Geospatial data analysis in R

Raster data II

Josh Merfeld

KDI School

November 5, 2024

What are we doing today?

  • A short review of in-class lab 1

  • Installing Python and Positron for the GEE API

In-class lab 1

  • Let’s go over a few things from in-class lab 1

  • Three things I want to cover:

    • Making maps look nice
    • Creating a spatial object from points
    • Distances

Making maps look nice

  • let’s look at the grid cells:
Code 
grids <- vect("assignments/in-class1/data/seoulgrid.shp")
ggplot(grids) +
  geom_spatvector(aes(fill = log(pop))) +
  scale_fill_distiller("Pop (log)", palette = "YlOrRd", direction = 1) +
  theme_bw()

Making maps look nice

Compare the previous map to this one:

Code 
ggplot(grids) +
  geom_spatvector(aes(fill = log(pop)), color = NA) +
  scale_fill_distiller("Pop (log)", palette = "YlOrRd", direction = 1) +
  theme_bw()

Compare the previous map to this one:

Together

Spatial objects from points

  • Now let’s create a spatial object from points

  • Let’s use the schools:

Code 
df <- read_csv("assignments/in-class1/data/seoulpoints.csv")
head(df)
# A tibble: 6 × 5
   code fclass           province   lon   lat
  <dbl> <chr>            <chr>    <dbl> <dbl>
1  2110 hospital         Seoul     127.  37.6
2  2082 middleschool     Seoul     127.  37.6
3  2082 highschool       Seoul     127.  37.6
4  2082 elementaryschool Seoul     127.  37.6
5  2082 elementaryschool Seoul     127.  37.6
6  2082 elementaryschool Seoul     127.  37.6
  • What is the crs for the points themselves?
  • They are in longitude/latitude (WGS 84): “EPSG:4326”

Creating the object

  • We have to specify the CRS based on what the POINTS represent, not what we want it to eventually be
    • Then we can project it
Code 
# create the object
df <- vect(df, geom = c("lon", "lat"), crs = "EPSG:4326")
# now project it
df <- project(df, crs(grids))

Compare the output

original object class : SpatVector geometry : points dimensions : 1459, 3 (geometries, attributes) extent : 126.9018, 127.1308, 37.46144, 37.65323 (xmin, xmax, ymin, ymax) coord. ref. : lon/lat WGS 84 (EPSG:4326)

after projection class : SpatVector geometry : points dimensions : 1459, 3 (geometries, attributes) extent : 947164.1, 967361.8, 1940349, 1961613 (xmin, xmax, ymin, ymax) coord. ref. : Korea 2000 / Unified CS (EPSG:5179)

Distances

  • We now have our grids (we’ll get rid of zero pop in a moment0)
  • And we have points in the same CRS
Code 
grids <- grids |>
  filter(!is.na(pop))
# create distance matrix for PRIMARY schools
distances <- distance(grids, df |> filter(fclass=="elementaryschool"))
dim(distances)
[1] 45849   555
Code 
head(distances)
         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
[1,] 11968.57 11934.85 11951.80 12043.08 12024.93 12357.01 12343.99 12320.89
[2,] 11978.48 11944.58 11961.33 12053.67 12035.60 12428.94 12415.88 12392.61
[3,] 11989.93 11955.83 11972.36 12065.83 12047.85 12506.53 12493.42 12469.98
[4,] 12002.19 11967.90 11984.22 12078.81 12060.92 12584.43 12571.29 12547.66
[5,] 11879.10 11845.17 11861.90 11954.37 11936.31 12365.90 12352.78 12329.29
[6,] 11890.64 11856.51 11873.03 11966.63 11948.66 12443.88 12430.72 12407.06
         [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16]
[1,] 12338.70 12355.75 12407.23 13618.28 13490.33 13669.29 13672.48 13660.10
[2,] 12410.40 12427.48 12479.00 13688.95 13560.60 13739.49 13742.80 13730.62
[3,] 12487.75 12504.86 12556.42 13765.17 13636.41 13815.22 13818.65 13806.69
[4,] 12565.42 12582.55 12634.16 13841.69 13712.52 13891.25 13894.80 13883.05
[5,] 12347.07 12364.18 12415.75 13624.25 13495.41 13674.21 13677.66 13665.74
[6,] 12424.81 12441.95 12493.56 13700.83 13571.57 13750.29 13753.87 13742.16
        [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24]
[1,] 13629.23 13222.72 13239.86 13273.02 13323.99 19346.24 19400.15 19440.78
[2,] 13699.88 13290.56 13307.60 13340.83 13391.86 19405.09 19458.51 19499.56
[3,] 13776.07 13363.79 13380.71 13414.02 13465.11 19468.62 19521.51 19563.00
[4,] 13852.57 13437.37 13454.16 13487.55 13538.70 19532.46 19584.81 19626.75
[5,] 13635.14 13222.48 13239.38 13272.70 13323.80 19327.84 19380.82 19422.24
[6,] 13711.70 13296.08 13312.87 13346.26 13397.42 19391.63 19444.07 19485.93
        [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32]
[1,] 19444.34 21972.68 22057.93 22059.73 21969.32 22031.99 22079.46 22079.72
[2,] 19503.12 22017.12 22102.15 22104.30 22013.38 22075.54 22123.08 22123.39
[3,] 19566.57 22065.20 22149.99 22152.52 22061.07 22122.68 22170.29 22170.65
[4,] 19630.32 22113.62 22198.17 22201.09 22109.10 22170.17 22217.85 22218.25
[5,] 19425.80 21929.39 22014.29 22016.65 21925.44 21987.31 22034.88 22035.22
[6,] 19489.51 21977.66 22062.32 22065.06 21973.31 22034.63 22082.28 22082.66
        [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40]
[1,] 22080.92 22082.52 22083.59 19811.11 19927.83 20019.63 20008.31 19998.55
[2,] 22124.69 22126.60 22127.85 19804.10 19922.35 20014.65 19980.78 19971.18
[3,] 22172.05 22174.30 22175.73 19797.60 19917.38 20010.16 19953.70 19944.28
[4,] 22219.76 22222.34 22223.96 19796.38 19916.46 20009.34 19948.47 19939.08
[5,] 22036.57 22038.67 22040.01 19704.33 19822.49 19914.76 19884.60 19874.95
[6,] 22084.12 22086.55 22088.08 19697.79 19817.49 19910.25 19857.39 19847.92
        [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48]
[1,] 19872.82 22911.63 22886.40 22967.58 22964.82 22976.38 22985.17 22962.55
[2,] 19845.03 22935.00 22909.58 22990.52 22987.82 22999.57 23008.42 22985.99
[3,] 19817.71 22960.50 22934.87 23015.56 23012.92 23024.87 23033.79 23011.56
[4,] 19812.42 22986.40 22960.57 23041.01 23038.43 23050.58 23059.56 23037.53
[5,] 19748.92 22838.26 22812.79 22893.67 22890.98 22902.78 22911.65 22889.27
[6,] 19721.47 22863.87 22838.19 22918.82 22916.19 22928.19 22937.12 22914.95
        [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56]
[1,] 22890.23 22901.58 17404.38 17416.36 17437.71 17455.23 17468.77 17451.97
[2,] 22913.49 22924.94 17375.94 17387.79 17409.31 17426.68 17440.24 17423.62
[3,] 22938.88 22950.44 17348.03 17359.75 17381.44 17398.65 17412.23 17395.79
[4,] 22964.67 22976.34 17342.64 17354.33 17376.05 17393.23 17406.82 17390.41
[5,] 22816.73 22828.21 17280.02 17291.90 17313.37 17330.79 17344.34 17327.67
[6,] 22842.22 22853.81 17251.95 17263.71 17285.35 17302.60 17316.18 17299.68
        [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64]
[1,] 17462.38 17404.38 17321.17 17384.40 17349.31 18038.02 20201.81 20360.15
[2,] 17434.14 17375.94 17292.86 17356.06 17321.13 18028.18 20182.08 20340.44
[3,] 17406.43 17348.03 17265.07 17328.25 17293.48 18018.89 20162.83 20321.22
[4,] 17401.07 17342.64 17259.71 17322.88 17288.14 18017.14 20159.12 20317.51
[5,] 17338.16 17280.02 17196.89 17260.10 17225.12 17928.64 20084.01 20242.37
[6,] 17310.29 17251.95 17168.96 17232.14 17197.32 17919.30 20064.66 20223.04
        [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72]
[1,] 20444.95 20354.77 20391.18 20704.47 20703.06 20598.24 21031.96 20959.62
[2,] 20425.11 20334.90 20371.60 20681.66 20680.81 20576.02 21012.12 20940.09
[3,] 20405.74 20315.50 20352.48 20659.32 20659.02 20554.26 20992.73 20921.01
[4,] 20402.01 20311.77 20348.80 20655.00 20654.81 20550.06 20989.00 20917.34
[5,] 20327.06 20236.86 20273.50 20584.26 20583.28 20478.48 20914.07 20841.97
[6,] 20307.60 20217.37 20254.29 20561.81 20561.38 20456.61 20894.59 20822.81
        [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80]
[1,] 21186.36 21157.93 21152.99 21110.16 21176.03 21253.93 21157.93 21978.77
[2,] 21164.31 21140.89 21135.95 21093.00 21158.35 21236.57 21140.89 21953.67
[3,] 21142.71 21124.32 21119.36 21076.30 21141.13 21219.68 21124.32 21929.01
[4,] 21138.54 21121.14 21116.17 21073.09 21137.81 21216.43 21121.14 21924.23
[5,] 21066.73 21042.32 21037.38 20994.45 21059.89 21138.06 21042.32 21856.83
[6,] 21045.03 21025.67 21020.71 20977.68 21042.59 21121.08 21025.67 21832.06
        [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88]
[1,] 22103.33 21978.77 25777.42 25816.74 25876.62 16843.58 16866.14 9094.441
[2,] 22078.16 21953.67 25779.38 25818.41 25878.41 16820.45 16843.18 9073.283
[3,] 22053.42 21929.01 25781.85 25820.57 25880.70 16797.89 16820.78 9053.180
[4,] 22048.63 21924.23 25784.71 25823.12 25883.39 16793.54 16816.47 9049.374
[5,] 21981.34 21856.83 25679.40 25718.43 25778.43 16723.11 16745.80 8975.458
[6,] 21956.49 21832.06 25681.89 25720.60 25780.74 16700.42 16723.28 8955.136
        [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96]
[1,] 9094.672 9061.502 9063.281 8611.989 8658.008 8644.331 8550.999 8543.729
[2,] 9073.711 9040.523 9042.101 8594.864 8641.421 8627.854 8534.329 8527.092
[3,] 9053.805 9020.603 9021.980 8578.870 8625.962 8612.507 8518.801 8511.598
[4,] 9050.038 9016.833 9018.171 8575.877 8623.072 8609.640 8515.899 8508.703
[5,] 8975.844 8942.660 8944.281 8496.261 8542.729 8529.143 8435.649 8428.407
[6,] 8955.721 8922.521 8923.939 8480.081 8527.090 8513.618 8419.939 8412.731
        [,97]    [,98]    [,99]   [,100]   [,101]   [,102]   [,103]   [,104]
[1,] 19394.17 19390.30 19318.49 19301.88 22248.48 22332.49 21805.18 21751.37
[2,] 19358.54 19354.75 19283.39 19266.71 22227.80 22311.94 21773.43 21719.84
[3,] 19323.37 19319.65 19248.75 19232.00 22207.56 22291.82 21742.08 21688.73
[4,] 19316.54 19312.85 19242.03 19225.27 22203.65 22287.94 21736.00 21682.69
[5,] 19265.05 19261.23 19189.70 19173.05 22129.93 22214.04 21678.56 21624.90
[6,] 19229.70 19225.96 19154.89 19138.17 22109.59 22193.83 21647.08 21593.64
       [,105]   [,106]   [,107]   [,108]   [,109]   [,110]   [,111]   [,112]
[1,] 21226.20 22406.23 22529.98 22430.05 22515.19 22597.53 22422.73 24157.57
[2,] 21193.64 22378.55 22500.63 22401.23 22480.75 22563.64 22388.53 24126.29
[3,] 21161.51 22351.28 22471.69 22372.82 22446.71 22530.14 22354.73 24095.39
[4,] 21155.28 22346.00 22466.08 22367.32 22440.10 22523.64 22348.17 24089.39
[5,] 21099.04 22282.41 22405.00 22305.43 22386.83 22469.51 22294.52 24031.27
[6,] 21066.77 22255.03 22375.93 22276.90 22352.64 22435.87 22260.57 24000.24
       [,113]   [,114]   [,115]   [,116]   [,117]   [,118]   [,119]   [,120]
[1,] 24002.76 19083.56 18644.14 18675.96 18685.24 18694.07 18817.53 18741.13
[2,] 23971.23 19116.49 18623.97 18655.04 18664.30 18673.14 18797.06 18721.34
[3,] 23940.07 19152.30 18604.31 18634.62 18643.88 18652.73 18777.10 18702.06
[4,] 23934.03 19188.57 18600.53 18630.69 18639.95 18648.79 18773.26 18698.35
[5,] 23876.29 19023.07 18525.98 18557.21 18566.48 18575.31 18699.13 18623.28
[6,] 23845.01 19059.06 18506.22 18536.69 18545.95 18554.79 18679.07 18603.90
       [,121]   [,122]   [,123]   [,124]   [,125]   [,126]   [,127]   [,128]
[1,] 18709.64 18484.76 18544.43 18546.75 18484.76 18545.46 18547.36 18525.49
[2,] 18689.35 18465.53 18524.94 18527.38 18465.53 18529.78 18531.69 18510.11
[3,] 18669.57 18446.83 18505.97 18508.53 18446.83 18514.63 18516.54 18495.26
[4,] 18665.76 18443.23 18502.32 18504.91 18443.23 18511.73 18513.64 18492.41
[5,] 18591.39 18367.36 18426.82 18429.23 18367.36 18430.98 18432.89 18411.27
[6,] 18571.50 18348.55 18407.74 18410.28 18348.55 18415.75 18417.66 18396.33
       [,129]   [,130]   [,131]   [,132]   [,133]   [,134]   [,135]   [,136]
[1,] 17928.57 18000.23 17939.04 14805.70 14826.03 25188.13 25181.53 25175.44
[2,] 17915.00 17986.87 17926.33 14857.74 14878.10 25220.30 25213.58 25207.39
[3,] 17901.98 17974.06 17914.16 14914.10 14934.48 25255.18 25248.35 25242.06
[4,] 17899.49 17971.62 17911.85 14970.91 14991.32 25290.42 25283.47 25277.07
[5,] 17815.89 17887.73 17827.11 14775.08 14795.46 25126.54 25119.78 25113.55
[6,] 17802.80 17874.85 17814.88 14831.75 14852.16 25161.56 25154.68 25148.35
       [,137]   [,138]   [,139]   [,140]   [,141]   [,142]   [,143]   [,144]
[1,] 25174.92 25182.68 25230.48 25236.06 25248.32 25278.85 25291.97 25188.13
[2,] 25206.86 25214.62 25262.38 25267.95 25280.21 25310.80 25324.13 25220.30
[3,] 25241.51 25249.26 25296.99 25302.56 25314.80 25345.47 25359.01 25255.18
[4,] 25276.51 25284.26 25331.94 25337.51 25349.74 25380.48 25394.24 25290.42
[5,] 25113.01 25120.77 25168.52 25174.09 25186.34 25216.97 25230.37 25126.54
[6,] 25147.79 25155.54 25203.26 25208.82 25221.07 25251.76 25265.38 25161.56
       [,145]   [,146]   [,147]   [,148]   [,149]   [,150]   [,151]   [,152]
[1,] 25626.46 25609.25 25594.65 25588.63 25577.14 25603.96 25728.56 25547.89
[2,] 25657.99 25640.79 25625.94 25619.83 25608.14 25634.76 25759.96 25577.32
[3,] 25692.19 25675.01 25659.90 25653.67 25641.77 25668.19 25794.03 25609.27
[4,] 25726.74 25709.57 25694.20 25687.86 25675.75 25701.95 25828.44 25641.57
[5,] 25563.98 25546.79 25531.84 25525.69 25513.92 25540.47 25665.90 25482.52
[6,] 25598.31 25581.13 25565.92 25559.66 25547.68 25574.02 25700.10 25514.59
       [,153]   [,154]   [,155]   [,156]   [,157]   [,158]   [,159]   [,160]
[1,] 25516.16 25418.08 22333.72 26328.73 26286.64 14723.63 14625.01 14688.01
[2,] 25545.57 25447.44 22299.77 26358.93 26317.14 14724.05 14625.43 14688.01
[3,] 25577.50 25479.33 22266.22 26391.71 26350.23 14725.14 14626.55 14688.33
[4,] 25609.79 25511.57 22259.71 26424.83 26383.65 14726.92 14628.35 14689.34
[5,] 25450.76 25352.63 22205.67 26264.42 26222.73 14624.05 14525.43 14588.01
[6,] 25482.82 25384.63 22171.97 26297.32 26255.94 14625.16 14526.56 14588.34
       [,161]   [,162]   [,163]   [,164]   [,165]   [,166]   [,167]   [,168]
[1,] 14716.89 14664.67 14684.82 14804.41 14803.35 14911.77 14896.71 14873.74
[2,] 14716.76 14664.29 14683.94 14803.29 14802.60 14911.77 14896.71 14873.75
[3,] 14716.81 14664.29 14683.72 14802.86 14802.48 14912.09 14897.13 14874.22
[4,] 14717.41 14664.60 14683.74 14802.85 14802.53 14913.07 14898.22 14875.36
[5,] 14616.76 14564.29 14583.94 14703.30 14702.60 14811.77 14796.71 14773.75
[6,] 14616.81 14564.29 14583.72 14702.86 14702.48 14812.09 14797.13 14774.22
       [,169]   [,170]   [,171]   [,172]   [,173]   [,174]   [,175]   [,176]
[1,] 14756.66 5239.312 5259.967 5155.908 5283.385 5270.723 15035.46 14970.47
[2,] 14756.67 5201.292 5224.011 5117.709 5243.504 5232.209 15084.80 15019.88
[3,] 14757.08 5164.929 5189.732 5081.192 5205.238 5195.335 15138.25 15073.44
[4,] 14758.18 5158.017 5183.230 5074.253 5197.950 5188.321 15192.18 15127.46
[5,] 14656.67 5108.603 5130.502 5025.091 5151.604 5139.726 15000.23 14935.38
[6,] 14657.09 5071.575 5095.595 4987.896 5112.651 5102.183 15053.99 14989.23
       [,177]   [,178]   [,179]   [,180]   [,181]   [,182]   [,183]   [,184]
[1,] 14962.87 14944.23 14938.18 14931.10 14917.86 14911.05 14919.55 14933.11
[2,] 15012.30 14993.66 14987.61 14980.51 14967.24 14960.28 14968.31 14981.89
[3,] 15065.86 15047.23 15041.16 15034.05 15020.75 15013.63 15021.17 15034.76
[4,] 15119.89 15101.27 15095.19 15088.07 15074.73 15067.45 15074.50 15088.10
[5,] 14927.80 14909.16 14903.10 14896.00 14882.71 14875.64 14883.37 14896.95
[6,] 14981.66 14963.04 14956.96 14949.84 14936.52 14929.29 14936.52 14950.12
       [,185]   [,186]   [,187]   [,188]   [,189]   [,190]   [,191]   [,192]
[1,] 14983.34 15056.63 5230.262 5228.207 5362.685 5407.448 5419.561 5404.538
[2,] 15032.12 15105.57 5183.967 5181.742 5316.864 5362.730 5375.408 5360.760
[3,] 15084.99 15158.60 5139.201 5136.804 5272.542 5319.517 5332.764 5318.503
[4,] 15138.34 15212.11 5130.632 5128.201 5264.056 5311.249 5324.607 5310.423
[5,] 14947.18 15020.73 5095.140 5093.005 5227.795 5273.100 5285.497 5270.665
[6,] 15000.35 15074.07 5049.587 5047.276 5182.711 5229.146 5242.122 5227.679
       [,193]   [,194]   [,195]   [,196]   [,197]   [,198]   [,199]   [,200]
[1,] 5223.716 15192.99 15167.68 15141.74 15230.98 15351.23 15222.52 14836.94
[2,] 5179.173 15240.82 15215.37 15189.18 15278.23 15398.65 15270.37 14890.96
[3,] 5136.192 15292.66 15267.08 15240.61 15329.46 15450.07 15322.25 14949.42
[4,] 5127.976 15344.98 15319.27 15292.52 15381.17 15501.96 15374.59 15008.32
[5,] 5089.449 15155.25 15129.72 15103.36 15192.29 15312.83 15184.82 14809.79
[6,] 5045.703 15207.38 15181.73 15155.08 15243.81 15364.53 15236.99 14868.57
       [,201]   [,202]   [,203]   [,204]   [,205]   [,206]   [,207]   [,208]
[1,] 14817.99 14808.09 14809.50 14847.97 14891.88 14920.25 14925.10 14925.41
[2,] 14872.01 14862.09 14863.32 14901.70 14945.66 14974.10 14979.11 14979.45
[3,] 14930.46 14920.53 14921.57 14959.85 15003.88 15032.38 15037.56 15037.94
[4,] 14989.36 14979.42 14980.27 15018.44 15062.53 15091.11 15096.45 15096.86
[5,] 14790.83 14780.90 14781.99 14820.30 14864.31 14892.80 14897.93 14898.29
[6,] 14849.61 14839.66 14840.57 14878.77 14922.84 14951.40 14956.70 14957.09
       [,209]   [,210]   [,211]   [,212]   [,213]   [,214]   [,215]   [,216]
[1,] 17981.96 17971.53 18007.62 18071.58 18020.58 17826.25 17806.80 17804.39
[2,] 17967.59 17947.35 17983.19 18047.55 17996.70 17808.21 17788.72 17786.03
[3,] 17953.77 17923.69 17959.28 18024.04 17973.34 17790.72 17771.19 17768.22
[4,] 17951.13 17919.13 17954.67 18019.51 17968.83 17787.36 17767.82 17764.80
[5,] 17868.60 17850.27 17886.17 17950.43 17899.54 17709.81 17690.33 17687.69
[6,] 17854.70 17826.48 17862.13 17926.79 17876.05 17692.22 17672.70 17669.78
       [,217]   [,218]   [,219]   [,220]   [,221]   [,222]   [,223]   [,224]
[1,] 17812.76 17820.76 17862.92 17869.33 17878.63 17879.20 17842.32 17839.58
[2,] 17794.07 17802.10 17844.28 17850.82 17860.26 17861.10 17824.25 17821.56
[3,] 17775.92 17783.97 17826.19 17832.84 17842.43 17843.54 17806.71 17804.09
[4,] 17772.43 17780.49 17822.71 17829.39 17839.01 17840.18 17803.35 17800.74
[5,] 17695.79 17703.81 17745.99 17752.50 17761.92 17762.71 17725.85 17723.16
[6,] 17677.54 17685.59 17727.80 17734.43 17743.99 17745.06 17708.22 17705.59
       [,225]   [,226]   [,227]   [,228]   [,229]   [,230]   [,231]   [,232]
[1,] 17783.56 17971.50 17932.34 17859.64 17313.16 17443.55 17252.23 18053.29
[2,] 17768.61 17956.33 17916.12 17844.07 17290.07 17420.91 17229.68 18028.66
[3,] 17754.21 17941.70 17900.45 17829.06 17267.54 17398.83 17207.69 18004.56
[4,] 17751.46 17938.91 17897.45 17826.19 17263.19 17394.57 17203.45 17999.91
[5,] 17669.70 17857.45 17817.41 17745.26 17192.72 17323.46 17132.21 17931.69
[6,] 17655.22 17842.74 17801.65 17730.16 17170.06 17301.25 17110.09 17907.46
       [,233]   [,234]   [,235]   [,236]   [,237]   [,238]   [,239]   [,240]
[1,] 18070.53 18167.89 18074.83 18011.01 17254.03 17212.39 17148.29 17067.69
[2,] 18045.86 18143.67 18050.80 17986.57 17234.18 17193.41 17129.22 17048.93
[3,] 18021.71 18119.98 18027.29 17962.66 17214.88 17174.99 17110.71 17030.73
[4,] 18017.05 18115.41 18022.76 17958.05 17211.17 17171.45 17107.16 17027.24
[5,] 17948.90 18046.60 17953.68 17889.56 17136.12 17095.18 17031.01 16950.66
[6,] 17924.62 18022.78 17930.05 17865.52 17116.72 17076.66 17012.39 16932.36
       [,241]   [,242]   [,243]   [,244]   [,245]   [,246]   [,247]   [,248]
[1,] 17153.10 17213.94 17137.02 16883.31 16848.52 18506.41 23482.18 23486.34
[2,] 17134.09 17195.02 17118.38 16858.16 16823.05 18483.67 23485.68 23489.84
[3,] 17115.65 17176.66 17100.31 16833.56 16798.14 18461.44 23489.84 23494.00
[4,] 17112.11 17173.14 17096.85 16828.82 16793.33 18457.15 23494.44 23498.59
[5,] 17035.87 17096.79 17020.09 16761.32 16726.30 18386.24 23385.75 23389.92
[6,] 17017.32 17078.32 17001.92 16736.58 16701.24 18363.89 23389.94 23394.10
       [,249]   [,250]   [,251]   [,252]   [,253]   [,254]   [,255]   [,256]
[1,] 23470.48 23547.57 23547.91 23546.35 23554.57 23558.53 23568.44 23551.58
[2,] 23473.67 23550.97 23551.27 23549.69 23557.90 23561.88 23571.89 23555.04
[3,] 23477.51 23555.04 23555.29 23553.68 23561.89 23565.90 23576.00 23559.16
[4,] 23481.77 23559.53 23559.74 23558.10 23566.30 23570.33 23580.54 23563.71
[5,] 23373.73 23451.05 23451.35 23449.76 23457.98 23461.96 23471.97 23455.11
[6,] 23377.59 23455.13 23455.39 23453.77 23461.98 23465.99 23476.10 23459.26
       [,257]   [,258]   [,259]   [,260]   [,261]   [,262]   [,263]   [,264]
[1,] 23530.90 23517.27 23483.86 23489.82 25288.70 25321.38 25392.62 25409.07
[2,] 23534.35 23520.47 23487.08 23493.29 25322.46 25355.06 25425.90 25442.35
[3,] 23538.46 23524.31 23490.97 23497.44 25359.06 25391.58 25461.99 25478.45
[4,] 23542.99 23528.59 23495.27 23502.02 25396.01 25428.45 25498.42 25514.88
[5,] 23434.42 23420.53 23387.15 23393.37 25229.36 25261.93 25332.60 25349.05
[6,] 23438.55 23424.40 23391.05 23397.54 25266.10 25298.59 25368.82 25385.28
       [,265]   [,266]   [,267]   [,268]   [,269]   [,270]   [,271]   [,272]
[1,] 25467.20 25475.82 25478.94 25488.40 25518.25 25535.91 25546.52 25550.57
[2,] 25500.50 25509.07 25512.17 25521.57 25551.28 25569.02 25579.68 25583.75
[3,] 25536.60 25545.12 25548.20 25557.53 25587.09 25604.92 25615.63 25619.72
[4,] 25573.04 25581.50 25584.56 25593.84 25623.25 25641.16 25651.92 25656.04
[5,] 25407.20 25415.75 25418.85 25428.22 25457.87 25475.65 25486.32 25490.40
[6,] 25443.44 25451.93 25455.00 25464.32 25493.82 25511.68 25522.41 25526.51
       [,273]   [,274]   [,275]   [,276]   [,277]   [,278]   [,279]   [,280]
[1,] 25551.81 25550.47 25549.22 25459.11 25414.10 25884.13 25821.94 25813.96
[2,] 25585.00 25583.81 25582.60 25492.56 25447.69 25913.26 25851.09 25842.97
[3,] 25620.99 25619.95 25618.79 25528.82 25484.10 25944.89 25882.73 25874.49
[4,] 25657.31 25656.44 25655.32 25565.43 25520.85 25976.86 25914.72 25906.35
[5,] 25491.66 25490.53 25489.34 25399.32 25354.51 25818.35 25756.19 25748.03
[6,] 25527.78 25526.81 25525.66 25435.72 25391.05 25850.10 25787.95 25779.66
       [,281]   [,282]   [,283]   [,284]   [,285]   [,286]   [,287]   [,288]
[1,] 25680.15 25666.43 25740.96 25710.22 25765.06 25784.11 25853.89 25873.37
[2,] 25709.10 25695.20 25769.61 25738.63 25793.41 25812.44 25882.40 25902.04
[3,] 25740.53 25726.45 25800.72 25769.49 25824.21 25843.22 25913.36 25933.18
[4,] 25772.32 25758.05 25832.18 25800.70 25855.35 25874.35 25944.68 25964.67
[5,] 25614.13 25600.17 25674.53 25643.47 25698.23 25717.26 25787.28 25806.97
[6,] 25645.68 25631.53 25705.76 25674.44 25729.14 25748.15 25818.35 25838.23
       [,289]   [,290]   [,291]   [,292]   [,293]   [,294]   [,295]   [,296]
[1,] 25900.29 25923.69 25917.87 25896.53 25884.13 24103.42 24106.14 24209.90
[2,] 25928.94 25952.69 25946.91 25925.65 25913.26 24124.67 24127.37 24231.09
[3,] 25960.06 25984.19 25978.45 25957.27 25944.89 24147.88 24150.57 24254.23
[4,] 25991.53 26016.04 26010.33 25989.24 25976.86 24171.48 24174.15 24277.76
[5,] 25833.87 25857.75 25851.97 25830.74 25818.35 24027.36 24030.06 24133.76
[6,] 25865.10 25889.36 25883.63 25862.48 25850.10 24050.67 24053.35 24157.00
       [,297]   [,298]   [,299]   [,300]   [,301]   [,302]   [,303]   [,304]
[1,] 24231.05 24228.04 24182.92 25186.48 25179.43 22702.89 22696.67 22718.62
[2,] 24252.64 24249.64 24204.56 25216.82 25209.65 22696.91 22690.58 22712.32
[3,] 24276.20 24273.22 24228.17 25249.77 25242.46 22691.37 22684.94 22706.47
[4,] 24300.16 24297.19 24252.18 25283.06 25275.62 22690.34 22683.88 22705.38
[5,] 24155.42 24152.42 24107.35 25122.37 25115.15 22597.08 22590.75 22612.51
[6,] 24179.08 24176.10 24131.06 25155.43 25148.08 22591.51 22585.08 22606.63
       [,305]   [,306]   [,307]   [,308]   [,309]   [,310]   [,311]   [,312]
[1,] 22723.88 22757.37 22707.72 15212.91 15238.14 15267.46 15269.66 15257.31
[2,] 22717.63 22751.45 22701.74 15208.68 15233.15 15262.49 15264.78 15252.52
[3,] 22711.82 22745.97 22696.19 15205.11 15228.81 15258.17 15260.56 15248.38
[4,] 22710.74 22744.95 22695.16 15204.49 15228.04 15257.40 15259.81 15247.64
[5,] 22617.81 22651.61 22601.90 15108.76 15133.26 15162.60 15164.89 15152.62
[6,] 22611.98 22646.11 22596.33 15105.17 15128.89 15158.25 15160.63 15148.45
       [,313]   [,314]   [,315]   [,316]   [,317]   [,318]   [,319]   [,320]
[1,] 15256.42 15266.78 15212.91 14930.74 14959.64 14951.86 14928.39 14918.82
[2,] 15251.68 15262.34 15208.68 14930.74 14959.44 14951.52 14927.87 14918.13
[3,] 15247.59 15258.56 15205.11 14931.07 14959.45 14951.52 14927.84 14918.04
[4,] 15246.87 15257.90 15204.49 14932.08 14959.93 14951.85 14928.01 14918.12
[5,] 15151.78 15162.43 15108.76 14830.74 14859.44 14851.52 14827.87 14818.13
[6,] 15147.67 15158.62 15105.17 14831.08 14859.45 14851.52 14827.84 14818.04
       [,321]   [,322]   [,323]   [,324]   [,325]   [,326]   [,327]   [,328]
[1,] 14884.65 14890.97 14868.48 14870.39 14872.26 14884.45 14904.45 14950.01
[2,] 14883.85 14890.09 14867.36 14869.20 14870.99 14882.91 14902.87 14948.23
[3,] 14883.69 14889.86 14866.92 14868.67 14870.39 14882.05 14901.95 14947.12
[4,] 14883.72 14889.87 14866.92 14868.65 14870.35 14881.96 14901.85 14946.98
[5,] 14783.85 14790.09 14767.37 14769.20 14770.99 14782.92 14802.87 14848.24
[6,] 14783.69 14789.86 14766.92 14768.67 14770.39 14782.05 14801.96 14847.12
       [,329]   [,330]   [,331]   [,332]   [,333]   [,334]   [,335]   [,336]
[1,] 14964.23 14997.13 15029.67 15053.01 15093.61 15129.86 15150.80 15152.99
[2,] 14962.32 14995.56 15027.96 15051.14 15091.60 15127.65 15148.62 15151.14
[3,] 14961.07 14994.66 15026.92 15049.94 15090.25 15126.09 15147.10 15149.94
[4,] 14960.91 14994.56 15026.79 15049.78 15090.06 15125.87 15146.88 15149.79
[5,] 14862.33 14895.57 14927.97 14951.15 14991.61 15027.66 15048.64 15051.15
[6,] 14861.08 14894.66 14926.92 14949.94 14990.25 15026.10 15047.11 15049.95
       [,337]   [,338]   [,339]   [,340]   [,341]   [,342]   [,343]   [,344]
[1,] 15138.53 15132.27 15032.47 15024.30 15027.81 15039.53 15042.06 15040.38
[2,] 15136.74 15130.51 15031.16 15023.03 15026.78 15038.72 15041.48 15039.83
[3,] 15135.61 15129.41 15030.51 15022.42 15026.43 15038.54 15041.43 15039.79
[4,] 15135.47 15129.27 15030.46 15022.38 15026.42 15038.57 15041.56 15039.94
[5,] 15036.75 15030.52 14931.16 14923.04 14926.79 14938.72 14941.48 14939.83
[6,] 15035.61 15029.41 14930.51 14922.42 14926.43 14938.54 14941.43 14939.79
       [,345]   [,346]   [,347]   [,348]   [,349]   [,350]   [,351]   [,352]
[1,] 15038.89 15019.43 15016.99 15016.18 15008.61 15001.66 14957.06 14950.68
[2,] 15038.36 15019.03 15016.64 15015.89 15008.58 15001.64 14957.05 14950.67
[3,] 15038.33 15019.03 15016.64 15015.89 15008.75 15001.83 14957.24 14950.88
[4,] 15038.50 15019.30 15016.96 15016.27 15009.54 15002.67 14958.09 14951.74
[5,] 14938.36 14919.03 14916.64 14915.89 14908.58 14901.64 14857.05 14850.67
[6,] 14938.33 14919.03 14916.64 14915.89 14908.75 14901.83 14857.25 14850.88
       [,353]   [,354]   [,355]   [,356]   [,357]   [,358]   [,359]   [,360]
[1,] 14930.74 25625.32 25539.09 25620.03 25625.32 16532.20 16560.67 16666.05
[2,] 14930.74 25660.16 25573.75 25654.50 25660.16 16507.78 16536.12 16642.43
[3,] 14931.07 25697.92 25611.31 25691.86 25697.92 16483.93 16512.14 16619.39
[4,] 14932.08 25736.01 25649.21 25729.55 25736.01 16479.33 16507.52 16614.95
[5,] 14830.74 25567.52 25481.03 25561.70 25567.52 16410.75 16439.13 16545.21
[6,] 14831.08 25605.42 25518.73 25599.19 25605.42 16386.76 16415.01 16522.03
       [,361]   [,362]   [,363]   [,364]   [,365]   [,366]   [,367]   [,368]
[1,] 16658.67 16676.28 16601.08 16439.19 25036.42 25127.40 25212.61 25251.46
[2,] 16635.21 16652.98 16577.69 16414.54 25058.33 25149.24 25234.63 25273.57
[3,] 16612.32 16630.26 16554.86 16390.46 25082.24 25173.06 25258.64 25297.69
[4,] 16607.92 16625.88 16550.47 16385.82 25106.52 25197.26 25283.03 25322.17
[5,] 16537.95 16555.68 16480.41 16317.57 24961.20 25052.09 25137.52 25176.49
[6,] 16514.93 16532.82 16457.45 16293.35 24985.20 25076.00 25161.62 25200.69
       [,369]   [,370]   [,371]   [,372]   [,373]   [,374]   [,375]   [,376]
[1,] 25098.57 24640.01 24635.28 24833.63 24800.87 24664.80 25344.67 25334.15
[2,] 25120.78 24666.64 24661.87 24860.35 24827.77 24691.51 25368.39 25357.60
[3,] 25145.00 24695.62 24690.79 24889.40 24857.02 24720.56 25394.22 25383.16
[4,] 25169.60 24724.96 24720.07 24918.82 24886.64 24749.97 25420.42 25409.08
[5,] 25023.72 24570.89 24566.10 24764.62 24732.10 24595.78 25271.75 25260.89
[6,] 25048.04 24599.98 24595.13 24793.79 24761.47 24624.94 25297.68 25286.54
       [,377]   [,378]   [,379]   [,380]   [,381]   [,382]   [,383]   [,384]
[1,] 25327.36 25460.25 21718.29 21805.18 21751.37 21662.43 11804.06 11797.13
[2,] 25350.77 25483.68 21686.13 21773.43 21719.84 21630.52 11862.89 11855.93
[3,] 25376.28 25509.20 21654.39 21742.08 21688.73 21599.03 11926.58 11919.60
[4,] 25402.15 25535.10 21648.23 21736.00 21682.69 21592.92 11990.77 11983.76
[5,] 25254.04 25386.96 21591.40 21678.56 21624.90 21535.70 11785.76 11778.78
[6,] 25279.65 25412.58 21559.51 21647.08 21593.64 21504.07 11849.87 11842.86
       [,385]   [,386]   [,387]   [,388]   [,389]   [,390]   [,391]   [,392]
[1,] 11903.97 11866.49 13353.14 13343.29 13322.83 13304.92 13346.92 13403.67
[2,] 11962.18 11925.23 13396.44 13386.46 13365.88 13346.94 13388.87 13445.75
[3,] 12025.20 11988.82 13443.51 13433.41 13412.70 13392.66 13434.52 13491.54
[4,] 12088.72 12052.91 13491.17 13480.93 13460.10 13438.96 13480.75 13537.91
[5,] 11884.50 11848.02 13308.14 13298.09 13277.45 13257.93 13299.82 13356.78
[6,] 11947.93 11912.02 13355.53 13345.35 13324.57 13303.95 13345.77 13402.87
       [,393]   [,394]   [,395]   [,396]   [,397]   [,398]   [,399]   [,400]
[1,] 13423.36 13545.91 13526.79 13531.91 13426.32 13418.20 13133.02 13091.12
[2,] 13465.47 13588.54 13569.59 13574.76 13469.75 13461.92 13177.42 13135.65
[3,] 13511.28 13634.91 13616.14 13621.35 13516.96 13509.45 13225.68 13184.05
[4,] 13557.67 13681.85 13663.26 13668.52 13564.74 13557.55 13274.53 13233.04
[5,] 13376.51 13499.87 13481.01 13486.20 13381.52 13373.87 13089.76 13048.07
[6,] 13422.62 13546.54 13527.86 13533.10 13429.04 13421.71 13138.35 13096.80
       [,401]   [,402]   [,403]   [,404]   [,405]   [,406]   [,407]   [,408]
[1,] 13130.84 13148.33 13216.70 13291.11 13186.72 13256.22 13215.26 13269.81
[2,] 13174.21 13191.58 13259.64 13334.62 13231.02 13300.78 13259.13 13313.17
[3,] 13221.37 13238.62 13306.34 13381.93 13279.18 13349.22 13306.82 13360.32
[4,] 13269.13 13286.25 13353.62 13429.82 13327.92 13398.22 13355.09 13408.05
[5,] 13085.96 13103.26 13171.14 13246.45 13143.31 13213.22 13171.16 13224.91
[6,] 13133.44 13150.62 13218.15 13294.07 13191.79 13261.98 13219.17 13272.38
       [,409]   [,410]   [,411]   [,412]   [,413]   [,414]   [,415]   [,416]
[1,] 13418.20 13323.21 13304.60 13283.88 13557.13 13582.96 13647.17 13615.95
[2,] 13461.92 13367.73 13349.26 13328.43 13600.58 13626.00 13690.18 13659.73
[3,] 13509.45 13416.11 13397.80 13376.84 13647.82 13672.79 13736.95 13707.31
[4,] 13557.55 13465.07 13446.90 13425.82 13695.62 13720.15 13784.27 13755.45
[5,] 13373.87 13280.14 13261.76 13240.86 13512.37 13537.55 13601.72 13571.70
[6,] 13421.71 13328.84 13310.62 13289.59 13559.91 13584.64 13648.78 13619.59
       [,417]   [,418]   [,419]   [,420]   [,421]   [,422]   [,423]   [,424]
[1,] 13767.72 13804.10 13637.83 13796.00 12295.92 12266.30 12288.99 12319.60
[2,] 13811.32 13847.60 13681.74 13839.39 12349.58 12319.52 12342.11 12372.64
[3,] 13858.70 13894.88 13729.46 13886.54 12407.74 12377.22 12399.70 12430.14
[4,] 13906.63 13942.72 13777.74 13934.25 12466.43 12435.46 12457.83 12488.18
[5,] 13723.18 13759.42 13593.79 13751.13 12268.18 12237.79 12260.30 12290.77
[6,] 13770.87 13807.00 13641.82 13798.59 12326.73 12295.88 12318.28 12348.66
       [,425]   [,426]   [,427]   [,428]   [,429]   [,430]   [,431]   [,432]
[1,] 12374.97 12365.01 12312.02 12295.92 16035.93 16021.59 15998.99 16684.09
[2,] 12428.13 12418.28 12365.60 12349.58 16074.41 16060.39 16037.86 16721.65
[3,] 12485.75 12476.03 12423.70 12407.74 16116.26 16102.56 16080.12 16762.48
[4,] 12543.91 12534.32 12482.32 12466.43 16158.61 16145.25 16122.89 16803.81
[5,] 12346.34 12336.59 12284.16 12268.18 15983.53 15969.65 15947.17 16630.30
[6,] 12404.35 12394.72 12342.63 12326.73 16025.61 16012.07 15989.67 16671.36
       [,433]   [,434]   [,435]   [,436]   [,437]   [,438]   [,439]   [,440]
[1,] 16678.24 16706.59 16734.04 16766.60 16819.90 16798.56 17061.47 17038.53
[2,] 16715.70 16744.01 16771.64 16804.29 16857.86 16836.92 17099.76 17076.65
[3,] 16756.44 16784.70 16812.52 16845.25 16899.10 16878.60 17141.36 17118.08
[4,] 16797.67 16825.89 16853.89 16886.71 16940.84 16920.76 17183.44 17159.99
[5,] 16624.32 16652.61 16680.32 16713.00 16766.70 16745.96 17008.76 16985.58
[6,] 16665.27 16693.52 16721.42 16754.19 16808.17 16787.86 17050.58 17027.23
       [,441]   [,442]   [,443]   [,444]   [,445]   [,446]   [,447]   [,448]
[1,] 17057.24 17154.28 17224.87 17084.43 17352.57 17317.80 17361.48 17576.44
[2,] 17094.94 17192.03 17262.80 17122.91 17389.27 17354.26 17398.19 17612.84
[3,] 17135.92 17233.05 17304.02 17164.72 17429.17 17393.89 17438.10 17652.41
[4,] 17177.38 17274.55 17345.71 17207.01 17469.54 17434.00 17478.49 17692.45
[5,] 17003.66 17100.77 17171.63 17032.01 17297.51 17262.38 17306.44 17520.94
[6,] 17044.86 17142.01 17213.07 17074.04 17337.62 17302.23 17346.56 17560.72
       [,449]   [,450]   [,451]   [,452]   [,453]   [,454]   [,455]   [,456]
[1,] 17577.62 17680.38 17576.44 16851.64 16947.70 17064.07 15125.22 15197.16
[2,] 17613.83 17715.90 17612.84 16891.81 16987.98 17104.41 15161.13 15233.17
[3,] 17653.19 17754.54 17652.41 16935.42 17031.72 17148.20 15200.26 15272.39
[4,] 17693.03 17793.65 17692.45 16979.51 17075.93 17192.46 15239.94 15312.17
[5,] 17521.84 17623.61 17520.94 16801.76 16898.00 17014.45 15069.04 15141.12
[6,] 17561.41 17662.45 17560.72 16845.61 16941.96 17058.47 15108.40 15180.58
       [,457]   [,458]   [,459]   [,460]   [,461]   [,462]   [,463]   [,464]
[1,] 15200.49 13869.69 13858.50 13867.28 13932.41 13993.98 13932.47 13295.88
[2,] 15236.90 13904.99 13893.60 13902.36 13967.09 14028.82 13967.66 13322.63
[3,] 15276.55 13943.49 13931.92 13940.65 14004.93 14066.84 14006.07 13352.04
[4,] 15316.75 13982.61 13970.84 13979.55 14043.39 14105.46 14045.08 13382.12
[5,] 15145.03 13812.62 13801.16 13809.91 13874.45 13936.25 13875.26 13226.98
[6,] 15184.92 13851.39 13839.73 13848.45 13912.55 13974.52 13913.92 13256.60
       [,465]   [,466]   [,467]   [,468]   [,469]   [,470]   [,471]   [,472]
[1,] 13245.92 13180.28 13163.98 13241.47 13399.54 13433.56 13458.61 13448.73
[2,] 13272.79 13205.83 13188.69 13266.37 13425.04 13459.26 13484.40 13475.14
[3,] 13302.31 13233.95 13215.91 13293.80 13453.10 13487.53 13512.77 13504.17
[4,] 13332.52 13262.77 13243.84 13321.91 13481.85 13516.48 13541.83 13533.87
[5,] 13177.17 13109.79 13092.39 13170.14 13328.99 13363.27 13388.44 13379.37
[6,] 13206.91 13138.12 13119.82 13197.76 13357.25 13391.74 13417.02 13408.61
       [,473]   [,474]   [,475]   [,476]   [,477]   [,478]   [,479]   [,480]
[1,] 13473.60 13446.86 13321.88 13295.88 17265.51 17291.74 17489.55 17572.35
[2,] 13500.53 13473.89 13349.26 13322.63 17284.58 17310.66 17508.28 17591.03
[3,] 13530.11 13503.58 13379.34 13352.04 17305.60 17331.52 17528.93 17611.62
[4,] 13560.36 13533.95 13410.09 13382.12 17327.18 17352.93 17550.12 17632.75
[5,] 13404.93 13378.33 13253.82 13226.98 17186.77 17212.81 17410.39 17493.13
[6,] 13434.72 13408.23 13284.11 13256.60 17207.91 17233.79 17431.15 17513.83
       [,481]   [,482]   [,483]   [,484]   [,485]   [,486]   [,487]   [,488]
[1,] 17576.91 17632.49 17523.71 14583.00 14552.58 14630.91 22554.71 23319.08
[2,] 17595.75 17651.31 17543.05 14593.13 14562.61 14641.09 22570.71 23330.87
[3,] 17616.51 17672.05 17564.35 14604.67 14574.03 14652.68 22588.30 23343.93
[4,] 17637.81 17693.33 17586.20 14616.88 14586.14 14664.94 22606.33 23357.42
[5,] 17497.88 17553.44 17445.30 14493.76 14463.23 14541.73 22472.24 23231.70
[6,] 17518.75 17574.29 17466.72 14505.38 14474.73 14553.40 22489.91 23244.82
       [,489]   [,490]   [,491]   [,492]   [,493]   [,494]   [,495]   [,496]
[1,] 23452.74 23451.60 23584.93 23548.01 22954.04 22914.97 22954.04 12887.92
[2,] 23465.23 23463.32 23596.65 23561.23 22967.09 22927.52 22967.09 12921.90
[3,] 23479.06 23476.33 23609.64 23575.83 22981.52 22941.41 22981.52 12959.04
[4,] 23493.31 23489.75 23623.04 23590.85 22996.37 22955.74 22996.37 12996.84
[5,] 23366.17 23364.15 23497.47 23462.27 22868.11 22828.46 22868.11 12828.97
[6,] 23380.06 23377.21 23510.52 23476.94 22882.60 22842.42 22882.60 12866.38
       [,497]   [,498]   [,499]   [,500]   [,501]   [,502]   [,503]   [,504]
[1,] 12913.26 13024.17 13166.29 13189.27 13197.88 13233.61 12942.53 18486.24
[2,] 12947.10 13057.96 13199.68 13222.97 13231.63 13267.29 12977.44 18538.01
[3,] 12984.10 13094.89 13236.18 13259.80 13268.53 13304.10 13015.58 18593.98
[4,] 13021.77 13132.49 13273.34 13297.29 13306.08 13341.56 13054.38 18650.32
[5,] 12854.12 12964.95 13106.50 13129.92 13138.61 13174.23 12884.92 18455.10
[6,] 12891.39 13002.15 13143.26 13167.02 13175.77 13211.30 12923.34 18511.33
       [,505]   [,506]   [,507]   [,508]   [,509]   [,510]   [,511]   [,512]
[1,] 18596.90 18578.12 13864.65 13850.05 13847.07 13841.64 13823.95 13864.62
[2,] 18648.68 18629.90 13899.53 13884.87 13881.91 13876.44 13858.60 13899.10
[3,] 18704.66 18685.89 13937.60 13922.87 13919.94 13914.41 13896.43 13936.74
[4,] 18761.00 18742.24 13976.28 13961.49 13958.57 13953.01 13934.86 13975.00
[5,] 18565.77 18547.01 13806.98 13792.30 13789.35 13783.85 13765.96 13806.38
[6,] 18622.00 18603.24 13845.31 13830.56 13827.63 13822.09 13804.03 13844.28
       [,513]   [,514]   [,515]   [,516]   [,517]   [,518]   [,519]   [,520]
[1,] 13898.99 13903.68 13906.59 13925.28 13910.89 13927.33 13955.14 13971.14
[2,] 13932.96 13937.81 13940.90 13959.54 13944.94 13961.32 13989.44 14005.61
[3,] 13970.06 13975.07 13978.36 13996.93 13982.12 13998.44 14026.88 14043.23
[4,] 14007.77 14012.95 14016.44 14034.94 14019.92 14036.18 14064.93 14081.46
[5,] 13840.02 13844.94 13848.11 13866.72 13852.04 13868.39 13896.64 13912.88
[6,] 13877.37 13882.45 13885.82 13904.36 13889.47 13905.76 13934.33 13950.75
       [,521]   [,522]   [,523]   [,524]   [,525]   [,526]   [,527]   [,528]
[1,] 13929.67 13868.03 13592.47 13587.00 13567.73 13590.94 13590.42 13684.62
[2,] 13964.28 13902.93 13626.02 13620.56 13601.34 13624.27 13623.70 13718.13
[3,] 14002.06 13941.01 13662.68 13657.23 13638.05 13660.69 13660.07 13754.74
[4,] 14040.45 13979.71 13699.98 13694.54 13675.40 13697.74 13697.07 13791.98
[5,] 13871.62 13810.39 13532.91 13527.45 13508.25 13531.06 13530.47 13625.00
[6,] 13909.65 13848.73 13569.82 13564.38 13545.22 13567.73 13567.09 13661.86
       [,529]   [,530]   [,531]   [,532]   [,533]   [,534]   [,535]   [,536]
[1,] 13683.97 13670.25 13298.36 13286.95 13284.88 13280.26 13269.68 13260.85
[2,] 13717.55 13703.90 13331.44 13320.04 13317.95 13313.34 13302.60 13293.79
[3,] 13754.24 13740.66 13367.61 13356.22 13354.10 13349.51 13338.60 13329.81
[4,] 13791.55 13778.04 13404.43 13393.04 13390.90 13386.32 13375.24 13366.48
[5,] 13624.45 13610.82 13238.13 13226.74 13224.63 13220.03 13209.22 13200.43
[6,] 13661.39 13647.83 13274.56 13263.17 13261.04 13256.45 13245.48 13236.70
       [,537]   [,538]   [,539]   [,540]   [,541]   [,542]   [,543]   [,544]
[1,] 13254.06 13282.00 13414.34 13473.02 13427.68 13402.05 6116.021 6135.637
[2,] 13286.91 13314.71 13446.75 13505.26 13460.56 13434.87 6070.353 6089.021
[3,] 13322.83 13350.49 13482.20 13540.52 13496.50 13470.76 6025.998 6043.699
[4,] 13359.41 13386.92 13518.29 13576.43 13533.09 13507.30 6017.484 6034.993
[5,] 13193.50 13221.26 13353.17 13411.61 13367.16 13341.46 5981.227 6000.391
[6,] 13229.68 13257.29 13388.86 13447.11 13403.36 13377.60 5936.207 5954.395
       [,545]   [,546]   [,547]   [,548]   [,549]   [,550]   [,551]   [,552]
[1,] 6142.811 6149.820 6195.210 6148.571 6219.898 6121.038 5890.290 5940.599
[2,] 6096.396 6103.486 6148.978 6102.348 6173.325 6074.281 5846.738 5897.970
[3,] 6051.279 6058.449 6104.035 6057.423 6128.031 6028.819 5804.581 5856.739
[4,] 6042.613 6049.799 6095.403 6048.795 6119.328 6020.086 5796.506 5848.844
[5,] 6007.661 6014.708 6060.148 6013.512 6084.675 5985.726 5756.548 5807.339
[6,] 5961.871 5969.001 6014.541 5967.918 6038.715 5939.587 5713.726 5765.460
       [,553]   [,554]   [,555]
[1,] 5937.552 5884.930 11788.54
[2,] 5894.878 5827.622 11750.24
[3,] 5853.601 5771.477 11712.66
[4,] 5845.698 5760.640 11705.40
[5,] 5804.268 5745.552 11657.77
[6,] 5762.342 5688.597 11619.90

Distances

  • We want to find the MINIMUM distance to a primary school for each grid cell
Code 
closest <- apply(distances, 1, "min")
grids$closest_primary <- closest

The map for primary school

The map for primary school

What if we want to calculate proportion of population?

  • Let’s create some new values
Code 
totalpop <- sum(grids$pop)
# within 1km
popwithin1km <- sum(grids$pop[grids$closest_primary <= 1000])/totalpop
# within 2km
popwithin2km <- sum(grids$pop[grids$closest_primary <= 2000])/totalpop
# within 5km
popwithin5km <- sum(grids$pop[grids$closest_primary <= 5000])/totalpop

popmat <- matrix(c(popwithin1km, popwithin2km, popwithin5km), nrow = 1)
rownames(popmat) <- "Primary school"
colnames(popmat) <- c("1km", "2km", "5km")

What if we want to calculate proportion of population?

  • Let’s create some new values
Code 
kable(popmat, digits = 3, row.names = TRUE) %>%
  kable_styling("striped", full_width = F) %>%
  column_spec(2:4, width = "2cm")
1km 2km 5km
Primary school 0.34 0.618 0.892

Your turn

  • Try it for middle and high schools!

Example code

distances <- distance(grids, df |> filter(fclass=="elementaryschool"))
distances <- apply(distances, 1, "min")

# within 1km
popwithin1km <- sum(grids$pop[distances <= 1000])/totalpop
# within 2km
popwithin2km <- sum(grids$pop[distances <= 2000])/totalpop
# within 5km
popwithin5km <- sum(grids$pop[distances <= 5000])/totalpop

popmat <- matrix(c(popwithin1km, popwithin2km, popwithin5km), nrow = 1)
rownames(popmat) <- "Primary school"
distancesmid <- distance(grids, df |> filter(fclass=="middleschool"))
distancesmid <- apply(distancesmid, 1, "min")

# within 1km
popwithin1kmmid <- sum(grids$pop[distancesmid <= 1000])/totalpop
# within 2km
popwithin2kmmid <- sum(grids$pop[distancesmid <= 2000])/totalpop
# within 5km
popwithin5kmmid <- sum(grids$pop[distancesmid <= 5000])/totalpop

popmatmid <- matrix(c(popwithin1kmmid, popwithin2kmmid, popwithin5kmmid), nrow = 1)
rownames(popmatmid) <- "Middle school"
distanceshigh <- distance(grids, df |> filter(fclass=="highschool"))
distanceshigh <- apply(distanceshigh, 1, "min")

# within 1km
popwithin1kmhigh <- sum(grids$pop[distanceshigh <= 1000])/totalpop
# within 2km
popwithin2kmhigh <- sum(grids$pop[distanceshigh <= 2000])/totalpop
# within 5km
popwithin5kmhigh <- sum(grids$pop[distanceshigh <= 5000])/totalpop

popmathigh <- matrix(c(popwithin1kmhigh, popwithin2kmhigh, popwithin5kmhigh), nrow = 1)
rownames(popmathigh) <- "High school"

The table

1km 2km 5km
Primary school 0.340 0.618 0.892
Middle school 0.328 0.628 0.910
High school 0.311 0.591 0.910

Using Python and the GEE API

Just for today, Python

  • We are going to:
    • Install Python
    • Install Positron
  • You should already have a GEE account from last week

Installing Python

  • If you already have Python installed, don’t install it!

  • You can check in the terminal/console:

Code 
python --version
  • If it returns a version number, you have Python installed
    • We want it to be Python 3.XX.X (some version of python3)

Installing Python

  • If it is not downloaded, you have two options:
  • I recommend Anaconda (or miniconda) for beginners

Installing Positron

  • We are going to use the same IDE

  • Let’s install Positron

    • Same company that makes RStudio
    • It’s my favorite Python IDE

  • Go to the Positron website

    • First post > Assets > correct version for your OS

Next steps

  • Here’s what we are going to do:
    • Open a folder (maybe make a new one?)
    • Create a “virtual environment”
    • Install the packages we need

Step 1: Open a folder

Step 2: Create an environment

  • Now let’s create a “virtual environment”

Step 2: Create an environment

Code 
python -m venv classenv
  • Positron will ask if you want to use the environment
    • Click “Yes”
  • It will also ask to install the ipykernel package
    • Click “Install”
  • This will create a new folder called classenv in your current directory (that you opened/made earlier)
    • This is where all the packages will be installed

Step 2: Create an environment

  • Finally, close Positron and reopen it

  • In the “Terminal” you should see the name of the environment you just created, something like this:

Code 
(classenv) Joshs-MacBook-Pro:geospatialdataR Josh$

Step 3: Install packages

  • We need two separate packages:
    • earthengine-api
    • geopandas
  • We do this in the “Terminal”
Code 
pip3 install earthengine-api geopandas

Step 3: Install packages

One last step: create a script!

  • In the upper left, you should see “New”
    • Click it, then click “New File”
    • Save it as inclassgee.py - MAKE SURE to add the .py extension!

Just like with R, load libraries

Code 
# load libraries
1import ee
2import geopandas as gpd
1
This is the Earth Engine API library
2
This is the geopandas library (you’ll see what the as gpd does later)
  • Note we can create comments just like in RStudio
  • You can run them just like in RStudio (highlight and press ctrl/cmd + enter)

We need to initialize the API

  • Last week, you created a “project”
    • You need to figure out its name to use here! (upper-right corner of the code editor on GEE)
    • This should open a pop-up in your browser
Code 
ee.Authenticate()
ee.Initialize(project="ee-geefolder")

Searching for data

Code 
# Let's look at NDVI
ndvi = ee.ImageCollection("MODIS/061/MOD13A3")

# we can use "print" and "getInfo()" to look at more information
# If the above call worked correctly, you should see a bunch of information printed in the console
print(ndvi.getInfo())

Filtering by date

Code 
# We can also filter the collection by date. Let's look september 2023
ndvi = ndvi.filterDate("2023-08-01", "2023-08-31")

# for assets that have many bands (raster layers), we can select the specific ones we want:
ndvi = ndvi.select("NDVI")
ndvi

# finally, just make sure we have an IMAGE, not an image collection
ndvi = ndvi.mean()
ndvi

Filtering by area

  • Let’s use Korea to pull data
    • week7files: kgrid.shp
    • Going to read this into Python using geopandas
Code 
# let's load the shapefile (note the use of "gpd" instead of "geopandas"!)
shape = gpd.read_file("week7files/kgrid.shp")
# make sure it is in lat/lon (project it)
shape = shape.to_crs("EPSG:4326")
# let's get the total bounds for the shapefile
bounds = shape.total_bounds
bounds

Downloading

Code 
# let's create a bounding box in earth engine. Note the syntax (xmin, ymin, xmax, ymax)
# this does not accept an array (which is what bounds was), so we will extract the individual components
# Also note that indexing in python starts at 0, not 1! bounds[0] gives the first value in the array
bbox = ee.Geometry.BBox(bounds[0], bounds[1], bounds[2], bounds[3])

task = ee.batch.Export.image.toDrive(image=ndvi,
    description="krndvi",
    scale=1000, # set scale the same as the raster's resolution (you can find this on GEE)
    region=bbox,
    crs="EPSG:4326",
    fileFormat="GeoTIFF")
# start the task. You must do this for GEE to actually run the command.
task.start()
# can check the status of the task
task.status()

Some notes on downloading

  • You do not have to check the status
    • It will finish automatically
  • You can start multiple tasks
  • Some tasks will take longer than others
    • One way to speed it up: use a larger resolution (e.g. 100 instead of 10)

Land classification

  • Now let’s download land classification for the most recent year

  • Find the appropriate GEE id

    • Let’s use the Copernicus Global Land Cover Layers
  • What is the id?
  • What are the available dates?

Land classification

Land classification

Code 
# land classification
lc = ee.ImageCollection("COPERNICUS/Landcover/100m/Proba-V-C3/Global")

# Only 2021
lc = lc.filterDate("2019-01-01", "2019-12-31")
# just make sure we have an IMAGE, not an image collection
lc = lc.first()
# let's try something different: download the discrete_classification only
lc = lc.select("discrete_classification")

task = ee.batch.Export.image.toDrive(image=lc,
    description="krlc",
    scale=100, # Let's do 100 (for time and memory)
    region=bbox,
    crs="EPSG:4326",
    fileFormat="GeoTIFF")
task.start()
task.status()

Land classification

  • While we wait for that to download, I’ve already downloaded it for you!
    • week7files/krlc.tf
  • Let’s look at it in R, using terra

The raster

  • What are we looking at here?
Code 
lc <- rast("week7files/krlc.tif")
head(lc)
  discrete_classification
1                     200
2                     200
3                     200
4                     200
5                     200
6                     200
  • We need to turn this into a factor!

This isn’t straightforward…

  • This discrete classification variable is not numeric
    • We need to find out what the values represent
    • How?
  • Let’s check the GEE page for this data

Land classification

How to get the values?

  • We could of course write them all by hand!

  • For example, let’s create a new variable that just has 8 values:

    • 0: No data
    • 1: Shrubs/plants
    • 2: Agricultural land
    • 3: Urban
    • 4: Bare land
    • 5: Snow/ice
    • 6: Water
    • 7: Forest

Creating the data

Code 
factorvalues <- data.frame(value = 0:7, 
  class = c("No data", "Shrubs/plants", "Agricultural land", "Urban", "Bare land", "Snow/ice", "Water", "Forest"))
factorvalues
  value             class
1     0           No data
2     1     Shrubs/plants
3     2 Agricultural land
4     3             Urban
5     4         Bare land
6     5          Snow/ice
7     6             Water
8     7            Forest

Now: change values of raster

Code 
lcnew <- lc |> 
  mutate(discrete_classification = case_when(
  discrete_classification == 0 ~ 0,
  discrete_classification %in% c(20, 30, 90, 100) ~ 1,
  discrete_classification == 40 ~ 2,
  discrete_classification == 50 ~ 3,
  discrete_classification == 60 ~ 4,
  discrete_classification == 70 ~ 5,
  discrete_classification %in% c(80, 200)  ~ 6,
  TRUE ~ 7
))
Code 
# Double check
summary(lcnew)
 discrete_classification
 Min.   :1.00           
 1st Qu.:6.00           
 Median :6.00           
 Mean   :5.79           
 3rd Qu.:6.00           
 Max.   :7.00

Now: create labels and assign

Code 
cls<- data.frame(id = 0:7,
  cover = c("No data", "Shrubs/plants", "Agricultural land", "Urban", "Bare land", "Snow/ice", "Water", "Forest"))
levels(lcnew) <- cls
lcnew
class       : SpatRaster 
dimensions  : 6128, 7078, 1  (nrow, ncol, nlyr)
resolution  : 0.0008983153, 0.0008983153  (x, y)
extent      : 124.608, 130.9663, 33.1128, 38.61768  (xmin, xmax, ymin, ymax)
coord. ref. : lon/lat WGS 84 (EPSG:4326) 
source(s)   : memory
color table : 1 
categories  : cover 
name        :         cover 
min value   : Shrubs/plants 
max value   :        Forest
Code 
levels(lcnew)
[[1]]
  id             cover
1  0           No data
2  1     Shrubs/plants
3  2 Agricultural land
4  3             Urban
5  4         Bare land
6  5          Snow/ice
7  6             Water
8  7            Forest

Plot it

Code 
ggplot() +
  geom_spatraster(data = lcnew, aes(fill = cover)) +
  # Note we need fewer than 8 colors! Only 7 show up in our raster
  scale_fill_manual("Classification", values = c("#ffbb22", "#f096ff", "#fa0000", "#b4b4b4", "#f0f0f0", "#0032c8", "#58481f")) +
  theme_bw()

Plot it

But what if we want ALL of the classes?

  • Do you want to do them all by hand?
    • I assume not.
  • So what are we to do?
  • The GEE API in Python has all the info!

Back to python

True
Code 
lcinfo = lc.getInfo()
type(lcinfo)
<class 'dict'>
Code 
lcinfo
{'type': 'Image', 'bands': [{'id': 'discrete_classification', 'data_type': {'type': 'PixelType', 'precision': 'int', 'min': 0, 'max': 255}, 'dimensions': [400750, 240450], 'crs': 'EPSG:3857', 'crs_transform': [100, 0, -20037550, 0, -100, 15538800]}], 'version': 1685078284447716, 'id': 'COPERNICUS/Landcover/100m/Proba-V-C3/Global/2019', 'properties': {'discrete_classification_class_names': ['Unknown. No or not enough satellite data available.', 'Shrubs. Woody perennial plants with persistent and woody stems\nand without any defined main stem being less than 5 m tall. The\nshrub foliage can be either evergreen or deciduous.\n', 'Herbaceous vegetation. Plants without persistent stem or shoots above ground\nand lacking definite firm structure. Tree and shrub cover is less\nthan 10 %.\n', 'Cultivated and managed vegetation / agriculture. Lands covered with temporary crops followed by harvest\nand a bare soil period (e.g., single and multiple cropping systems).\nNote that perennial woody crops will be classified as the appropriate\nforest or shrub land cover type.\n', 'Urban / built up. Land covered by buildings and other man-made structures.', 'Bare / sparse vegetation. Lands with exposed soil, sand, or rocks and never has\nmore than 10 % vegetated cover during any time of the year.\n', 'Snow and ice. Lands under snow or ice cover throughout the year.', 'Permanent water bodies. Lakes, reservoirs, and rivers. Can be either fresh or salt-water bodies.', 'Herbaceous wetland. Lands with a permanent mixture of water and herbaceous\nor woody vegetation. The vegetation can be present in either salt,\nbrackish, or fresh water.\n', 'Moss and lichen.', 'Closed forest, evergreen needle leaf. Tree canopy >70 %, almost all needle leaf trees remain\ngreen all year. Canopy is never without green foliage.\n', 'Closed forest, evergreen broad leaf. Tree canopy >70 %, almost all broadleaf trees remain\ngreen year round. Canopy is never without green foliage.\n', 'Closed forest, deciduous needle leaf. Tree canopy >70 %, consists of seasonal needle leaf\ntree communities with an annual cycle of leaf-on and leaf-off\nperiods.\n', 'Closed forest, deciduous broad leaf. Tree canopy >70 %, consists of seasonal broadleaf\ntree communities with an annual cycle of leaf-on and leaf-off periods.\n', 'Closed forest, mixed.', 'Closed forest, not matching any of the other definitions.', 'Open forest, evergreen needle leaf. Top layer- trees 15-70 % and second layer- mixed of shrubs\nand grassland, almost all needle leaf trees remain green all year.\nCanopy is never without green foliage.\n', 'Open forest, evergreen broad leaf. Top layer- trees 15-70 % and second layer- mixed of shrubs\nand grassland, almost all broadleaf trees remain green year round.\nCanopy is never without green foliage.\n', 'Open forest, deciduous needle leaf. Top layer- trees 15-70 % and second layer- mixed of shrubs\nand grassland, consists of seasonal needle leaf tree communities with\nan annual cycle of leaf-on and leaf-off periods.\n', 'Open forest, deciduous broad leaf. Top layer- trees 15-70 % and second layer- mixed of shrubs\nand grassland, consists of seasonal broadleaf tree communities with\nan annual cycle of leaf-on and leaf-off periods.\n', 'Open forest, mixed.', 'Open forest, not matching any of the other definitions.', 'Oceans, seas. Can be either fresh or salt-water bodies.'], 'forest_type_class_names': ['Unknown', 'Evergreen needle leaf', 'Evergreen broad leaf', 'Deciduous needle leaf', 'Deciduous broad leaf', 'Mix of forest types'], 'forest_type_class_palette': ['282828', '666000', '009900', '70663e', 'a0dc00', '929900'], 'system:time_end': 1577836800000, 'discrete_classification_class_values': [0, 20, 30, 40, 50, 60, 70, 80, 90, 100, 111, 112, 113, 114, 115, 116, 121, 122, 123, 124, 125, 126, 200], 'system:time_start': 1546300800000, 'discrete_classification_class_palette': ['282828', 'ffbb22', 'ffff4c', 'f096ff', 'fa0000', 'b4b4b4', 'f0f0f0', '0032c8', '0096a0', 'fae6a0', '58481f', '009900', '70663e', '00cc00', '4e751f', '007800', '666000', '8db400', '8d7400', 'a0dc00', '929900', '648c00', '000080'], 'system:footprint': {'type': 'LinearRing', 'coordinates': [[-180, -90], [180, -90], [180, 90], [-180, 90], [-180, -90]]}, 'forest_type_class_values': [0, 1, 2, 3, 4, 5], 'system:asset_size': 84728363000, 'system:index': '2019'}}

“properties” is what we want

Code 
import pandas as pd
lcprop = lcinfo["properties"]
lcprop = pd.DataFrame.from_dict({"id": lcprop["discrete_classification_class_values"], 
  "cover": lcprop["discrete_classification_class_names"]})
lcprop
     id                                              cover
0     0  Unknown. No or not enough satellite data avail...
1    20  Shrubs. Woody perennial plants with persistent...
2    30  Herbaceous vegetation. Plants without persiste...
3    40  Cultivated and managed vegetation / agricultur...
4    50  Urban / built up. Land covered by buildings an...
5    60  Bare / sparse vegetation. Lands with exposed s...
6    70  Snow and ice. Lands under snow or ice cover th...
7    80  Permanent water bodies. Lakes, reservoirs, and...
8    90  Herbaceous wetland. Lands with a permanent mix...
9   100                                   Moss and lichen.
10  111  Closed forest, evergreen needle leaf. Tree can...
11  112  Closed forest, evergreen broad leaf. Tree cano...
12  113  Closed forest, deciduous needle leaf. Tree can...
13  114  Closed forest, deciduous broad leaf. Tree cano...
14  115                              Closed forest, mixed.
15  116  Closed forest, not matching any of the other d...
16  121  Open forest, evergreen needle leaf. Top layer-...
17  122  Open forest, evergreen broad leaf. Top layer- ...
18  123  Open forest, deciduous needle leaf. Top layer-...
19  124  Open forest, deciduous broad leaf. Top layer- ...
20  125                                Open forest, mixed.
21  126  Open forest, not matching any of the other def...
22  200  Oceans, seas. Can be either fresh or salt-wate...

Let’s save it as a .csv file

Code 
lcprop.to_csv("week7files/lcprop.csv", index = False)

Bring it into R

Code 
lcprop <- read_csv("week7files/lcprop.csv")
head(lcprop)
# A tibble: 6 × 2
     id cover                                                                   
  <dbl> <chr>                                                                   
1     0 "Unknown. No or not enough satellite data available."                   
2    20 "Shrubs. Woody perennial plants with persistent and woody stems\nand wi…
3    30 "Herbaceous vegetation. Plants without persistent stem or shoots above …
4    40 "Cultivated and managed vegetation / agriculture. Lands covered with te…
5    50 "Urban / built up. Land covered by buildings and other man-made structu…
6    60 "Bare / sparse vegetation. Lands with exposed soil, sand, or rocks and …
Code 
lcnew <- lc
levels(lcnew) <- data.frame(lcprop[,1:2])

Quick plot

Code 
plot(lcnew)

It already has the colors!

  • The information on colors is actually already in the raster!
Code 
coltab(lcnew)
[[1]]
    value red green blue alpha
1       0  40    40   40   255
2       1   0     0    0   255
3       2   0     0    0   255
4       3   0     0    0   255
5       4   0     0    0   255
6       5   0     0    0   255
7       6   0     0    0   255
8       7   0     0    0   255
9       8   0     0    0   255
10      9   0     0    0   255
11     10   0     0    0   255
12     11   0     0    0   255
13     12   0     0    0   255
14     13   0     0    0   255
15     14   0     0    0   255
16     15   0     0    0   255
17     16   0     0    0   255
18     17   0     0    0   255
19     18   0     0    0   255
20     19   0     0    0   255
21     20 255   187   34   255
22     21   0     0    0   255
23     22   0     0    0   255
24     23   0     0    0   255
25     24   0     0    0   255
26     25   0     0    0   255
27     26   0     0    0   255
28     27   0     0    0   255
29     28   0     0    0   255
30     29   0     0    0   255
31     30 255   255   76   255
32     31   0     0    0   255
33     32   0     0    0   255
34     33   0     0    0   255
35     34   0     0    0   255
36     35   0     0    0   255
37     36   0     0    0   255
38     37   0     0    0   255
39     38   0     0    0   255
40     39   0     0    0   255
41     40 240   150  255   255
42     41   0     0    0   255
43     42   0     0    0   255
44     43   0     0    0   255
45     44   0     0    0   255
46     45   0     0    0   255
47     46   0     0    0   255
48     47   0     0    0   255
49     48   0     0    0   255
50     49   0     0    0   255
51     50 250     0    0   255
52     51   0     0    0   255
53     52   0     0    0   255
54     53   0     0    0   255
55     54   0     0    0   255
56     55   0     0    0   255
57     56   0     0    0   255
58     57   0     0    0   255
59     58   0     0    0   255
60     59   0     0    0   255
61     60 180   180  180   255
62     61   0     0    0   255
63     62   0     0    0   255
64     63   0     0    0   255
65     64   0     0    0   255
66     65   0     0    0   255
67     66   0     0    0   255
68     67   0     0    0   255
69     68   0     0    0   255
70     69   0     0    0   255
71     70 240   240  240   255
72     71   0     0    0   255
73     72   0     0    0   255
74     73   0     0    0   255
75     74   0     0    0   255
76     75   0     0    0   255
77     76   0     0    0   255
78     77   0     0    0   255
79     78   0     0    0   255
80     79   0     0    0   255
81     80   0    50  200   255
82     81   0     0    0   255
83     82   0     0    0   255
84     83   0     0    0   255
85     84   0     0    0   255
86     85   0     0    0   255
87     86   0     0    0   255
88     87   0     0    0   255
89     88   0     0    0   255
90     89   0     0    0   255
91     90   0   150  160   255
92     91   0     0    0   255
93     92   0     0    0   255
94     93   0     0    0   255
95     94   0     0    0   255
96     95   0     0    0   255
97     96   0     0    0   255
98     97   0     0    0   255
99     98   0     0    0   255
100    99   0     0    0   255
101   100 250   230  160   255
102   101   0     0    0   255
103   102   0     0    0   255
104   103   0     0    0   255
105   104   0     0    0   255
106   105   0     0    0   255
107   106   0     0    0   255
108   107   0     0    0   255
109   108   0     0    0   255
110   109   0     0    0   255
111   110   0     0    0   255
112   111  88    72   31   255
113   112   0   153    0   255
114   113 112   102   62   255
115   114   0   204    0   255
116   115  78   117   31   255
117   116   0   120    0   255
118   117   0     0    0   255
119   118   0     0    0   255
120   119   0     0    0   255
121   120   0     0    0   255
122   121 102    96    0   255
123   122 141   180    0   255
124   123 141   116    0   255
125   124 160   220    0   255
126   125 146   153    0   255
127   126 100   140    0   255
128   127   0     0    0   255
129   128   0     0    0   255
130   129   0     0    0   255
131   130   0     0    0   255
132   131   0     0    0   255
133   132   0     0    0   255
134   133   0     0    0   255
135   134   0     0    0   255
136   135   0     0    0   255
137   136   0     0    0   255
138   137   0     0    0   255
139   138   0     0    0   255
140   139   0     0    0   255
141   140   0     0    0   255
142   141   0     0    0   255
143   142   0     0    0   255
144   143   0     0    0   255
145   144   0     0    0   255
146   145   0     0    0   255
147   146   0     0    0   255
148   147   0     0    0   255
149   148   0     0    0   255
150   149   0     0    0   255
151   150   0     0    0   255
152   151   0     0    0   255
153   152   0     0    0   255
154   153   0     0    0   255
155   154   0     0    0   255
156   155   0     0    0   255
157   156   0     0    0   255
158   157   0     0    0   255
159   158   0     0    0   255
160   159   0     0    0   255
161   160   0     0    0   255
162   161   0     0    0   255
163   162   0     0    0   255
164   163   0     0    0   255
165   164   0     0    0   255
166   165   0     0    0   255
167   166   0     0    0   255
168   167   0     0    0   255
169   168   0     0    0   255
170   169   0     0    0   255
171   170   0     0    0   255
172   171   0     0    0   255
173   172   0     0    0   255
174   173   0     0    0   255
175   174   0     0    0   255
176   175   0     0    0   255
177   176   0     0    0   255
178   177   0     0    0   255
179   178   0     0    0   255
180   179   0     0    0   255
181   180   0     0    0   255
182   181   0     0    0   255
183   182   0     0    0   255
184   183   0     0    0   255
185   184   0     0    0   255
186   185   0     0    0   255
187   186   0     0    0   255
188   187   0     0    0   255
189   188   0     0    0   255
190   189   0     0    0   255
191   190   0     0    0   255
192   191   0     0    0   255
193   192   0     0    0   255
194   193   0     0    0   255
195   194   0     0    0   255
196   195   0     0    0   255
197   196   0     0    0   255
198   197   0     0    0   255
199   198   0     0    0   255
200   199   0     0    0   255
201   200   0     0  128   255
202   201   0     0    0   255
203   202   0     0    0   255
204   203   0     0    0   255
205   204   0     0    0   255
206   205   0     0    0   255
207   206   0     0    0   255
208   207   0     0    0   255
209   208   0     0    0   255
210   209   0     0    0   255
211   210   0     0    0   255
212   211   0     0    0   255
213   212   0     0    0   255
214   213   0     0    0   255
215   214   0     0    0   255
216   215   0     0    0   255
217   216   0     0    0   255
218   217   0     0    0   255
219   218   0     0    0   255
220   219   0     0    0   255
221   220   0     0    0   255
222   221   0     0    0   255
223   222   0     0    0   255
224   223   0     0    0   255
225   224   0     0    0   255
226   225   0     0    0   255
227   226   0     0    0   255
228   227   0     0    0   255
229   228   0     0    0   255
230   229   0     0    0   255
231   230   0     0    0   255
232   231   0     0    0   255
233   232   0     0    0   255
234   233   0     0    0   255
235   234   0     0    0   255
236   235   0     0    0   255
237   236   0     0    0   255
238   237   0     0    0   255
239   238   0     0    0   255
240   239   0     0    0   255
241   240   0     0    0   255
242   241   0     0    0   255
243   242   0     0    0   255
244   243   0     0    0   255
245   244   0     0    0   255
246   245   0     0    0   255
247   246   0     0    0   255
248   247   0     0    0   255
249   248   0     0    0   255
250   249   0     0    0   255
251   250   0     0    0   255
252   251   0     0    0   255
253   252   0     0    0   255
254   253   0     0    0   255
255   254   0     0    0   255
256   255   0     0    0   255

Plot it

Code 
ggplot() +
  geom_spatraster(data = lcnew, aes(fill = cover), show.legend = FALSE) +
  theme_bw()

Plot it

Adding a legend (need to make it small)

Code 
ggplot() +
  geom_spatraster(data = lcnew, aes(fill = cover)) +
  theme_bw() +
  labs(fill = "Land cover") +
  theme(legend.text=element_text(size=rel(0.5)), legend.key.size = unit(0.25, "cm"))

Adding a legend (need to make it small)

Extracting the data

  • Let’s see what happens if we extract the data using exactextractr
  • We need to read the shapefile using sf, NOT terra
Code 
library(exactextractr)
kgrid <- sf::read_sf("week7files/kgrid.shp") # this way I don't have to load sf!
# reproject
lcnew <- project(lcnew, crs(kgrid))
extracted <- exact_extract(lcnew, kgrid, progress = FALSE)
# it's a list!
class(extracted)
[1] "list"

Extracting the data

  • The list is the same length as the number of grid cells
Code 
nrow(kgrid)
[1] 4906
Code 
length(extracted)
[1] 4906
Code 
# here's the first one
extracted[[1]]
     value coverage_fraction
1      124         0.6772069
2      114         0.7274001
3      114         0.7274001
4      114         0.7274001
5      124         0.7274001
6      124         0.7274001
7      114         0.7274001
8      114         0.7274001
9      114         0.7274001
10     114         0.7274001
11     114         0.7274001
12     116         0.7274001
13     116         0.7274001
14     114         0.7274001
15     114         0.7274001
16     114         0.7274001
17      30         0.7274001
18      30         0.7274001
19      30         0.7274001
20     126         0.7274001
21     126         0.7274001
22      40         0.7274001
23      40         0.7274001
24      30         0.7274001
25      30         0.7274001
26      30         0.7274001
27      30         0.7274001
28      90         0.7274001
29      30         0.7274001
30      20         0.7274001
31      20         0.7274001
32     126         0.7274001
33     124         0.7274001
34     114         0.7274001
35     114         0.7274001
36     114         0.7274001
37     114         0.7274001
38     116         0.7274001
39     116         0.7274001
40     114         0.7274001
41     116         0.7274001
42     116         0.7274001
43     116         0.7274001
44     116         0.7274001
45     116         0.7274001
46     116         0.7274001
47     116         0.7274001
48     116         0.7274001
49     116         0.7274001
50      30         0.7274001
51      30         0.7274001
52      30         0.7274001
53      30         0.7274001
54     114         0.7274001
55     114         0.7274001
56     114         0.6823409
57     114         0.9309964
58     114         1.0000000
59     114         1.0000000
60     114         1.0000000
61     114         1.0000000
62     114         1.0000000
63     114         1.0000000
64     114         1.0000000
65     114         1.0000000
66     114         1.0000000
67     114         1.0000000
68     114         1.0000000
69     124         1.0000000
70     124         1.0000000
71     114         1.0000000
72     124         1.0000000
73      30         1.0000000
74      30         1.0000000
75      30         1.0000000
76     126         1.0000000
77      40         1.0000000
78      40         1.0000000
79      40         1.0000000
80      40         1.0000000
81      30         1.0000000
82      30         1.0000000
83      30         1.0000000
84      30         1.0000000
85      30         1.0000000
86      90         1.0000000
87      90         1.0000000
88      40         1.0000000
89     124         1.0000000
90     114         1.0000000
91     114         1.0000000
92     114         1.0000000
93     114         1.0000000
94     116         1.0000000
95     116         1.0000000
96     114         1.0000000
97     116         1.0000000
98     116         1.0000000
99     116         1.0000000
100    116         1.0000000
101    116         1.0000000
102    116         1.0000000
103    116         1.0000000
104    116         1.0000000
105    116         1.0000000
106     30         1.0000000
107     30         1.0000000
108     30         1.0000000
109    116         1.0000000
110    114         1.0000000
111    114         1.0000000
112    114         0.9380544
113    114         0.9309964
114    114         1.0000000
115    114         1.0000000
116    114         1.0000000
117    114         1.0000000
118    114         1.0000000
119    114         1.0000000
120    114         1.0000000
121    114         1.0000000
122    124         1.0000000
123    124         1.0000000
124    124         1.0000000
125    124         1.0000000
126    114         1.0000000
127    114         1.0000000
128    114         1.0000000
129    124         1.0000000
130     30         1.0000000
131     30         1.0000000
132    126         1.0000000
133     40         1.0000000
134     40         1.0000000
135     40         1.0000000
136     40         1.0000000
137     20         1.0000000
138     30         1.0000000
139     30         1.0000000
140     30         1.0000000
141     30         1.0000000
142     90         1.0000000
143     90         1.0000000
144     20         1.0000000
145    124         1.0000000
146    114         1.0000000
147    114         1.0000000
148    114         1.0000000
149    116         1.0000000
150    116         1.0000000
151    116         1.0000000
152    114         1.0000000
153    116         1.0000000
154    116         1.0000000
155    116         1.0000000
156    116         1.0000000
157    116         1.0000000
158    116         1.0000000
159    116         1.0000000
160    116         1.0000000
161    116         1.0000000
162     30         1.0000000
163     30         1.0000000
164     30         1.0000000
165    116         1.0000000
166    114         1.0000000
167    114         1.0000000
168    114         0.9380544
169    114         0.9309964
170    114         1.0000000
171    114         1.0000000
172    114         1.0000000
173    114         1.0000000
174    114         1.0000000
175    114         1.0000000
176    114         1.0000000
177    124         1.0000000
178    124         1.0000000
179    124         1.0000000
180    124         1.0000000
181    124         1.0000000
182    114         1.0000000
183    114         1.0000000
184    124         1.0000000
185     30         1.0000000
186     30         1.0000000
187     30         1.0000000
188     40         1.0000000
189     40         1.0000000
190     40         1.0000000
191     40         1.0000000
192     40         1.0000000
193     40         1.0000000
194     30         1.0000000
195     30         1.0000000
196     30         1.0000000
197     30         1.0000000
198     90         1.0000000
199     90         1.0000000
200     20         1.0000000
201    126         1.0000000
202    114         1.0000000
203    114         1.0000000
204    116         1.0000000
205    116         1.0000000
206    116         1.0000000
207    116         1.0000000
208    116         1.0000000
209    116         1.0000000
210    116         1.0000000
211    116         1.0000000
212    116         1.0000000
213    116         1.0000000
214    116         1.0000000
215    116         1.0000000
216    114         1.0000000
217    116         1.0000000
218     30         1.0000000
219     30         1.0000000
220    114         1.0000000
221    114         1.0000000
222    114         1.0000000
223    114         1.0000000
224    114         0.9380544
225    114         0.9309964
226    114         1.0000000
227    114         1.0000000
228    114         1.0000000
229    114         1.0000000
230    114         1.0000000
231    114         1.0000000
232    114         1.0000000
233    124         1.0000000
234    124         1.0000000
235    124         1.0000000
236     30         1.0000000
237    124         1.0000000
238    114         1.0000000
239    114         1.0000000
240    124         1.0000000
241     30         1.0000000
242     30         1.0000000
243     30         1.0000000
244     40         1.0000000
245     40         1.0000000
246     40         1.0000000
247     40         1.0000000
248     50         1.0000000
249     50         1.0000000
250     30         1.0000000
251     30         1.0000000
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2760   114         1.0000000
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2765   124         1.0000000
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2780   114         1.0000000
2781    30         1.0000000
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2784    40         1.0000000
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2800   114         0.9380544
2801   114         0.9309964
2802   114         1.0000000
2803   114         1.0000000
2804   114         1.0000000
2805   114         1.0000000
2806   114         1.0000000
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2825   124         1.0000000
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2827   116         1.0000000
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2832   114         1.0000000
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2835   114         1.0000000
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2837    30         1.0000000
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2839   126         1.0000000
2840    40         1.0000000
2841    30         1.0000000
2842    30         1.0000000
2843    20         1.0000000
2844    30         1.0000000
2845   114         1.0000000
2846   114         1.0000000
2847   116         1.0000000
2848   114         1.0000000
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2850   114         1.0000000
2851   114         1.0000000
2852   114         1.0000000
2853   114         1.0000000
2854   114         1.0000000
2855   114         1.0000000
2856   114         0.9380544
2857   114         0.9309964
2858   114         1.0000000
2859   114         1.0000000
2860   114         1.0000000
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2881   126         1.0000000
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2893   126         1.0000000
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2895    20         1.0000000
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2900   126         1.0000000
2901   116         1.0000000
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2911   114         1.0000000
2912   114         0.9380544
2913   114         0.9309964
2914   114         1.0000000
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2922   114         1.0000000
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2925   114         1.0000000
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2927   114         1.0000000
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2929   114         1.0000000
2930   114         1.0000000
2931   114         1.0000000
2932   114         1.0000000
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2935   114         1.0000000
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2937   126         1.0000000
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2940   114         1.0000000
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2944   114         1.0000000
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2949   126         1.0000000
2950    40         1.0000000
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2957   114         1.0000000
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2968   114         0.9380544
2969   114         0.9309964
2970   114         1.0000000
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2981   114         1.0000000
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2983   114         1.0000000
2984   114         1.0000000
2985   114         1.0000000
2986   114         1.0000000
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2988   114         1.0000000
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2990   114         1.0000000
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2992   114         1.0000000
2993   114         1.0000000
2994   114         1.0000000
2995   114         1.0000000
2996   114         1.0000000
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2998   114         1.0000000
2999   114         1.0000000
3000   114         1.0000000
3001   114         1.0000000
3002   114         1.0000000
3003   124         1.0000000
3004   114         1.0000000
3005   126         1.0000000
3006    40         1.0000000
3007   126         1.0000000
3008    30         1.0000000
3009    30         1.0000000
3010    30         1.0000000
3011    40         1.0000000
3012   126         1.0000000
3013   114         1.0000000
3014   114         1.0000000
3015   114         1.0000000
3016   114         1.0000000
3017   114         1.0000000
3018   114         1.0000000
3019   114         1.0000000
3020   114         1.0000000
3021   114         1.0000000
3022   114         1.0000000
3023   114         1.0000000
3024   114         0.9380544
3025   114         0.9309964
3026   114         1.0000000
3027   114         1.0000000
3028   114         1.0000000
3029   114         1.0000000
3030   114         1.0000000
3031   114         1.0000000
3032   114         1.0000000
3033   114         1.0000000
3034   114         1.0000000
3035   124         1.0000000
3036   126         1.0000000
3037   114         1.0000000
3038   114         1.0000000
3039   114         1.0000000
3040   114         1.0000000
3041   114         1.0000000
3042   114         1.0000000
3043   114         1.0000000
3044   114         1.0000000
3045   114         1.0000000
3046   114         1.0000000
3047   114         1.0000000
3048   114         1.0000000
3049   114         1.0000000
3050   114         1.0000000
3051   114         1.0000000
3052   114         1.0000000
3053   114         1.0000000
3054   114         1.0000000
3055   114         1.0000000
3056   114         1.0000000
3057   114         1.0000000
3058   114         1.0000000
3059   114         1.0000000
3060   114         1.0000000
3061   126         1.0000000
3062   126         1.0000000
3063    40         1.0000000
3064    90         1.0000000
3065    30         1.0000000
3066    30         1.0000000
3067    40         1.0000000
3068    30         1.0000000
3069   124         1.0000000
3070   124         1.0000000
3071   124         1.0000000
3072   114         1.0000000
3073   114         1.0000000
3074   114         1.0000000
3075   114         1.0000000
3076   114         1.0000000
3077   114         1.0000000
3078   114         1.0000000
3079   114         1.0000000
3080   114         0.9380544
3081   114         0.9309964
3082   114         1.0000000
3083   114         1.0000000
3084   114         1.0000000
3085   114         1.0000000
3086   114         1.0000000
3087   114         1.0000000
3088   114         1.0000000
3089   114         1.0000000
3090   114         1.0000000
3091   114         1.0000000
3092   114         1.0000000
3093   114         1.0000000
3094   114         1.0000000
3095   114         1.0000000
3096   114         1.0000000
3097   114         1.0000000
3098   114         1.0000000
3099   114         1.0000000
3100   114         1.0000000
3101   114         1.0000000
3102   114         1.0000000
3103   114         1.0000000
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3105   114         1.0000000
3106   114         1.0000000
3107   114         1.0000000
3108   114         1.0000000
3109   114         1.0000000
3110   114         1.0000000
3111   114         1.0000000
3112   114         1.0000000
3113   114         1.0000000
3114   114         1.0000000
3115   114         1.0000000
3116   114         1.0000000
3117   114         1.0000000
3118   114         1.0000000
3119   126         1.0000000
3120    40         1.0000000
3121    30         1.0000000
3122    30         1.0000000
3123    40         1.0000000
3124   126         1.0000000
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3126   126         1.0000000
3127   114         1.0000000
3128   114         1.0000000
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3130   114         1.0000000
3131   114         1.0000000
3132   114         1.0000000
3133   114         1.0000000
3134   114         1.0000000
3135   114         1.0000000
3136   114         0.9380544
3137   114         0.1318764
3138   114         0.1416508
3139   114         0.1416508
3140   114         0.1416508
3141   114         0.1416508
3142   114         0.1416508
3143   114         0.1416508
3144   114         0.1416508
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3153   114         0.1416508
3154   114         0.1416508
3155   114         0.1416508
3156   114         0.1416508
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3162   114         0.1416508
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3166   114         0.1416508
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3176   124         0.1416508
3177    90         0.1416508
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3179    40         0.1416508
3180   126         0.1416508
3181   114         0.1416508
3182   114         0.1416508
3183   114         0.1416508
3184   114         0.1416508
3185   114         0.1416508
3186   114         0.1416508
3187   114         0.1416508
3188   114         0.1416508
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3192   114         0.1328761

Extracting the data

  • The first element is ALL of the raster cells that overlap with the first grid cell
    • The total area for the first grid cell is 2.5e+07
    • The total “coverage_fraction” in the first grid cell is 3121
    • How can we find the area of each grid cell?
Code 
res(lcnew)
[1] 89.49499 89.49499
  • Area of each grid cell is 89.49499x89.49499 or 8009
  • So total area is 89.49499^2 * sum(extracted[[1]]$coverage_fraction) = 2.5000001^{7}

What do we want to do?

  • We need to go through each element in the list and:
    • Calculate the proportion of the total area that is covered by each class
    • Importantly, we need to make sure we include ALL of the values, even if they are zero (and do not show up in the list)
Code 
example <- as_tibble(extracted[[1]])
example <- example |>
  complete(value = unique(lc)$discrete_classification)
summary(example)
     value        coverage_fraction
 Min.   : 20.00   Min.   :0.1319   
 1st Qu.:114.00   1st Qu.:1.0000   
 Median :114.00   Median :1.0000   
 Mean   : 99.36   Mean   :0.9779   
 3rd Qu.:114.00   3rd Qu.:1.0000   
 Max.   :200.00   Max.   :1.0000   
                  NA's   :10

Aggregate to value

Code 
example$coverage_fraction[is.na(example$coverage_fraction)] <- 0
example <- example |>
  group_by(value) |>
  summarize(coverage_fraction = sum(coverage_fraction)) |>
  ungroup() |>
  mutate(coverage_fraction = coverage_fraction/sum(coverage_fraction))
head(example)
# A tibble: 6 × 2
  value coverage_fraction
  <dbl>             <dbl>
1    20          0.0219  
2    30          0.0815  
3    40          0.0962  
4    50          0.00256 
5    60          0       
6    80          0.000320

Reshape wide

Code 
# long to wide
example <- example |>
  pivot_wider(names_from = value, values_from = coverage_fraction,
    names_prefix = "coveragefraction")
example
# A tibble: 1 × 20
  coveragefraction20 coveragefraction30 coveragefraction40 coveragefraction50
               <dbl>              <dbl>              <dbl>              <dbl>
1             0.0219             0.0815             0.0962            0.00256
# ℹ 16 more variables: coveragefraction60 <dbl>, coveragefraction80 <dbl>,
#   coveragefraction90 <dbl>, coveragefraction111 <dbl>,
#   coveragefraction112 <dbl>, coveragefraction113 <dbl>,
#   coveragefraction114 <dbl>, coveragefraction115 <dbl>,
#   coveragefraction116 <dbl>, coveragefraction121 <dbl>,
#   coveragefraction122 <dbl>, coveragefraction123 <dbl>,
#   coveragefraction124 <dbl>, coveragefraction125 <dbl>, …

We need to do that for the ENTIRE list!

Code 
wrapper <- function(x){
  x <- as_tibble(x)
  x <- x |>
    complete(value = unique(lc)$discrete_classification)
  x$coverage_fraction[is.na(x$coverage_fraction)] <- 0
  x <- x |>
    group_by(value) |>
    summarize(coverage_fraction = sum(coverage_fraction)) |>
    ungroup() |>
    mutate(coverage_fraction = coverage_fraction/sum(coverage_fraction)) |>
    pivot_wider(names_from = value, values_from = coverage_fraction,
      names_prefix = "coveragefraction")
}
# Takes a LONG time! so I've uploaded it for you
extracted <- lapply(extracted, wrapper)
extracted <- bind_rows(extracted)

Now we can add those values to kgrid

Code 
extracted <- read_csv("week7files/extracted.csv")
kgrid <- vect("week7files/kgrid.shp")
kgrid <- cbind(kgrid, extracted)
names(kgrid)
 [1] "id"                  "coveragefraction20"  "coveragefraction30" 
 [4] "coveragefraction40"  "coveragefraction50"  "coveragefraction60" 
 [7] "coveragefraction80"  "coveragefraction90"  "coveragefraction111"
[10] "coveragefraction112" "coveragefraction113" "coveragefraction114"
[13] "coveragefraction115" "coveragefraction116" "coveragefraction121"
[16] "coveragefraction122" "coveragefraction123" "coveragefraction124"
[19] "coveragefraction125" "coveragefraction126" "coveragefraction200"

Now we can add those values to kgrid