.506,0.514,0.522,0.529,0.537,0.544,0.552,0.559,0.566,0.572,0.579,0.585,0.592,0.598,0.604,0.61,0.616,0.621 63 | 61,0.116,0.134,0.152,0.169,0.185,0.202,0.218,0.233,0.248,0.262,0.277,0.29,0.304,0.317,0.33,0.342,0.355,0.366,0.378,0.389,0.4,0.411,0.422,0.432,0.442,0.452,0.461,0.47,0.48,0.488,0.497,0.506,0.514,0.522,0.53,0.538,0.545,0.553,0.56,0.567,0.574,0.581,0.587,0.594,0.6,0.606,0.612,0.618,0.624,0.63 64 | 62,0.118,0.137,0.155,0.172,0.189,0.206,0.222,0.238,0.253,0.268,0.282,0.296,0.31,0.323,0.336,0.349,0.361,0.373,0.385,0.397,0.408,0.419,0.429,0.44,0.45,0.46,0.469,0.479,0.488,0.497,0.505,0.514,0.522,0.531,0.538,0.546,0.554,0.561,0.569,0.576,0.583,0.589,0.596,0.603,0.609,0.615,0.621,0.627,0.633,0.639 65 | 63,0.121,0.14,0.158,0.176,0.194,0.211,0.227,0.243,0.259,0.274,0.288,0.303,0.317,0.33,0.343,0.356,0.369,0.381,0.393,0.404,0.416,0.427,0.437,0.448,0.458,0.468,0.478,0.488,0.497,0.506,0.515,0.523,0.532,0.54,0.548,0.556,0.563,0.571,0.578,0.585,0.592,0.599,0.606,0.612,0.618,0.625,0.631,0.637,0.642,0.648 66 | 64,0.125,0.144,0.163,0.182,0.199,0.217,0.233,0.25,0.265,0.281,0.296,0.31,0.324,0.338,0.351,0.365,0.377,0.39,0.402,0.413,0.425,0.436,0.447,0.458,0.468,0.478,0.488,0.498,0.507,0.516,0.525,0.533,0.542,0.55,0.558,0.566,0.574,0.581,0.588,0.596,0.602,0.609,0.616,0.622,0.629,0.635,0.641,0.647,0.653,0.658 67 | 65,0.129,0.149,0.168,0.187,0.205,0.223,0.24,0.256,0.272,0.288,0.303,0.318,0.332,0.346,0.36,0.373,0.386,0.399,0.411,0.423,0.434,0.446,0.457,0.467,0.478,0.488,0.498,0.507,0.517,0.526,0.535,0.544,0.552,0.561,0.569,0.577,0.584,0.592,0.599,0.606,0.613,0.62,0.627,0.633,0.639,0.645,0.651,0.657,0.663,0.669 68 | 66,0.133,0.154,0.173,0.192,0.211,0.229,0.247,0.263,0.28,0.296,0.311,0.326,0.341,0.355,0.369,0.383,0.396,0.409,0.421,0.433,0.445,0.456,0.467,0.478,0.488,0.499,0.509,0.519,0.528,0.537,0.546,0.555,0.564,0.572,0.58,0.588,0.595,0.603,0.61,0.617,0.624,0.631,0.638,0.644,0.65,0.657,0.663,0.668,0.674,0.68 69 | 67,0.137,0.158,0.179,0.198,0.217,0.236,0.254,0.271,0.288,0.304,0.32,0.335,0.35,0.365,0.379,0.392,0.406,0.418,0.431,0.443,0.455,0.467,0.478,0.489,0.499,0.51,0.52,0.529,0.539,0.548,0.557,0.566,0.574,0.583,0.591,0.599,0.606,0.614,0.621,0.628,0.635,0.642,0.649,0.655,0.661,0.667,0.673,0.679,0.685,0.69 70 | 68,0.141,0.163,0.184,0.204,0.223,0.242,0.26,0.278,0.295,0.312,0.328,0.344,0.359,0.374,0.388,0.402,0.415,0.429,0.441,0.454,0.466,0.477,0.489,0.5,0.51,0.521,0.531,0.541,0.55,0.56,0.569,0.577,0.586,0.594,0.602,0.61,0.618,0.626,0.633,0.64,0.647,0.654,0.66,0.667,0.673,0.679,0.685,0.691,0.696,0.702 71 | 69,0.146,0.168,0.189,0.21,0.23,0.249,0.268,0.286,0.304,0.321,0.337,0.353,0.369,0.384,0.398,0.413,0.426,0.44,0.453,0.465,0.477,0.489,0.5,0.512,0.522,0.533,0.543,0.553,0.563,0.572,0.581,0.59,0.598,0.607,0.615,0.623,0.631,0.638,0.646,0.653,0.66,0.666,0.673,0.679,0.685,0.691,0.697,0.703,0.708,0.714 72 | 70,0.151,0.174,0.196,0.217,0.238,0.257,0.277,0.295,0.313,0.331,0.347,0.364,0.38,0.395,0.41,0.424,0.438,0.452,0.465,0.478,0.49,0.502,0.514,0.525,0.536,0.546,0.557,0.567,0.576,0.586,0.595,0.604,0.612,0.62,0.629,0.636,0.644,0.652,0.659,0.666,0.673,0.679,0.686,0.692,0.698,0.704,0.71,0.716,0.721,0.726 73 | 71,0.156,0.18,0.203,0.224,0.246,0.266,0.286,0.305,0.323,0.341,0.358,0.375,0.391,0.407,0.422,0.437,0.451,0.464,0.478,0.491,0.503,0.515,0.527,0.538,0.549,0.56,0.57,0.58,0.59,0.599,0.608,0.617,0.626,0.634,0.642,0.65,0.658,0.665,0.672,0.679,0.686,0.693,0.699,0.705,0.711,0.717,0.723,0.728,0.734,0.739 74 | 72,0.162,0.187,0.21,0.233,0.254,0.275,0.296,0.315,0.334,0.353,0.37,0.387,0.404,0.42,0.435,0.45,0.464,0.478,0.492,0.505,0.517,0.53,0.541,0.553,0.564,0.575,0.585,0.595,0.605,0.614,0.623,0.632,0.641,0.649,0.657,0.665,0.672,0.68,0.687,0.694,0.7,0.707,0.713,0.719,0.725,0.731,0.737,0.742,0.747,0.753 75 | 73,0.168,0.193,0.218,0.241,0.263,0.285,0.306,0.326,0.346,0.364,0.382,0.4,0.417,0.433,0.449,0.464,0.479,0.493,0.506,0.52,0.532,0.545,0.556,0.568,0.579,0.59,0.6,0.61,0.62,0.63,0.639,0.648,0.656,0.664,0.672,0.68,0.688,0.695,0.702,0.709,0.716,0.722,0.728,0.734,0.74,0.746,0.751,0.757,0.762,0.767 76 | 74,0.176,0.202,0.227,0.251,0.275,0.297,0.319,0.34,0.36,0.379,0.397,0.415,0.432,0.449,0.465,0.48,0.495,0.51,0.523,0.537,0.55,0.562,0.574,0.586,0.597,0.607,0.618,0.628,0.638,0.647,0.656,0.665,0.673,0.682,0.69,0.697,0.705,0.712,0.719,0.725,0.732,0.738,0.744,0.75,0.756,0.761,0.767,0.772,0.777,0.782 77 | 75,0.184,0.211,0.238,0.263,0.287,0.31,0.332,0.353,0.374,0.394,0.413,0.431,0.449,0.466,0.482,0.498,0.513,0.527,0.541,0.555,0.568,0.58,0.592,0.604,0.615,0.626,0.636,0.646,0.656,0.665,0.674,0.682,0.691,0.699,0.707,0.714,0.721,0.728,0.735,0.742,0.748,0.754,0.76,0.766,0.772,0.778,0.783,0.788,0.793,0.798 78 | 76,0.194,0.222,0.25,0.276,0.301,0.325,0.348,0.37,0.391,0.411,0.431,0.449,0.467,0.484,0.501,0.517,0.532,0.547,0.561,0.575,0.588,0.6,0.612,0.624,0.635,0.646,0.656,0.666,0.675,0.684,0.693,0.702,0.71,0.718,0.726,0.733,0.74,0.747,0.754,0.76,0.766,0.772,0.778,0.783,0.789,0.794,0.799,0.804,0.809,0.813 79 | 77,0.204,0.233,0.262,0.289,0.315,0.34,0.364,0.386,0.408,0.429,0.449,0.468,0.487,0.504,0.521,0.537,0.553,0.567,0.582,0.595,0.608,0.621,0.633,0.644,0.656,0.666,0.676,0.686,0.696,0.705,0.713,0.722,0.73,0.737,0.745,0.752,0.759,0.766,0.772,0.778,0.784,0.79,0.795,0.801,0.806,0.811,0.816,0.82,0.825,0.829 80 | 78,0.214,0.245,0.275,0.303,0.33,0.356,0.38,0.404,0.427,0.448,0.469,0.488,0.507,0.525,0.542,0.558,0.574,0.589,0.603,0.617,0.63,0.643,0.655,0.666,0.677,0.688,0.698,0.707,0.717,0.725,0.734,0.742,0.75,0.757,0.765,0.772,0.778,0.785,0.791,0.797,0.802,0.808,0.813,0.818,0.823,0.828,0.833,0.837,0.841,0.845 81 | 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27,0.021,0.029,0.038,0.045,0.053,0.061,0.069,0.076,0.083,0.09,0.098,0.105,0.111,0.118,0.125,0.132,0.138,0.145,0.151,0.157,0.164,0.17,0.176,0.182,0.188,0.194,0.199,0.205,0.211,0.216,0.222,0.227,0.233,0.238,0.244,0.249,0.254,0.259,0.264,0.269,0.274,0.279,0.284,0.289,0.294,0.298,0.303,0.308,0.312,0.317 30 | 28,0.021,0.03,0.038,0.046,0.054,0.061,0.069,0.076,0.084,0.091,0.098,0.105,0.112,0.119,0.126,0.132,0.139,0.145,0.152,0.158,0.164,0.171,0.177,0.183,0.189,0.195,0.201,0.206,0.212,0.218,0.223,0.229,0.234,0.24,0.245,0.25,0.255,0.261,0.266,0.271,0.276,0.281,0.286,0.29,0.295,0.3,0.305,0.309,0.314,0.318 31 | 29,0.021,0.03,0.038,0.046,0.054,0.062,0.069,0.077,0.084,0.091,0.099,0.106,0.113,0.12,0.126,0.133,0.14,0.146,0.153,0.159,0.165,0.172,0.178,0.184,0.19,0.196,0.202,0.207,0.213,0.219,0.224,0.23,0.235,0.241,0.246,0.252,0.257,0.262,0.267,0.272,0.277,0.282,0.287,0.292,0.297,0.302,0.306,0.311,0.316,0.32 32 | 30,0.021,0.03,0.038,0.046,0.054,0.062,0.07,0.077,0.085,0.092,0.099,0.106,0.113,0.12,0.127,0.134,0.141,0.147,0.154,0.16,0.166,0.173,0.179,0.185,0.191,0.197,0.203,0.209,0.214,0.22,0.226,0.231,0.237,0.242,0.248,0.253,0.258,0.264,0.269,0.274,0.279,0.284,0.289,0.294,0.299,0.303,0.308,0.313,0.317,0.322 33 | 31,0.021,0.03,0.038,0.046,0.054,0.062,0.07,0.078,0.085,0.092,0.1,0.107,0.114,0.121,0.128,0.135,0.141,0.148,0.155,0.161,0.167,0.174,0.18,0.186,0.192,0.198,0.204,0.21,0.216,0.221,0.227,0.233,0.238,0.244,0.249,0.255,0.26,0.265,0.27,0.275,0.281,0.286,0.291,0.295,0.3,0.305,0.31,0.315,0.319,0.324 34 | 32,0.021,0.03,0.038,0.047,0.055,0.063,0.07,0.078,0.086,0.093,0.1,0.108,0.115,0.122,0.129,0.136,0.142,0.149,0.156,0.162,0.168,0.175,0.181,0.187,0.193,0.199,0.205,0.211,0.217,0.223,0.229,0.234,0.24,0.245,0.251,0.256,0.262,0.267,0.272,0.277,0.282,0.287,0.292,0.297,0.302,0.307,0.312,0.317,0.321,0.326 35 | 33,0.021,0.03,0.039,0.047,0.055,0.063,0.071,0.079,0.086,0.094,0.101,0.108,0.116,0.123,0.13,0.136,0.143,0.15,0.157,0.163,0.17,0.176,0.182,0.189,0.195,0.201,0.207,0.213,0.219,0.224,0.23,0.236,0.241,0.247,0.252,0.258,0.263,0.269,0.274,0.279,0.284,0.289,0.294,0.299,0.304,0.309,0.314,0.319,0.323,0.328 36 | 34,0.021,0.03,0.039,0.047,0.055,0.063,0.071,0.079,0.087,0.094,0.102,0.109,0.116,0.123,0.13,0.137,0.144,0.151,0.158,0.164,0.171,0.177,0.184,0.19,0.196,0.202,0.208,0.214,0.22,0.226,0.232,0.237,0.243,0.249,0.254,0.26,0.265,0.27,0.276,0.281,0.286,0.291,0.296,0.301,0.306,0.311,0.316,0.321,0.326,0.33 37 | 35,0.022,0.03,0.039,0.047,0.056,0.064,0.072,0.08,0.087,0.095,0.102,0.11,0.117,0.124,0.131,0.138,0.145,0.152,0.159,0.165,0.172,0.179,0.185,0.191,0.197,0.204,0.21,0.216,0.222,0.228,0.233,0.239,0.245,0.25,0.256,0.261,0.267,0.272,0.278,0.283,0.288,0.293,0.298,0.303,0.308,0.313,0.318,0.323,0.328,0.333 38 | 36,0.022,0.03,0.039,0.048,0.056,0.064,0.072,0.08,0.088,0.096,0.103,0.111,0.118,0.125,0.132,0.139,0.146,0.153,0.16,0.167,0.173,0.18,0.186,0.193,0.199,0.205,0.211,0.217,0.223,0.229,0.235,0.241,0.247,0.252,0.258,0.263,0.269,0.274,0.28,0.285,0.29,0.295,0.301,0.306,0.311,0.316,0.32,0.325,0.33,0.335 39 | 37,0.022,0.031,0.039,0.048,0.056,0.065,0.073,0.081,0.089,0.096,0.104,0.111,0.119,0.126,0.133,0.141,0.148,0.154,0.161,0.168,0.175,0.181,0.188,0.194,0.201,0.207,0.213,0.219,0.225,0.231,0.237,0.243,0.249,0.254,0.26,0.265,0.271,0.276,0.282,0.287,0.292,0.298,0.303,0.308,0.313,0.318,0.323,0.328,0.333,0.337 40 | 38,0.022,0.031,0.04,0.048,0.057,0.065,0.073,0.081,0.089,0.097,0.105,0.112,0.12,0.127,0.134,0.142,0.149,0.156,0.163,0.169,0.176,0.183,0.189,0.196,0.202,0.208,0.215,0.221,0.227,0.233,0.239,0.245,0.251,0.256,0.262,0.268,0.273,0.279,0.284,0.289,0.295,0.3,0.305,0.31,0.315,0.32,0.325,0.33,0.335,0.34 41 | 39,0.022,0.031,0.04,0.049,0.057,0.066,0.074,0.082,0.09,0.098,0.106,0.113,0.121,0.128,0.136,0.143,0.15,0.157,0.164,0.171,0.178,0.184,0.191,0.197,0.204,0.21,0.216,0.223,0.229,0.235,0.241,0.247,0.253,0.258,0.264,0.27,0.275,0.281,0.286,0.292,0.297,0.302,0.308,0.313,0.318,0.323,0.328,0.333,0.338,0.343 42 | 40,0.022,0.031,0.04,0.049,0.058,0.066,0.074,0.083,0.091,0.099,0.107,0.114,0.122,0.129,0.137,0.144,0.151,0.158,0.165,0.172,0.179,0.186,0.193,0.199,0.206,0.212,0.218,0.225,0.231,0.237,0.243,0.249,0.255,0.261,0.266,0.272,0.278,0.283,0.289,0.294,0.3,0.305,0.31,0.315,0.321,0.326,0.331,0.336,0.341,0.346 43 | 41,0.022,0.031,0.04,0.049,0.058,0.067,0.075,0.083,0.092,0.1,0.107,0.115,0.123,0.131,0.138,0.145,0.153,0.16,0.167,0.174,0.181,0.188,0.194,0.201,0.207,0.214,0.22,0.227,0.233,0.239,0.245,0.251,0.257,0.263,0.269,0.274,0.28,0.286,0.291,0.297,0.302,0.308,0.313,0.318,0.323,0.329,0.334,0.339,0.344,0.349 44 | 42,0.022,0.031,0.041,0.05,0.059,0.067,0.076,0.084,0.092,0.1,0.108,0.116,0.124,0.132,0.139,0.147,0.154,0.161,0.168,0.175,0.182,0.189,0.196,0.203,0.209,0.216,0.222,0.229,0.235,0.241,0.247,0.253,0.259,0.265,0.271,0.277,0.283,0.288,0.294,0.3,0.305,0.31,0.316,0.321,0.326,0.332,0.337,0.342,0.347,0.352 45 | 43,0.022,0.032,0.041,0.05,0.059,0.068,0.076,0.085,0.093,0.101,0.109,0.117,0.125,0.133,0.141,0.148,0.156,0.163,0.17,0.177,0.184,0.191,0.198,0.205,0.211,0.218,0.225,0.231,0.237,0.244,0.25,0.256,0.262,0.268,0.274,0.28,0.285,0.291,0.297,0.302,0.308,0.313,0.319,0.324,0.329,0.335,0.34,0.345,0.35,0.355 46 | 44,0.022,0.032,0.041,0.05,0.06,0.068,0.077,0.086,0.094,0.102,0.111,0.119,0.127,0.134,0.142,0.15,0.157,0.164,0.172,0.179,0.186,0.193,0.2,0.207,0.214,0.22,0.227,0.233,0.24,0.246,0.252,0.258,0.265,0.271,0.277,0.282,0.288,0.294,0.3,0.305,0.311,0.316,0.322,0.327,0.333,0.338,0.343,0.348,0.353,0.358 47 | 45,0.022,0.032,0.042,0.051,0.06,0.069,0.078,0.086,0.095,0.103,0.112,0.12,0.128,0.136,0.143,0.151,0.159,0.166,0.174,0.181,0.188,0.195,0.202,0.209,0.216,0.222,0.229,0.236,0.242,0.249,0.255,0.261,0.267,0.273,0.279,0.285,0.291,0.297,0.303,0.308,0.314,0.32,0.325,0.331,0.336,0.341,0.346,0.352,0.357,0.362 48 | 46,0.022,0.032,0.042,0.051,0.061,0.07,0.079,0.087,0.096,0.104,0.113,0.121,0.129,0.137,0.145,0.153,0.16,0.168,0.175,0.183,0.19,0.197,0.204,0.211,0.218,0.225,0.232,0.238,0.245,0.251,0.258,0.264,0.27,0.276,0.282,0.288,0.294,0.3,0.306,0.312,0.317,0.323,0.329,0.334,0.339,0.345,0.35,0.355,0.36,0.366 49 | 47,0.023,0.033,0.042,0.052,0.061,0.07,0.079,0.088,0.097,0.106,0.114,0.122,0.131,0.139,0.147,0.155,0.162,0.17,0.177,0.185,0.192,0.199,0.207,0.214,0.221,0.227,0.234,0.241,0.247,0.254,0.26,0.267,0.273,0.279,0.285,0.292,0.298,0.303,0.309,0.315,0.321,0.326,0.332,0.338,0.343,0.348,0.354,0.359,0.364,0.37 50 | 48,0.023,0.033,0.043,0.052,0.062,0.071,0.08,0.089,0.098,0.107,0.115,0.124,0.132,0.14,0.148,0.156,0.164,0.172,0.179,0.187,0.194,0.202,0.209,0.216,0.223,0.23,0.237,0.244,0.25,0.257,0.263,0.27,0.277,0.283,0.289,0.295,0.301,0.307,0.313,0.319,0.325,0.331,0.336,0.342,0.347,0.353,0.358,0.364,0.369,0.374 51 | 49,0.023,0.034,0.044,0.053,0.063,0.072,0.082,0.091,0.1,0.109,0.117,0.126,0.134,0.142,0.151,0.159,0.167,0.174,0.182,0.19,0.197,0.205,0.212,0.219,0.226,0.233,0.24,0.247,0.254,0.26,0.267,0.274,0.28,0.286,0.293,0.299,0.305,0.311,0.317,0.323,0.329,0.334,0.34,0.346,0.351,0.357,0.362,0.368,0.373,0.378 52 | 50,0.024,0.034,0.044,0.054,0.064,0.074,0.083,0.092,0.101,0.11,0.119,0.128,0.136,0.145,0.153,0.161,0.169,0.177,0.185,0.192,0.2,0.208,0.215,0.222,0.229,0.237,0.244,0.25,0.257,0.264,0.271,0.277,0.284,0.29,0.297,0.303,0.309,0.315,0.321,0.327,0.333,0.339,0.345,0.35,0.356,0.361,0.367,0.372,0.378,0.383 53 | 51,0.024,0.035,0.045,0.055,0.065,0.075,0.084,0.094,0.103,0.112,0.121,0.13,0.138,0.147,0.155,0.163,0.172,0.18,0.187,0.195,0.203,0.211,0.218,0.225,0.233,0.24,0.247,0.254,0.261,0.268,0.275,0.281,0.288,0.294,0.301,0.307,0.313,0.319,0.325,0.332,0.338,0.343,0.349,0.355,0.361,0.366,0.372,0.377,0.383,0.388 54 | 52,0.025,0.035,0.046,0.056,0.066,0.076,0.085,0.095,0.104,0.113,0.122,0.131,0.14,0.149,0.157,0.166,0.174,0.182,0.19,0.198,0.206,0.213,0.221,0.228,0.236,0.243,0.25,0.257,0.264,0.271,0.278,0.285,0.292,0.298,0.305,0.311,0.317,0.324,0.33,0.336,0.342,0.348,0.354,0.36,0.365,0.371,0.377,0.382,0.388,0.393 55 | 53,0.025,0.036,0.046,0.057,0.067,0.077,0.087,0.096,0.106,0.115,0.124,0.133,0.142,0.151,0.159,0.168,0.176,0.185,0.193,0.201,0.209,0.216,0.224,0.232,0.239,0.247,0.254,0.261,0.268,0.275,0.282,0.289,0.296,0.302,0.309,0.315,0.322,0.328,0.334,0.34,0.347,0.353,0.359,0.364,0.37,0.376,0.382,0.387,0.393,0.398 56 | 54,0.025,0.036,0.047,0.058,0.068,0.078,0.088,0.098,0.107,0.117,0.126,0.135,0.144,0.153,0.162,0.171,0.179,0.188,0.196,0.204,0.212,0.22,0.228,0.235,0.243,0.25,0.258,0.265,0.273,0.28,0.287,0.294,0.301,0.307,0.314,0.32,0.327,0.333,0.34,0.346,0.352,0.358,0.364,0.37,0.376,0.382,0.388,0.393,0.399,0.404 57 | 55,0.026,0.037,0.048,0.059,0.069,0.08,0.09,0.1,0.109,0.119,0.129,0.138,0.147,0.156,0.165,0.174,0.182,0.191,0.199,0.207,0.216,0.224,0.232,0.239,0.247,0.255,0.262,0.269,0.277,0.284,0.291,0.298,0.305,0.312,0.319,0.325,0.332,0.338,0.345,0.351,0.357,0.363,0.369,0.376,0.381,0.387,0.393,0.399,0.405,0.41 58 | 56,0.027,0.039,0.05,0.061,0.071,0.082,0.092,0.102,0.112,0.122,0.132,0.141,0.15,0.16,0.169,0.177,0.186,0.195,0.203,0.212,0.22,0.228,0.236,0.244,0.252,0.26,0.267,0.275,0.282,0.289,0.297,0.304,0.311,0.318,0.324,0.331,0.338,0.344,0.351,0.357,0.364,0.37,0.376,0.382,0.388,0.394,0.4,0.406,0.411,0.417 59 | 57,0.027,0.039,0.05,0.061,0.072,0.083,0.093,0.104,0.114,0.124,0.134,0.143,0.153,0.162,0.171,0.18,0.189,0.198,0.207,0.215,0.224,0.232,0.24,0.248,0.256,0.264,0.271,0.279,0.287,0.295,0.302,0.309,0.316,0.323,0.33,0.337,0.344,0.351,0.357,0.364,0.37,0.376,0.383,0.389,0.395,0.401,0.407,0.413,0.418,0.424 60 | 58,0.029,0.04,0.052,0.063,0.074,0.085,0.096,0.106,0.117,0.127,0.137,0.147,0.156,0.166,0.175,0.184,0.193,0.202,0.211,0.22,0.228,0.237,0.245,0.253,0.261,0.269,0.277,0.285,0.292,0.3,0.307,0.315,0.322,0.329,0.336,0.343,0.35,0.356,0.363,0.37,0.376,0.383,0.389,0.395,0.401,0.407,0.413,0.419,0.425,0.431 61 | 59,0.029,0.041,0.053,0.064,0.076,0.087,0.098,0.108,0.119,0.129,0.139,0.149,0.159,0.169,0.178,0.188,0.197,0.206,0.215,0.224,0.232,0.241,0.249,0.258,0.266,0.274,0.282,0.29,0.297,0.305,0.313,0.32,0.327,0.335,0.342,0.349,0.356,0.362,0.369,0.376,0.382,0.389,0.395,0.402,0.408,0.414,0.42,0.426,0.432,0.438 62 | 60,0.029,0.041,0.053,0.065,0.077,0.088,0.099,0.11,0.121,0.131,0.142,0.152,0.162,0.172,0.181,0.191,0.2,0.21,0.219,0.228,0.237,0.245,0.254,0.262,0.271,0.279,0.287,0.295,0.303,0.311,0.318,0.326,0.333,0.341,0.348,0.355,0.362,0.369,0.376,0.383,0.389,0.396,0.402,0.409,0.415,0.421,0.428,0.434,0.44,0.446 63 | 61,0.029,0.042,0.054,0.066,0.078,0.09,0.101,0.112,0.123,0.134,0.144,0.155,0.165,0.175,0.185,0.195,0.204,0.214,0.223,0.232,0.241,0.25,0.259,0.267,0.276,0.284,0.292,0.301,0.309,0.316,0.324,0.332,0.34,0.347,0.354,0.362,0.369,0.376,0.383,0.39,0.396,0.403,0.41,0.416,0.423,0.429,0.435,0.441,0.447,0.453 64 | 62,0.03,0.043,0.055,0.067,0.079,0.091,0.103,0.114,0.125,0.136,0.147,0.158,0.168,0.179,0.189,0.199,0.208,0.218,0.227,0.237,0.246,0.255,0.264,0.273,0.281,0.29,0.298,0.307,0.315,0.323,0.331,0.339,0.346,0.354,0.361,0.369,0.376,0.383,0.39,0.397,0.404,0.411,0.418,0.424,0.431,0.437,0.443,0.45,0.456,0.462 65 | 63,0.03,0.043,0.056,0.069,0.081,0.093,0.105,0.117,0.128,0.139,0.15,0.161,0.172,0.182,0.193,0.203,0.213,0.223,0.232,0.242,0.251,0.26,0.269,0.278,0.287,0.296,0.305,0.314,0.322,0.33,0.339,0.346,0.354,0.362,0.37,0.377,0.385,0.392,0.399,0.406,0.413,0.42,0.427,0.433,0.44,0.447,0.453,0.459,0.466,0.472 66 | 64,0.032,0.046,0.059,0.072,0.084,0.097,0.109,0.121,0.132,0.144,0.155,0.166,0.177,0.188,0.198,0.209,0.219,0.229,0.239,0.249,0.258,0.268,0.277,0.287,0.296,0.305,0.314,0.322,0.331,0.339,0.347,0.355,0.363,0.371,0.379,0.386,0.394,0.401,0.409,0.416,0.423,0.43,0.437,0.444,0.45,0.457,0.463,0.47,0.476,0.482 67 | 65,0.034,0.048,0.061,0.074,0.087,0.1,0.113,0.125,0.137,0.148,0.16,0.171,0.183,0.194,0.204,0.215,0.225,0.236,0.246,0.256,0.265,0.275,0.285,0.294,0.303,0.312,0.321,0.33,0.338,0.348,0.356,0.365,0.373,0.381,0.389,0.396,0.404,0.411,0.419,0.426,0.433,0.44,0.447,0.454,0.461,0.468,0.474,0.481,0.487,0.494 68 | 66,0.036,0.05,0.064,0.078,0.091,0.104,0.117,0.129,0.142,0.154,0.165,0.177,0.189,0.2,0.211,0.222,0.233,0.243,0.254,0.264,0.274,0.284,0.293,0.303,0.312,0.321,0.331,0.34,0.349,0.357,0.366,0.375,0.383,0.391,0.399,0.407,0.415,0.422,0.43,0.437,0.445,0.452,0.459,0.466,0.473,0.48,0.486,0.493,0.499,0.506 69 | 67,0.038,0.052,0.067,0.08,0.094,0.107,0.121,0.133,0.146,0.158,0.171,0.183,0.194,0.206,0.217,0.228,0.239,0.25,0.261,0.271,0.281,0.292,0.301,0.311,0.321,0.33,0.34,0.349,0.358,0.367,0.375,0.384,0.392,0.401,0.409,0.417,0.425,0.433,0.44,0.448,0.455,0.463,0.47,0.477,0.484,0.491,0.498,0.504,0.511,0.517 70 | 68,0.038,0.053,0.068,0.082,0.096,0.11,0.124,0.137,0.15,0.163,0.175,0.187,0.2,0.211,0.223,0.235,0.246,0.257,0.268,0.278,0.289,0.299,0.309,0.319,0.329,0.339,0.349,0.358,0.367,0.376,0.385,0.394,0.402,0.411,0.419,0.428,0.436,0.444,0.451,0.459,0.467,0.474,0.481,0.489,0.496,0.503,0.51,0.516,0.523,0.53 71 | 69,0.039,0.055,0.07,0.085,0.099,0.113,0.127,0.141,0.154,0.168,0.18,0.193,0.206,0.218,0.23,0.242,0.253,0.265,0.276,0.287,0.298,0.308,0.319,0.329,0.339,0.349,0.359,0.368,0.378,0.387,0.396,0.405,0.414,0.423,0.431,0.44,0.449,0.457,0.465,0.472,0.48,0.488,0.495,0.502,0.51,0.517,0.524,0.531,0.537,0.544 72 | 70,0.041,0.057,0.072,0.088,0.103,0.117,0.132,0.146,0.16,0.173,0.187,0.2,0.213,0.226,0.238,0.25,0.262,0.274,0.286,0.297,0.308,0.319,0.33,0.34,0.351,0.361,0.371,0.381,0.39,0.4,0.409,0.418,0.427,0.436,0.445,0.454,0.462,0.47,0.478,0.486,0.494,0.502,0.509,0.517,0.524,0.531,0.538,0.545,0.552,0.559 73 | 71,0.042,0.059,0.075,0.091,0.107,0.122,0.137,0.151,0.166,0.18,0.193,0.207,0.22,0.233,0.246,0.259,0.271,0.283,0.295,0.307,0.318,0.329,0.34,0.351,0.362,0.372,0.383,0.393,0.403,0.412,0.422,0.431,0.44,0.449,0.458,0.467,0.476,0.484,0.492,0.5,0.508,0.516,0.524,0.531,0.539,0.546,0.553,0.56,0.567,0.574 74 | 72,0.044,0.061,0.078,0.095,0.111,0.126,0.142,0.157,0.172,0.187,0.201,0.215,0.229,0.242,0.255,0.268,0.281,0.294,0.306,0.318,0.33,0.341,0.353,0.364,0.375,0.386,0.396,0.406,0.417,0.427,0.436,0.446,0.455,0.465,0.474,0.483,0.491,0.5,0.508,0.517,0.525,0.533,0.54,0.548,0.556,0.563,0.57,0.577,0.584,0.591 75 | 73,0.045,0.063,0.08,0.097,0.114,0.131,0.147,0.163,0.178,0.193,0.208,0.223,0.237,0.251,0.265,0.278,0.291,0.304,0.317,0.329,0.342,0.354,0.365,0.377,0.388,0.399,0.41,0.421,0.432,0.442,0.452,0.462,0.472,0.481,0.491,0.5,0.509,0.517,0.526,0.534,0.543,0.551,0.559,0.566,0.574,0.581,0.589,0.596,0.603,0.61 76 | 74,0.048,0.067,0.085,0.103,0.121,0.138,0.155,0.172,0.188,0.203,0.219,0.234,0.249,0.263,0.278,0.292,0.305,0.319,0.332,0.345,0.357,0.37,0.382,0.394,0.405,0.417,0.428,0.439,0.45,0.46,0.47,0.48,0.49,0.501,0.51,0.519,0.528,0.537,0.546,0.554,0.563,0.571,0.579,0.587,0.594,0.602,0.609,0.616,0.623,0.63 77 | 75,0.051,0.071,0.09,0.109,0.127,0.145,0.163,0.18,0.197,0.213,0.229,0.245,0.261,0.276,0.291,0.305,0.32,0.333,0.347,0.36,0.374,0.386,0.399,0.411,0.423,0.435,0.446,0.458,0.469,0.479,0.49,0.5,0.51,0.52,0.53,0.539,0.548,0.557,0.566,0.575,0.583,0.591,0.599,0.608,0.616,0.624,0.631,0.638,0.646,0.653 78 | 76,0.056,0.077,0.097,0.117,0.136,0.155,0.173,0.191,0.209,0.226,0.243,0.26,0.276,0.291,0.307,0.322,0.337,0.351,0.366,0.379,0.393,0.406,0.419,0.432,0.444,0.456,0.468,0.48,0.491,0.502,0.513,0.523,0.533,0.543,0.553,0.563,0.572,0.581,0.59,0.598,0.607,0.615,0.623,0.631,0.639,0.646,0.654,0.661,0.668,0.675 79 | 77,0.059,0.081,0.102,0.123,0.144,0.163,0.183,0.202,0.22,0.239,0.256,0.274,0.291,0.307,0.323,0.339,0.355,0.37,0.385,0.399,0.413,0.427,0.44,0.453,0.466,0.478,0.491,0.502,0.514,0.525,0.536,0.547,0.557,0.567,0.577,0.587,0.596,0.606,0.615,0.623,0.632,0.64,0.648,0.656,0.663,0.671,0.678,0.685,0.692,0.699 80 | 78,0.061,0.084,0.107,0.129,0.15,0.172,0.192,0.212,0.232,0.251,0.27,0.288,0.306,0.324,0.341,0.357,0.373,0.389,0.405,0.42,0.434,0.449,0.463,0.476,0.489,0.502,0.515,0.527,0.539,0.55,0.561,0.572,0.583,0.593,0.603,0.613,0.622,0.631,0.64,0.649,0.658,0.666,0.674,0.682,0.689,0.696,0.704,0.711,0.717,0.724 81 | 79,0.063,0.088,0.112,0.136,0.159,0.181,0.203,0.225,0.246,0.267,0.287,0.306,0.325,0.343,0.361,0.379,0.396,0.413,0.429,0.444,0.46,0.474,0.489,0.503,0.516,0.53,0.542,0.555,0.567,0.579,0.59,0.601,0.612,0.622,0.633,0.642,0.652,0.661,0.67,0.679,0.687,0.695,0.703,0.71,0.718,0.725,0.732,0.739,0.746,0.752 82 | 80,0.07,0.096,0.123,0.148,0.173,0.197,0.221,0.244,0.267,0.289,0.31,0.33,0.35,0.37,0.389,0.408,0.426,0.443,0.46,0.476,0.493,0.508,0.523,0.537,0.551,0.564,0.577,0.59,0.602,0.614,0.625,0.636,0.647,0.658,0.668,0.677,0.687,0.696,0.704,0.713,0.721,0.729,0.736,0.743,0.75,0.757,0.764,0.77,0.776,0.782 83 | 81,0.078,0.107,0.136,0.163,0.19,0.216,0.242,0.267,0.291,0.314,0.337,0.359,0.38,0.401,0.421,0.44,0.459,0.477,0.495,0.512,0.528,0.544,0.559,0.574,0.588,0.601,0.615,0.627,0.639,0.651,0.662,0.673,0.684,0.695,0.704,0.714,0.723,0.731,0.74,0.748,0.756,0.763,0.77,0.777,0.784,0.79,0.797,0.803,0.808,0.814 84 | 82,0.088,0.12,0.151,0.181,0.21,0.239,0.267,0.294,0.32,0.345,0.369,0.393,0.416,0.438,0.459,0.479,0.499,0.518,0.536,0.553,0.57,0.586,0.602,0.617,0.631,0.644,0.657,0.67,0.682,0.693,0.704,0.715,0.725,0.735,0.744,0.753,0.761,0.77,0.777,0.785,0.792,0.799,0.806,0.812,0.818,0.824,0.83,0.835,0.84,0.845 85 | 83,0.094,0.129,0.165,0.199,0.231,0.263,0.294,0.323,0.352,0.379,0.406,0.432,0.456,0.48,0.502,0.524,0.544,0.564,0.582,0.6,0.617,0.633,0.649,0.664,0.678,0.691,0.704,0.716,0.727,0.738,0.749,0.759,0.768,0.777,0.786,0.794,0.802,0.809,0.816,0.823,0.83,0.836,0.842,0.847,0.853,0.858,0.863,0.868,0.872,0.877 86 | 84,0.103,0.144,0.184,0.222,0.259,0.295,0.33,0.363,0.394,0.424,0.453,0.48,0.506,0.531,0.554,0.577,0.599,0.618,0.637,0.655,0.672,0.688,0.703,0.717,0.73,0.743,0.755,0.766,0.777,0.787,0.797,0.806,0.814,0.822,0.83,0.837,0.844,0.851,0.857,0.863,0.868,0.873,0.878,0.883,0.888,0.892,0.896,0.9,0.904,0.907 87 | 85,0.119,0.166,0.212,0.257,0.299,0.341,0.379,0.416,0.45,0.483,0.514,0.543,0.571,0.597,0.621,0.644,0.665,0.684,0.703,0.72,0.736,0.751,0.765,0.778,0.79,0.801,0.811,0.821,0.831,0.839,0.847,0.855,0.862,0.869,0.875,0.881,0.887,0.892,0.897,0.902,0.906,0.91,0.914,0.918,0.921,0.924,0.928,0.931,0.933,0.936 88 | 86,0.14,0.197,0.252,0.305,0.355,0.402,0.446,0.487,0.525,0.56,0.593,0.623,0.651,0.676,0.7,0.721,0.741,0.759,0.776,0.791,0.805,0.818,0.83,0.841,0.851,0.86,0.868,0.876,0.884,0.89,0.897,0.902,0.908,0.913,0.918,0.922,0.926,0.93,0.933,0.937,0.94,0.943,0.946,0.948,0.951,0.953,0.955,0.957,0.959,0.961 89 | 87,0.167,0.242,0.312,0.377,0.437,0.492,0.542,0.587,0.627,0.663,0.696,0.725,0.75,0.773,0.793,0.812,0.828,0.842,0.855,0.867,0.878,0.887,0.896,0.904,0.911,0.917,0.923,0.928,0.933,0.938,0.942,0.946,0.949,0.952,0.955,0.958,0.961,0.963,0.965,0.967,0.969,0.971,0.972,0.974,0.975,0.977,0.978,0.979,0.98,0.981 90 | 88,0.218,0.323,0.417,0.5,0.572,0.634,0.685,0.729,0.766,0.797,0.823,0.845,0.864,0.88,0.894,0.906,0.916,0.925,0.933,0.94,0.946,0.951,0.955,0.959,0.963,0.966,0.969,0.972,0.974,0.976,0.978,0.98,0.982,0.983,0.984,0.985,0.987,0.988,0.989,0.989,0.99,0.991,0.991,0.992,0.993,0.993,0.994,0.994,0.995,0.995 91 | 89,0.358,0.525,0.649,0.739,0.804,0.85,0.884,0.908,0.927,0.941,0.952,0.961,0.968,0.973,0.977,0.981,0.984,0.986,0.988,0.99,0.992,0.993,0.994,0.995,0.995,0.996,0.997,0.997,0.997,0.998,0.998,0.998,0.999,0.999,0.999,0.999,0.999,0.999,0.999,0.999,1,1,1,1,1,1,1,1,1,1 92 | -------------------------------------------------------------------------------- /main_albedo.R: -------------------------------------------------------------------------------- 1 | ##################################################################################### 2 | # Set up directories and solar optical depth << change these >> 3 | ##################################################################################### 4 | 5 | # Set your working directory. Contains R scripts (main_aledo.R, f_albedo.R, proc_albedo.R), lookup tables (vis_lut.csv, nir_lut, sw_lut.csv), and input NetCDF 6 | wkd <- '/path/to/your/working/directory/' 7 | setwd(wkd) 8 | 9 | # Set path and filename for input NetCDF. Default output from AppEEARS should be MCD43A1.006_aid0001.nc 10 | nc_in = paste0(wkd, 'example-data/', 'MCD43A1.006_aid0001.nc') 11 | 12 | # Set solar optical depth (value between 0.00 and 0.98 x0.02 with 2-digit precision) 13 | SolOptDepth <- 0.20 14 | # Set solar zenith angle (0.0-89.0 degrees, or "local" for local solar noon) 15 | SolZenAngle <- 'local' 16 | 17 | # Set path to output NetCDF 18 | out_dir <- paste0(wkd, 'example-output/') 19 | out_filename <- 'MCD43A_calcalbedo.nc' 20 | suppressWarnings(dir.create(out_dir)) 21 | 22 | ##################################################################################### 23 | # Import libraries 24 | ##################################################################################### 25 | 26 | library(ncdf4) 27 | library(raster) 28 | library(RAtmosphere) 29 | 30 | ##################################################################################### 31 | # Read external files and functions 32 | ##################################################################################### 33 | 34 | # Open look up tables 35 | vislut <- t(read.csv('vis_lut.csv')) 36 | nirlut <- t(read.csv('nir_lut.csv')) 37 | swlut <- t(read.csv('sw_lut.csv')) 38 | # External functions 39 | source('f_albedo.R') 40 | 41 | ##################################################################################### 42 | # Read NetCDF; get variables and dimensions 43 | ##################################################################################### 44 | 45 | nc <- nc_open(nc_in) 46 | 47 | # Get data.frame of latlon combinations and separate to vectors 48 | nc_latlon <- expand.grid(nc$dim$lat$vals, nc$dim$lon$vals) 49 | lat <- nc_latlon[1] 50 | lon <- nc_latlon[2] 51 | 52 | # Set coordinate reference system 53 | crs <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs+ towgs84=0,0,0") 54 | 55 | # Get time dimension values as array and number of timesteps 56 | nc_time <- nc$dim$time$vals 57 | nt <- length(nc_time) 58 | 59 | print(paste('There are',nrow(nc_latlon), 'pixels and', 60 | length(nc_time), 'timesteps in this dataset.', sep = ' ')) 61 | 62 | # Define output dimensions 63 | outlat <- ncdim_def('lat', nc$dim$lat$units, as.double(nc$dim$lat$vals), create_dimvar=TRUE) 64 | outlon <- ncdim_def('lon', nc$dim$lon$units, as.double(nc$dim$lon$vals), create_dimvar=TRUE) 65 | outtime <- ncdim_def('time', nc$dim$time$units, as.integer(nc_time), create_dimvar=TRUE, unlim = TRUE) 66 | 67 | # Define new variables for calculated albedo 68 | vis_bsa <- ncvar_def('visible_black_sky_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 69 | vis_wsa <- ncvar_def('visible_white_sky_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 70 | vis_asa <- ncvar_def('visible_actual_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 71 | nir_bsa <- ncvar_def('nir_black_sky_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 72 | nir_wsa <- ncvar_def('nir_white_sky_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 73 | nir_asa <- ncvar_def('nir_actual_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 74 | sw_bsa <- ncvar_def('shortwave_black_sky_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 75 | sw_wsa <- ncvar_def('shortwave_white_sky_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 76 | sw_asa <- ncvar_def('shortwave_actual_albedo', units = '', dim = list(outlat, outlon, outtime), missval = -9999, prec = "float") 77 | 78 | # Get CRS variable from input NetCDF and write put attributes 79 | crs_var <- nc$var[['crs']] 80 | 81 | # Set output filename and create output netcdf file 82 | albedo_out <- paste0(out_dir, out_filename) 83 | nc_out <- nc_create(albedo_out, list(vis_bsa, vis_wsa, vis_asa, nir_bsa, nir_wsa, nir_asa, sw_bsa, sw_wsa, sw_asa, crs_var)) 84 | 85 | ##################################################################################### 86 | # Process visible, near-infrared, and shortwave albedo (f_albedo.R) 87 | # 1. Mask QC 88 | # 2. Calculate black sky albedo 89 | # 3. Calculate white sky albedo 90 | # 4. Calculate actual albedo 91 | ##################################################################################### 92 | 93 | ###################################### Visible ###################################### 94 | 95 | # Get variable 96 | var <- nc$var[['BRDF_Albedo_Parameters_vis']] 97 | # Get QC variable 98 | varqc <- nc$var[['BRDF_Albedo_Band_Mandatory_Quality_vis']] 99 | 100 | # Get _FillValue 101 | fillvalue <- ncatt_get(nc, 'BRDF_Albedo_Parameters_vis', "_FillValue") 102 | 103 | # Get variable size and dimension count (4) 104 | varsize <- var$varsize 105 | varndims <- var$ndims 106 | 107 | # Get qc size and dimension count (3) 108 | qcndims <- varqc$ndims 109 | qcsize <- varqc$varsize 110 | 111 | # Loop through timesteps 112 | for(tstep in 1:nt){ 113 | 114 | print(paste("Processing visible band timestep", tstep, "of", nt, ". . .", sep = " ")) 115 | 116 | # Convert tstep to real date 117 | dt <- as.Date(nc_time[tstep], origin = as.Date("2000-01-01")) 118 | 119 | # Calculate array of solar zenith numbers for each pixel for timestep n 120 | if(SolZenAngle == 'local'){ 121 | SZN <- (mapply(SZA, timein = rep(dt, nrow(nc_latlon)), Lat = nc_latlon[,1], Lon = nc_latlon[,2]) - 90) 122 | } 123 | if(SolZenAngle != 'local'){ 124 | SZN <- rep(SolZenAngle, nrow(nc_latlon)) 125 | } 126 | 127 | # Get array of lookup table values for each solar zenith number 128 | LUTarr <- as.vector(mapply(LUT, band = rep('vis', length(SZN)), szn = SZN, sod = rep(SolOptDepth, length(SZN)))) 129 | 130 | # Initialize start and count to read one timestep of the variable 131 | vstart <- rep(1,varndims) 132 | vstart[varndims] <- tstep 133 | vcount <- varsize 134 | vcount[varndims] <- 1 135 | 136 | # Initialize start and count to read one timestep of the variable qc data 137 | qstart <- rep(1,qcndims) 138 | qstart[qcndims] <- tstep 139 | qcount <- qcsize 140 | qcount[qcndims] <- 1 141 | 142 | # Read variable data for timestep n from nc structure 143 | vardata <- ncvar_get(nc, var, start=vstart, count=vcount) 144 | # Read qc data for timestep n from nc structure 145 | qcdata <- ncvar_get(nc, varqc, start=qstart, count=qcount) 146 | 147 | # Set _FillValue to NA 148 | vardata[vardata == fillvalue$value] <- NA 149 | 150 | # Get 3 parameters as raster objects 151 | vardata1 <- raster(t(vardata[1,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 152 | vardata2 <- raster(t(vardata[2,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 153 | vardata3 <- raster(t(vardata[3,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 154 | 155 | # Apply QC mask to vardata (valid == 0 or 1) 156 | vardata[!qcdata %in% c(0,1)] <- NA 157 | 158 | # Calculate black sky albedo for timestep n 159 | nBlack <- BlackSA(vardata1, vardata2, vardata3, SZN) 160 | 161 | # Calculate white sky albedo for timestep n 162 | nWhite <- WhiteSA(vardata1, vardata2, vardata3) 163 | 164 | # Calculate actual albedo for timestep n 165 | nActual <- ActualSA(nWhite, nBlack, LUTarr) 166 | 167 | ncvar_put(nc_out, vis_bsa, as.matrix(nBlack), start = c(1,1,tstep), count = c(-1, -1, 1)) 168 | ncvar_put(nc_out, vis_wsa, as.matrix(nWhite), start = c(1,1,tstep), count = c(-1, -1, 1)) 169 | ncvar_put(nc_out, vis_asa, as.matrix(nActual), start = c(1,1,tstep), count = c(-1, -1, 1)) 170 | 171 | } 172 | 173 | # Clear temporary variables from workspace 174 | remove(var, varqc, fillvalue, varsize, varndims, qcndims, qcsize, dt, SZN, LUTarr, vstart, vcount, 175 | qstart, qcount, vardata, qcdata, vardata1, vardata2, vardata3, nBlack, nWhite, nActual) 176 | 177 | ################################### Near-infrared ################################### 178 | 179 | # Get variable 180 | var <- nc$var[['BRDF_Albedo_Parameters_nir']] 181 | # Get QC variable 182 | varqc <- nc$var[['BRDF_Albedo_Band_Mandatory_Quality_nir']] 183 | 184 | # Get _FillValue 185 | fillvalue <- ncatt_get(nc, 'BRDF_Albedo_Parameters_nir', "_FillValue") 186 | 187 | # Get variable size and dimension count (4) 188 | varsize <- var$varsize 189 | varndims <- var$ndims 190 | 191 | # Get qc size and dimension count (3) 192 | qcndims <- varqc$ndims 193 | qcsize <- varqc$varsize 194 | 195 | # Loop through timesteps 196 | for(tstep in 1:nt){ 197 | 198 | print(paste("Processing near-infrared band timestep", tstep, "of", nt, ". . .", sep = " ")) 199 | 200 | # Convert tstep to real date 201 | dt <- as.Date(nc_time[tstep], origin = as.Date("2000-01-01")) 202 | 203 | # Calculate array of solar zenith numbers for each pixel for timestep n 204 | ################################################################################# 205 | # ORNL DAAC uses an executable (32-bit) that takes date and latitude as input and 206 | # returns a "solar zenith number" between 0-90. Is this the same as SZA? 207 | # Need to figure out how that calculation works. For now, results will not be the 208 | # same as MODIS Global Tool output. 209 | ################################################################################# 210 | if(SolZenAngle == 'local'){ 211 | SZN <- (mapply(SZA, timein = rep(dt, nrow(nc_latlon)), Lat = nc_latlon[,1], Lon = nc_latlon[,2]) - 90) 212 | } 213 | if(SolZenAngle != 'local'){ 214 | SZN <- rep(SolZenAngle, nrow(nc_latlon)) 215 | } 216 | 217 | # Get array of lookup table values for each solar zenith number 218 | LUTarr <- as.vector(mapply(LUT, band = rep('nir', length(SZN)), szn = SZN, sod = rep(SolOptDepth, length(SZN)))) 219 | 220 | # Initialize start and count to read one timestep of the variable 221 | vstart <- rep(1,varndims) 222 | vstart[varndims] <- tstep 223 | vcount <- varsize 224 | vcount[varndims] <- 1 225 | 226 | # Initialize start and count to read one timestep of the variable qc data 227 | qstart <- rep(1,qcndims) 228 | qstart[qcndims] <- tstep 229 | qcount <- qcsize 230 | qcount[qcndims] <- 1 231 | 232 | # Read variable data for timestep n from nc structure 233 | vardata <- ncvar_get(nc, var, start=vstart, count=vcount) 234 | # Read qc data for timestep n from nc structure 235 | qcdata <- ncvar_get(nc, varqc, start=qstart, count=qcount) 236 | 237 | # Set _FillValue to NA 238 | vardata[vardata == fillvalue$value] <- NA 239 | 240 | # Get 3 parameters as raster objects 241 | vardata1 <- raster(t(vardata[1,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 242 | vardata2 <- raster(t(vardata[2,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 243 | vardata3 <- raster(t(vardata[3,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 244 | 245 | # Apply QC mask to vardata (valid == 0 or 1) 246 | vardata[!qcdata %in% c(0,1)] <- NA 247 | 248 | # Calculate black sky albedo for timestep n 249 | nBlack <- BlackSA(vardata1, vardata2, vardata3, SZN) 250 | 251 | # Calculate white sky albedo for timestep n 252 | nWhite <- WhiteSA(vardata1, vardata2, vardata3) 253 | 254 | # Calculate actual albedo for timestep n 255 | nActual <- ActualSA(nWhite, nBlack, LUTarr) 256 | 257 | ncvar_put(nc_out, nir_bsa, as.matrix(nBlack), start = c(1,1,tstep), count = c(-1, -1, 1)) 258 | ncvar_put(nc_out, nir_wsa, as.matrix(nWhite), start = c(1,1,tstep), count = c(-1, -1, 1)) 259 | ncvar_put(nc_out, nir_asa, as.matrix(nActual), start = c(1,1,tstep), count = c(-1, -1, 1)) 260 | 261 | } 262 | 263 | # Clear temporary variables from workspace 264 | remove(var, varqc, fillvalue, varsize, varndims, qcndims, qcsize, dt, SZN, LUTarr, vstart, vcount, 265 | qstart, qcount, vardata, qcdata, vardata1, vardata2, vardata3, nBlack, nWhite, nActual) 266 | 267 | ##################################### Shortwave ##################################### 268 | 269 | # Get variable 270 | var <- nc$var[['BRDF_Albedo_Parameters_shortwave']] 271 | # Get QC variable 272 | varqc <- nc$var[['BRDF_Albedo_Band_Mandatory_Quality_shortwave']] 273 | 274 | # Get _FillValue 275 | fillvalue <- ncatt_get(nc, 'BRDF_Albedo_Parameters_shortwave', "_FillValue") 276 | 277 | # Get variable size and dimension count (4) 278 | varsize <- var$varsize 279 | varndims <- var$ndims 280 | 281 | # Get qc size and dimension count (3) 282 | qcndims <- varqc$ndims 283 | qcsize <- varqc$varsize 284 | 285 | # Loop through timesteps 286 | for(tstep in 1:nt){ 287 | 288 | print(paste("Processing shortwave infrared band timestep", tstep, "of", nt, ". . .", sep = " ")) 289 | 290 | # Convert tstep to real date 291 | dt <- as.Date(nc_time[tstep], origin = as.Date("2000-01-01")) 292 | 293 | # Calculate array of solar zenith numbers for each pixel for timestep n 294 | ################################################################################# 295 | # ORNL DAAC uses an executable (32-bit) that takes date and latitude as input and 296 | # returns a "solar zenith number" between 0-90. Is this the same as SZA? 297 | # Need to figure out how that calculation works. For now, results will not be the 298 | # same as MODIS Global Tool output. 299 | ################################################################################# 300 | if(SolZenAngle == 'local'){ 301 | SZN <- (mapply(SZA, timein = rep(dt, nrow(nc_latlon)), Lat = nc_latlon[,1], Lon = nc_latlon[,2]) - 90) 302 | } 303 | if(SolZenAngle != 'local'){ 304 | SZN <- rep(SolZenAngle, nrow(nc_latlon)) 305 | } 306 | 307 | # Get array of lookup table values for each solar zenith number 308 | LUTarr <- as.vector(mapply(LUT, band = rep('shortwave', length(SZN)), szn = SZN, sod = rep(SolOptDepth, length(SZN)))) 309 | 310 | # Initialize start and count to read one timestep of the variable 311 | vstart <- rep(1,varndims) 312 | vstart[varndims] <- tstep 313 | vcount <- varsize 314 | vcount[varndims] <- 1 315 | 316 | # Initialize start and count to read one timestep of the variable qc data 317 | qstart <- rep(1,qcndims) 318 | qstart[qcndims] <- tstep 319 | qcount <- qcsize 320 | qcount[qcndims] <- 1 321 | 322 | # Read variable data for timestep n from nc structure 323 | vardata <- ncvar_get(nc, var, start=vstart, count=vcount) 324 | # Read qc data for timestep n from nc structure 325 | qcdata <- ncvar_get(nc, varqc, start=qstart, count=qcount) 326 | 327 | # Set _FillValue to NA 328 | vardata[vardata == fillvalue$value] <- NA 329 | 330 | # Get 3 parameters as raster objects 331 | vardata1 <- raster(t(vardata[1,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 332 | vardata2 <- raster(t(vardata[2,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 333 | vardata3 <- raster(t(vardata[3,,]), xmn = min(lon), xmx = max(lon), ymn = min(lat), ymx = max(lat)) 334 | 335 | # Apply QC mask to vardata (valid == 0 or 1) 336 | vardata[!qcdata %in% c(0,1)] <- NA 337 | 338 | # Calculate black sky albedo for timestep n 339 | nBlack <- BlackSA(vardata1, vardata2, vardata3, SZN) 340 | 341 | # Calculate white sky albedo for timestep n 342 | nWhite <- WhiteSA(vardata1, vardata2, vardata3) 343 | 344 | # Calculate actual albedo for timestep n 345 | nActual <- ActualSA(nWhite, nBlack, LUTarr) 346 | 347 | ncvar_put(nc_out, sw_bsa, as.matrix(nBlack), start = c(1,1,tstep), count = c(-1, -1, 1)) 348 | ncvar_put(nc_out, sw_wsa, as.matrix(nWhite), start = c(1,1,tstep), count = c(-1, -1, 1)) 349 | ncvar_put(nc_out, sw_asa, as.matrix(nActual), start = c(1,1,tstep), count = c(-1, -1, 1)) 350 | 351 | } 352 | 353 | # Clear temporary variables from workspace 354 | remove(var, varqc, fillvalue, varsize, varndims, qcndims, qcsize, dt, SZN, LUTarr, vstart, vcount, 355 | qstart, qcount, vardata, qcdata, vardata1, vardata2, vardata3, nBlack, nWhite, nActual) 356 | 357 | ##################################################################################### 358 | # Set attributes in NetCDF variables 359 | ##################################################################################### 360 | 361 | # Put attributes in crs variable 362 | ncatt_put(nc_out, 'crs', attname = 'epsg_code', attval = 4326, prec = NA, verbose=FALSE, definemode=FALSE ) 363 | ncatt_put(nc_out, 'crs', attname = 'horizontal_datum_name', attval = 'WGS84', prec = NA, verbose=FALSE, definemode=FALSE ) 364 | ncatt_put(nc_out, 'crs', attname = 'semi_major_axis', attval = 6378137, prec = NA, verbose=FALSE, definemode=FALSE ) 365 | ncatt_put(nc_out, 'crs', attname = 'inverse_flattening', attval = 298.257223563, prec = NA, verbose=FALSE, definemode=FALSE ) 366 | ncatt_put(nc_out, 'crs', attname = 'longitude_of_prime_meridian', attval = 0.0, prec = NA, verbose=FALSE, definemode=FALSE ) 367 | ncatt_put(nc_out, 'crs', attname = 'grid_mapping_name', attval = 'latitude_longitude', prec = NA, verbose=FALSE, definemode=FALSE ) 368 | ncatt_put(nc_out, 'crs', attname = '_CoordinateAxisTypes', attval = 'GeoX GeoY', prec = NA, verbose=FALSE, definemode=FALSE ) 369 | ncatt_put(nc_out, 'crs', attname = '_CoordinateTransformType', attval = 'Projection', prec = NA, verbose=FALSE, definemode=FALSE ) 370 | 371 | # Put attributes in visible_*_albedo variables 372 | ncatt_put(nc_out, 'visible_black_sky_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 373 | ncatt_put(nc_out, 'visible_white_sky_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 374 | ncatt_put(nc_out, 'visible_actual_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 375 | ncatt_put(nc_out, 'visible_black_sky_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 376 | ncatt_put(nc_out, 'visible_white_sky_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 377 | ncatt_put(nc_out, 'visible_actual_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 378 | ncatt_put(nc_out, 'visible_black_sky_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 379 | ncatt_put(nc_out, 'visible_white_sky_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 380 | ncatt_put(nc_out, 'visible_actual_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 381 | ncatt_put(nc_out, 'visible_black_sky_albedo', attname = 'long_name', attval = 'Visible_black_sky_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 382 | ncatt_put(nc_out, 'visible_white_sky_albedo', attname = 'long_name', attval = 'Visible_white_sky_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 383 | ncatt_put(nc_out, 'visible_actual_albedo', attname = 'long_name', attval = 'Visible_actual_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 384 | ncatt_put(nc_out, 'visible_black_sky_albedo', attname = 'Description', attval = 'Visible band (8) black sky albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 385 | ncatt_put(nc_out, 'visible_white_sky_albedo', attname = 'Description', attval = 'Visible band (8) white sky albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 386 | ncatt_put(nc_out, 'visible_actual_albedo', attname = 'Description', attval = 'Visible band (8) actual (blue sky) albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 387 | 388 | # Put attributes in nir_*_albedo variables 389 | ncatt_put(nc_out, 'nir_black_sky_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 390 | ncatt_put(nc_out, 'nir_white_sky_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 391 | ncatt_put(nc_out, 'nir_actual_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 392 | ncatt_put(nc_out, 'nir_black_sky_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 393 | ncatt_put(nc_out, 'nir_white_sky_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 394 | ncatt_put(nc_out, 'nir_actual_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 395 | ncatt_put(nc_out, 'nir_black_sky_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 396 | ncatt_put(nc_out, 'nir_white_sky_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 397 | ncatt_put(nc_out, 'nir_actual_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 398 | ncatt_put(nc_out, 'nir_black_sky_albedo', attname = 'long_name', attval = 'NIR_black_sky_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 399 | ncatt_put(nc_out, 'nir_white_sky_albedo', attname = 'long_name', attval = 'NIR_white_sky_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 400 | ncatt_put(nc_out, 'nir_actual_albedo', attname = 'long_name', attval = 'NIR_actual_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 401 | ncatt_put(nc_out, 'nir_black_sky_albedo', attname = 'Description', attval = 'Near-infrared band (9) black sky albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 402 | ncatt_put(nc_out, 'nir_white_sky_albedo', attname = 'Description', attval = 'Near-infrared band (9) white sky albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 403 | ncatt_put(nc_out, 'nir_actual_albedo', attname = 'Description', attval = 'Near-infrared band (9) actual (blue sky) albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 404 | 405 | # Put attributes in shortwave_*_albedo variables 406 | ncatt_put(nc_out, 'shortwave_black_sky_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 407 | ncatt_put(nc_out, 'shortwave_white_sky_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 408 | ncatt_put(nc_out, 'shortwave_actual_albedo', attname = 'coordinates', attval = 'time lat lon', prec = NA, verbose=FALSE, definemode=FALSE ) 409 | ncatt_put(nc_out, 'shortwave_black_sky_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 410 | ncatt_put(nc_out, 'shortwave_white_sky_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 411 | ncatt_put(nc_out, 'shortwave_actual_albedo', attname = 'grid_mapping', attval = 'crs', prec = NA, verbose=FALSE, definemode=FALSE ) 412 | ncatt_put(nc_out, 'shortwave_black_sky_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 413 | ncatt_put(nc_out, 'shortwave_white_sky_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 414 | ncatt_put(nc_out, 'shortwave_actual_albedo', attname = 'units', attval = 'unitless', prec = NA, verbose=FALSE, definemode=FALSE ) 415 | ncatt_put(nc_out, 'shortwave_black_sky_albedo', attname = 'long_name', attval = 'Shortwave_black_sky_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 416 | ncatt_put(nc_out, 'shortwave_white_sky_albedo', attname = 'long_name', attval = 'Shortwave_white_sky_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 417 | ncatt_put(nc_out, 'shortwave_actual_albedo', attname = 'long_name', attval = 'Shortwave_actual_albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 418 | ncatt_put(nc_out, 'shortwave_black_sky_albedo', attname = 'Description', attval = 'Shortwave-infrared band (10) black sky albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 419 | ncatt_put(nc_out, 'shortwave_white_sky_albedo', attname = 'Description', attval = 'Shortwave-infrared band (10) white sky albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 420 | ncatt_put(nc_out, 'shortwave_actual_albedo', attname = 'Description', attval = 'Shortwave-infrared band (10) actual (blue sky) albedo calculated from MCD43A1', prec = NA, verbose=FALSE, definemode=FALSE ) 421 | 422 | # Put attributes in lat and lon variables 423 | ncatt_put(nc_out, 'lat', attname = 'standard_name', attval = 'latitude', prec = NA, verbose=FALSE, definemode=FALSE ) 424 | ncatt_put(nc_out, 'lat', attname = 'units', attval = 'degrees_north', prec = NA, verbose=FALSE, definemode=FALSE ) 425 | ncatt_put(nc_out, 'lat', attname = '_CoordinateAxisType', attval = 'GeoY', prec = NA, verbose=FALSE, definemode=FALSE ) 426 | ncatt_put(nc_out, 'lat', attname = 'axis', attval = 'Y', prec = NA, verbose=FALSE, definemode=FALSE ) 427 | ncatt_put(nc_out, 'lon', attname = 'standard_name', attval = 'longitude', prec = NA, verbose=FALSE, definemode=FALSE ) 428 | ncatt_put(nc_out, 'lon', attname = 'units', attval = 'degrees_east', prec = NA, verbose=FALSE, definemode=FALSE ) 429 | ncatt_put(nc_out, 'lon', attname = '_CoordinateAxisType', attval = 'GeoX', prec = NA, verbose=FALSE, definemode=FALSE ) 430 | ncatt_put(nc_out, 'lon', attname = 'axis', attval = 'X', prec = NA, verbose=FALSE, definemode=FALSE ) 431 | 432 | # Put global attributes in file 433 | ncatt_put(nc_out, varid = 0, attname = 'title', attval = 'MCD43A Calculated Albedo based on RossThickLiSparseReciprocal BRDF model', prec = NA, verbose=FALSE, definemode=FALSE ) 434 | ncatt_put(nc_out, varid = 0, attname = 'description', attval = 'Calculated from MCD43A1 BRDF/Albedo Model Parameters Product (MODIS/Terra BRDF/Albedo Model_1 Daily L3 Global 500m SIN Grid)\n 435 | https://www.umb.edu/spectralmass/terra_aqua_modis/v006/mcd43a1_brdif_albedo_model_parameters_product', prec = NA, verbose=FALSE, definemode=FALSE ) 436 | ncatt_put(nc_out, varid = 0, attname = 'Conventions', attval = 'CF-1.6', prec = NA, verbose=FALSE, definemode=FALSE ) 437 | ncatt_put(nc_out, varid = 0, attname = 'source1', attval = 'MCD43A1 NetCDF sourced from APPEEARS: https://lpdaac.usgs.gov/tools/data_access/appeears', prec = NA, verbose=FALSE, definemode=FALSE ) 438 | ncatt_put(nc_out, varid = 0, attname = 'source2', attval = 'Processed using albedo formula implemented in R; https://github.com/jjmcnelis/mcd43-calculated-albedo', prec = NA, verbose=FALSE, definemode=FALSE ) 439 | 440 | # Write out and close 441 | nc_out <- nc_open(albedo_out, write = TRUE) 442 | nc_close(nc_out) 443 | --------------------------------------------------------------------------------