Dencronología Mediterránea, retos metodológicos de la datación
MARÍA GRANDE BLANCO
2023-05-08
Library
library(dplR)## This is dplR version 1.7.4.
## dplR is part of openDendro https://opendendro.org.
## New users can visit https://opendendro.github.io/dplR-workshop/ to get started.library(utils)
library(readr)
library(readxl)
library(knitr)
library(ggplot2)1) Lectura de los datos de Arlanza y generación de los datos del grupo 2
Los resultados de las funciones son del grupo 2 (Arlanza).
El procedimiento con las muestras del grupo 1 (Mambrillas de Lara, Hontoria del Pinar, Hortigüela y Carazo) fue el mismo, pero leyendo el archivo “JTBUR.rwl”
Los datos del grupo 3 leyendo el archivo “series_simuladas.rwl”.
Los datos seleccionados con una correlación superior al 30% (rho>0,3) leyendo el archivo “JTBURcorregidasrho0.3.rwl”
jt<-read.rwl("MARLANZA.rwl")## Attempting to automatically detect format.
## Assuming a Tucson format file.## Warning in readLines(con): incomplete final line found on 'MARLANZA.rwl'## There does not appear to be a header in the rwl file
## There are 33 series
## 1 AR01N 1940 2007 0.001
## 2 AR01S2 1938 2007 0.001
## 3 AR01SW 1925 2007 0.001
## 4 AR02SW 1940 2007 0.001
## 5 AR02SW2 1933 2007 0.001
## 6 AR03SW 1947 2007 0.001
## 7 AR03SE 1957 2007 0.001
## 8 AR04NE 1951 2007 0.001
## 9 AR06SW 1938 2007 0.001
## 10 AR06W 1934 2007 0.001
## 11 AR07SE 1930 2007 0.001
## 12 AR07E 1933 2007 0.001
## 13 AR07NW 1921 2007 0.001
## 14 AR08S 1938 2007 0.001
## 15 AR08E 1955 2007 0.001
## 16 AR09W 1932 2007 0.001
## 17 AR09N 1926 2007 0.001
## 18 AR10N 1947 2007 0.001
## 19 AR10NE 1944 2007 0.001
## 20 AR11NE 1948 2007 0.001
## 21 AR11E 1943 2007 0.001
## 22 AR12E 1937 2007 0.001
## 23 AR12SE 1936 2007 0.001
## 24 AR13SE 1950 2007 0.001
## 25 AR13S 1935 2007 0.001
## 26 AR14S 1948 2006 0.001
## 27 AR15E 1943 2007 0.001
## 28 AR15N 1937 2007 0.001
## 29 AR16W 1926 2007 0.001
## 30 AR16N 1927 2007 0.001
## 31 AR19S 1936 2007 0.001
## 32 AR20E2 1923 2007 0.001
## 33 AR21N 1944 2007 0.001summary.rwl(jt)## series first last year mean median stdev skew gini ar1
## 1 AR01N 1940 2007 68 1.165 0.956 0.617 0.910 0.288 0.688
## 2 AR01S2 1938 2007 70 1.292 1.186 0.649 0.857 0.275 0.681
## 3 AR01SW 1925 2007 83 1.276 1.214 0.533 0.448 0.234 0.433
## 4 AR02SW 1940 2007 68 0.895 0.598 0.883 2.614 0.449 0.731
## 5 AR02SW2 1933 2007 75 1.229 0.758 1.111 1.967 0.423 0.900
## 6 AR03SW 1947 2007 61 1.428 1.087 0.852 1.457 0.299 0.792
## 7 AR03SE 1957 2007 51 1.270 0.946 0.897 2.477 0.308 0.764
## 8 AR04NE 1951 2007 57 1.342 1.310 0.423 0.383 0.177 0.738
## 9 AR06SW 1938 2007 70 1.254 0.661 1.150 1.383 0.462 0.760
## 10 AR06W 1934 2007 74 1.606 1.481 0.898 0.943 0.302 0.659
## 11 AR07SE 1930 2007 78 1.026 0.956 0.588 0.906 0.313 0.723
## 12 AR07E 1933 2007 75 0.929 0.714 0.682 2.109 0.351 0.756
## 13 AR07NW 1921 2007 87 1.050 0.842 0.745 1.645 0.360 0.470
## 14 AR08S 1938 2007 70 1.006 0.885 0.522 1.837 0.248 0.609
## 15 AR08E 1955 2007 53 1.110 1.004 0.599 1.159 0.283 0.725
## 16 AR09W 1932 2007 76 1.191 1.116 0.769 1.225 0.345 0.772
## 17 AR09N 1926 2007 82 0.884 0.935 0.562 0.283 0.359 0.776
## 18 AR10N 1947 2007 61 1.593 1.405 0.826 1.124 0.276 0.647
## 19 AR10NE 1944 2007 64 1.947 1.648 1.106 1.475 0.288 0.757
## 20 AR11NE 1948 2007 60 1.416 1.289 0.558 1.339 0.205 0.517
## 21 AR11E 1943 2007 65 1.307 1.161 0.581 1.181 0.231 0.356
## 22 AR12E 1937 2007 71 1.376 1.104 0.851 2.119 0.303 0.403
## 23 AR12SE 1936 2007 72 1.464 1.232 0.935 1.787 0.317 0.806
## 24 AR13SE 1950 2007 58 1.429 1.138 1.016 1.024 0.382 0.710
## 25 AR13S 1935 2007 73 1.598 1.332 1.141 1.323 0.374 0.598
## 26 AR14S 1948 2006 59 1.653 1.387 0.907 1.914 0.266 0.663
## 27 AR15E 1943 2007 65 1.463 1.267 0.934 0.681 0.354 0.333
## 28 AR15N 1937 2007 71 1.978 1.553 1.226 1.226 0.325 0.465
## 29 AR16W 1926 2007 82 1.690 1.400 0.863 1.130 0.271 0.394
## 30 AR16N 1927 2007 81 1.269 1.120 0.602 0.624 0.263 0.442
## 31 AR19S 1936 2007 72 1.228 1.130 0.729 1.019 0.319 0.724
## 32 AR20E2 1923 2007 85 2.110 1.581 1.660 2.322 0.361 0.842
## 33 AR21N 1944 2007 64 1.308 1.180 0.635 1.580 0.244 0.677Lectura de las medidas de las series
Se indica el nombre de la serie, el primer año, el último año y la precisión con la que fueron medidas.
jt<-read.rwl("MARLANZA.rwl")## Attempting to automatically detect format.
## Assuming a Tucson format file.
## There does not appear to be a header in the rwl file
## There are 33 series
## 1 AR01N 1940 2007 0.001
## 2 AR01S2 1938 2007 0.001
## 3 AR01SW 1925 2007 0.001
## 4 AR02SW 1940 2007 0.001
## 5 AR02SW2 1933 2007 0.001
## 6 AR03SW 1947 2007 0.001
## 7 AR03SE 1957 2007 0.001
## 8 AR04NE 1951 2007 0.001
## 9 AR06SW 1938 2007 0.001
## 10 AR06W 1934 2007 0.001
## 11 AR07SE 1930 2007 0.001
## 12 AR07E 1933 2007 0.001
## 13 AR07NW 1921 2007 0.001
## 14 AR08S 1938 2007 0.001
## 15 AR08E 1955 2007 0.001
## 16 AR09W 1932 2007 0.001
## 17 AR09N 1926 2007 0.001
## 18 AR10N 1947 2007 0.001
## 19 AR10NE 1944 2007 0.001
## 20 AR11NE 1948 2007 0.001
## 21 AR11E 1943 2007 0.001
## 22 AR12E 1937 2007 0.001
## 23 AR12SE 1936 2007 0.001
## 24 AR13SE 1950 2007 0.001
## 25 AR13S 1935 2007 0.001
## 26 AR14S 1948 2006 0.001
## 27 AR15E 1943 2007 0.001
## 28 AR15N 1937 2007 0.001
## 29 AR16W 1926 2007 0.001
## 30 AR16N 1927 2007 0.001
## 31 AR19S 1936 2007 0.001
## 32 AR20E2 1923 2007 0.001
## 33 AR21N 1944 2007 0.001summary.rwl(jt)## series first last year mean median stdev skew gini ar1
## 1 AR01N 1940 2007 68 1.165 0.956 0.617 0.910 0.288 0.688
## 2 AR01S2 1938 2007 70 1.292 1.186 0.649 0.857 0.275 0.681
## 3 AR01SW 1925 2007 83 1.276 1.214 0.533 0.448 0.234 0.433
## 4 AR02SW 1940 2007 68 0.895 0.598 0.883 2.614 0.449 0.731
## 5 AR02SW2 1933 2007 75 1.229 0.758 1.111 1.967 0.423 0.900
## 6 AR03SW 1947 2007 61 1.428 1.087 0.852 1.457 0.299 0.792
## 7 AR03SE 1957 2007 51 1.270 0.946 0.897 2.477 0.308 0.764
## 8 AR04NE 1951 2007 57 1.342 1.310 0.423 0.383 0.177 0.738
## 9 AR06SW 1938 2007 70 1.254 0.661 1.150 1.383 0.462 0.760
## 10 AR06W 1934 2007 74 1.606 1.481 0.898 0.943 0.302 0.659
## 11 AR07SE 1930 2007 78 1.026 0.956 0.588 0.906 0.313 0.723
## 12 AR07E 1933 2007 75 0.929 0.714 0.682 2.109 0.351 0.756
## 13 AR07NW 1921 2007 87 1.050 0.842 0.745 1.645 0.360 0.470
## 14 AR08S 1938 2007 70 1.006 0.885 0.522 1.837 0.248 0.609
## 15 AR08E 1955 2007 53 1.110 1.004 0.599 1.159 0.283 0.725
## 16 AR09W 1932 2007 76 1.191 1.116 0.769 1.225 0.345 0.772
## 17 AR09N 1926 2007 82 0.884 0.935 0.562 0.283 0.359 0.776
## 18 AR10N 1947 2007 61 1.593 1.405 0.826 1.124 0.276 0.647
## 19 AR10NE 1944 2007 64 1.947 1.648 1.106 1.475 0.288 0.757
## 20 AR11NE 1948 2007 60 1.416 1.289 0.558 1.339 0.205 0.517
## 21 AR11E 1943 2007 65 1.307 1.161 0.581 1.181 0.231 0.356
## 22 AR12E 1937 2007 71 1.376 1.104 0.851 2.119 0.303 0.403
## 23 AR12SE 1936 2007 72 1.464 1.232 0.935 1.787 0.317 0.806
## 24 AR13SE 1950 2007 58 1.429 1.138 1.016 1.024 0.382 0.710
## 25 AR13S 1935 2007 73 1.598 1.332 1.141 1.323 0.374 0.598
## 26 AR14S 1948 2006 59 1.653 1.387 0.907 1.914 0.266 0.663
## 27 AR15E 1943 2007 65 1.463 1.267 0.934 0.681 0.354 0.333
## 28 AR15N 1937 2007 71 1.978 1.553 1.226 1.226 0.325 0.465
## 29 AR16W 1926 2007 82 1.690 1.400 0.863 1.130 0.271 0.394
## 30 AR16N 1927 2007 81 1.269 1.120 0.602 0.624 0.263 0.442
## 31 AR19S 1936 2007 72 1.228 1.130 0.729 1.019 0.319 0.724
## 32 AR20E2 1923 2007 85 2.110 1.581 1.660 2.322 0.361 0.842
## 33 AR21N 1944 2007 64 1.308 1.180 0.635 1.580 0.244 0.677STATS
rwl.stats(jt)## series first last year mean median stdev skew gini ar1
## 1 AR01N 1940 2007 68 1.165 0.956 0.617 0.910 0.288 0.688
## 2 AR01S2 1938 2007 70 1.292 1.186 0.649 0.857 0.275 0.681
## 3 AR01SW 1925 2007 83 1.276 1.214 0.533 0.448 0.234 0.433
## 4 AR02SW 1940 2007 68 0.895 0.598 0.883 2.614 0.449 0.731
## 5 AR02SW2 1933 2007 75 1.229 0.758 1.111 1.967 0.423 0.900
## 6 AR03SW 1947 2007 61 1.428 1.087 0.852 1.457 0.299 0.792
## 7 AR03SE 1957 2007 51 1.270 0.946 0.897 2.477 0.308 0.764
## 8 AR04NE 1951 2007 57 1.342 1.310 0.423 0.383 0.177 0.738
## 9 AR06SW 1938 2007 70 1.254 0.661 1.150 1.383 0.462 0.760
## 10 AR06W 1934 2007 74 1.606 1.481 0.898 0.943 0.302 0.659
## 11 AR07SE 1930 2007 78 1.026 0.956 0.588 0.906 0.313 0.723
## 12 AR07E 1933 2007 75 0.929 0.714 0.682 2.109 0.351 0.756
## 13 AR07NW 1921 2007 87 1.050 0.842 0.745 1.645 0.360 0.470
## 14 AR08S 1938 2007 70 1.006 0.885 0.522 1.837 0.248 0.609
## 15 AR08E 1955 2007 53 1.110 1.004 0.599 1.159 0.283 0.725
## 16 AR09W 1932 2007 76 1.191 1.116 0.769 1.225 0.345 0.772
## 17 AR09N 1926 2007 82 0.884 0.935 0.562 0.283 0.359 0.776
## 18 AR10N 1947 2007 61 1.593 1.405 0.826 1.124 0.276 0.647
## 19 AR10NE 1944 2007 64 1.947 1.648 1.106 1.475 0.288 0.757
## 20 AR11NE 1948 2007 60 1.416 1.289 0.558 1.339 0.205 0.517
## 21 AR11E 1943 2007 65 1.307 1.161 0.581 1.181 0.231 0.356
## 22 AR12E 1937 2007 71 1.376 1.104 0.851 2.119 0.303 0.403
## 23 AR12SE 1936 2007 72 1.464 1.232 0.935 1.787 0.317 0.806
## 24 AR13SE 1950 2007 58 1.429 1.138 1.016 1.024 0.382 0.710
## 25 AR13S 1935 2007 73 1.598 1.332 1.141 1.323 0.374 0.598
## 26 AR14S 1948 2006 59 1.653 1.387 0.907 1.914 0.266 0.663
## 27 AR15E 1943 2007 65 1.463 1.267 0.934 0.681 0.354 0.333
## 28 AR15N 1937 2007 71 1.978 1.553 1.226 1.226 0.325 0.465
## 29 AR16W 1926 2007 82 1.690 1.400 0.863 1.130 0.271 0.394
## 30 AR16N 1927 2007 81 1.269 1.120 0.602 0.624 0.263 0.442
## 31 AR19S 1936 2007 72 1.228 1.130 0.729 1.019 0.319 0.724
## 32 AR20E2 1923 2007 85 2.110 1.581 1.660 2.322 0.361 0.842
## 33 AR21N 1944 2007 64 1.308 1.180 0.635 1.580 0.244 0.6772) Gráfica tipo spaguetti de los datos de Arlanza
plot.rwl(jt,plot.type="spag",
col = 'cornflowerblue')
Grafica en la que se representan la anchura de los anillos de las muestras de Arlanza, con un intervalo de 20 años
3) Co-datado de los datos en bruto
- El azul indica buena correlación
- El verde indica falta de correlación
- El rojo indica que hay mala correlación
crs <- corr.rwl.seg(jt, seg.length = 30, bin.floor = 40, pcrit = 0.05, label.cex = 1)
rwl.report(jt)## Number of dated series: 33
## Number of measurements: 2301
## Avg series length: 69.72727
## Range: 87
## Span: 1921 - 2007
## Mean (Std dev) series intercorrelation: 0.502032 (0.1227314)
## Mean (Std dev) AR1: 0.6457879 (0.1533042)
## -------------
## Years with absent rings listed by series
## Series AR12E -- 1937
## 1 absent rings (0.043%)
## -------------
## Years with internal NA values listed by series
## None4) Cronología maestra con los datos en bruto
chron <- chron(jt, biweight = TRUE, prewhiten = FALSE)
plot.crn(chron,
crn.line.col = 'seagreen',
samp.depth.col = 'lightyellow')
5) Estandarizado de las muestras
En la cronología maestra con los datos en bruto se observa que hay una tendencia relacionada con la edad que provoca la disminución del crecimiento de anillo. El estandarizado de las muestras tiene como objetivo principal eliminar esta tendencia. Para ello, aplica una normalización en las series de crecimiento, ajustándolas a una función matemática que recoge dicha tendencia. La diferencia entre el valor real y el calculado es el residuo, que recoge la variabilidad intranual, de alta frecuencia, relacionada con eventos climáticos.
Se aplica un estandarizado de todas las series con el método Spline.
detr_jt <- detrend(jt, y.name = names(jt), make.plot = TRUE,
method = c("Spline"),
nyrs = NULL, f = 0.5, pos.slope = FALSE,
constrain.nls = c("always"),
verbose = FALSE, return.info = FALSE,
span = "cv", bass = 0, difference = FALSE)
detr_jt## AR01N AR01S2 AR01SW AR02SW AR02SW2 AR03SW AR03SE
## 1921 NA NA NA NA NA NA NA
## 1922 NA NA NA NA NA NA NA
## 1923 NA NA NA NA NA NA NA
## 1924 NA NA NA NA NA NA NA
## 1925 NA NA 1.0170583 NA NA NA NA
## 1926 NA NA 0.8786426 NA NA NA NA
## 1927 NA NA 0.9564270 NA NA NA NA
## 1928 NA NA 1.2053856 NA NA NA NA
## 1929 NA NA 0.9322388 NA NA NA NA
## 1930 NA NA 1.2913903 NA NA NA NA
## 1931 NA NA 1.3855434 NA NA NA NA
## 1932 NA NA 1.2254023 NA NA NA NA
## 1933 NA NA 0.8154324 NA 0.5320731 NA NA
## 1934 NA NA 0.1342660 NA 0.5722234 NA NA
## 1935 NA NA 0.6390116 NA 0.5628856 NA NA
## 1936 NA NA 1.0783826 NA 0.6024778 NA NA
## 1937 NA NA 1.3563587 NA 1.4876967 NA NA
## 1938 NA 1.2464116 1.6839393 NA 1.3865135 NA NA
## 1939 NA 1.5857943 0.5569082 NA 1.6174123 NA NA
## 1940 1.6340225 0.7629972 0.7842396 1.7284837 1.9230935 NA NA
## 1941 1.0205755 0.6250809 0.7427858 1.2429935 1.4845272 NA NA
## 1942 0.7134774 0.7769408 0.8497922 0.9178690 1.2737213 NA NA
## 1943 0.7150344 0.7775903 1.1817119 0.8205520 1.0047633 NA NA
## 1944 0.9218880 1.0997309 0.3414873 0.9502594 1.0471403 NA NA
## 1945 0.2123826 0.3215015 1.4581343 1.0046285 1.1926772 NA NA
## 1946 1.1468501 1.2295315 1.3951192 1.0232665 1.1518276 NA NA
## 1947 1.0176922 1.1584795 0.1790537 0.7908119 0.8478839 0.8890237 NA
## 1948 0.9741554 1.1946327 1.3677877 0.8475533 0.7926534 0.8497288 NA
## 1949 0.4876999 0.6688725 0.8230746 0.5118015 0.4752552 0.2291915 NA
## 1950 1.0815606 1.0520006 1.0480656 0.7159949 0.6639120 0.6164022 NA
## 1951 1.0688724 1.2068523 1.2260044 0.6853607 0.6177333 1.1295016 NA
## 1952 1.5418201 1.4670308 1.5400800 1.0252295 1.0565301 1.4524798 NA
## 1953 1.2418790 1.2383296 1.2360876 0.8260646 0.6803655 0.7962995 NA
## 1954 0.7963029 0.9503008 0.6658545 0.4122481 0.1747929 1.4626943 NA
## 1955 0.9777666 0.9864100 0.7631416 0.8792392 0.6665424 1.6928749 NA
## 1956 0.8984699 0.8480343 1.2507386 0.8276930 1.2039859 1.4607224 NA
## 1957 0.8600205 0.8828534 1.1795422 1.1320923 1.0582236 1.1459777 1.4043363
## 1958 1.1766296 1.0652454 1.0379641 0.8449865 0.7330934 1.3719718 1.2390087
## 1959 1.7957316 1.1083762 1.1165293 1.3964519 1.3612300 1.1253858 1.2715150
## 1960 1.4905529 0.8810342 1.0460686 1.1616946 1.0821064 1.1270853 0.9553145
## 1961 1.3085216 0.8937408 0.8253893 1.2086623 0.8013721 0.8326499 0.7887387
## 1962 1.1003425 0.9288562 0.9739499 1.0789165 0.6782776 0.8732508 0.6534657
## 1963 0.7743045 0.7488124 0.6597783 0.9824162 0.6812979 0.6293505 0.6175017
## 1964 0.9726674 0.9772571 0.4342418 0.9106260 0.6422371 0.5790659 0.6857878
## 1965 0.7037580 0.7856414 0.6052059 0.8353722 0.8930010 0.5358314 0.5013265
## 1966 1.1180849 0.9711251 1.1141416 1.2417028 1.5258440 0.7789665 0.7454842
## 1967 1.2179554 1.3031901 1.8235736 1.5237588 1.4710438 1.4024806 1.0527461
## 1968 0.8046716 1.0235492 1.3677942 1.4222093 1.4033171 1.1564479 1.1418651
## 1969 0.7861214 0.9833096 1.0956706 1.4936542 1.3519687 0.9399299 1.0834783
## 1970 0.6896384 0.8450002 1.1193200 1.1110601 0.9612355 0.9018322 1.0761562
## 1971 0.8346826 1.5050162 1.1477140 1.2299770 1.1026054 1.2141840 1.2947680
## 1972 0.7033176 1.5089778 1.0505212 0.7727341 1.0148028 0.8804526 1.0258531
## 1973 0.5788108 0.8958469 0.8781767 0.8138131 0.8935445 0.6295638 0.7273423
## 1974 1.0362315 0.9941237 1.2707162 0.9172328 1.0206568 0.7636414 0.9489120
## 1975 1.2403612 1.0068645 1.2215353 1.7078850 1.0076667 0.7906130 1.1628123
## 1976 0.9185497 1.0063214 0.9524997 1.1830719 0.7819273 0.7603888 0.9870874
## 1977 1.3017882 0.9667928 0.7519751 1.2420349 1.1109523 0.9211688 1.1014847
## 1978 1.1911775 1.1534560 1.0953602 1.0633882 1.2492132 1.3023278 1.5293272
## 1979 0.6843252 0.6216558 0.7181395 0.5977913 0.6171379 0.7065897 0.8646330
## 1980 0.9557199 1.0039651 1.2114436 0.6974564 0.8242295 1.1341663 1.0654511
## 1981 0.8661300 0.9384300 0.9704908 0.6799622 0.8679854 1.0284017 0.9118729
## 1982 1.0086479 0.9795454 1.0360310 0.7630343 0.9318259 1.0106287 0.9542553
## 1983 0.9759283 1.1303157 1.0268010 0.5544593 0.8597005 1.3414546 1.1575410
## 1984 1.0049101 1.1353563 1.0696778 0.6847231 1.1249226 0.9364038 0.8966751
## 1985 0.9058104 1.0167727 0.8522761 0.8422416 1.1207139 1.0935256 1.0830709
## 1986 0.7238325 0.7119643 0.6274352 0.4732509 0.7297676 0.8323092 0.8536343
## 1987 0.6777287 0.7304793 0.5751837 0.6507762 0.7992585 0.9095172 0.8420869
## 1988 1.0941575 0.8160021 0.8641596 0.9311542 0.9096675 1.1408106 1.1240544
## 1989 1.0375718 0.9654536 0.7775138 1.0955384 0.9651746 1.1774994 1.2914265
## 1990 1.1916000 0.8516148 0.8832142 1.3898425 1.4056040 1.2446366 1.1096966
## 1991 0.8891672 0.6050893 0.6987945 0.9627552 0.9935410 0.9927637 1.0429932
## 1992 1.1649091 0.7921167 0.9808070 1.4596704 1.3254608 1.1266516 1.1146937
## 1993 1.2050749 1.1352151 1.1477056 1.3844641 1.1710543 1.0171530 0.9684442
## 1994 1.0591590 1.0852530 0.9635234 1.2000621 1.1946589 0.8845972 0.8509949
## 1995 1.3512269 1.3809895 1.1045803 1.5878725 1.2853831 0.8940321 0.8609161
## 1996 1.1077814 0.9927400 1.0082244 1.3441901 1.4406540 1.1137279 1.0599273
## 1997 1.3159422 1.1806428 1.0789652 1.3735444 1.3946956 1.0889204 1.1343147
## 1998 1.1965159 1.4047054 1.1463808 1.0510875 1.1196830 1.1275267 1.0431586
## 1999 1.1459447 1.0895875 0.8344604 0.6894233 0.8198533 0.9345055 0.9160242
## 2000 0.8445487 0.8983984 1.0250947 0.6880845 0.9548929 0.8070965 0.9180177
## 2001 0.7916326 0.7279482 0.7775328 0.6565448 0.7480738 0.9477708 0.9572395
## 2002 0.9331116 0.7681999 0.9375782 0.6207373 0.9954267 0.9748542 1.0632915
## 2003 0.7087790 0.8429420 0.9365621 0.6359938 0.8732910 0.8790972 0.9275882
## 2004 0.9379452 1.0706488 1.1251990 0.9641985 0.9982423 1.1068972 1.1028765
## 2005 0.8111298 1.0449564 1.0154027 0.7992988 0.6053431 0.8685232 0.7467335
## 2006 0.8405313 0.9748420 1.0769415 1.0875780 0.8708013 0.9062888 0.9649220
## 2007 1.2781679 1.4552158 1.5738330 1.9090696 1.1276422 1.2886989 1.2789280
## AR04NE AR06SW AR06W AR07SE AR07E AR07NW AR08S
## 1921 NA NA NA NA NA 0.41639781 NA
## 1922 NA NA NA NA NA 0.45642593 NA
## 1923 NA NA NA NA NA 0.63695466 NA
## 1924 NA NA NA NA NA 0.92952572 NA
## 1925 NA NA NA NA NA 0.83056435 NA
## 1926 NA NA NA NA NA 1.52417334 NA
## 1927 NA NA NA NA NA 1.11137010 NA
## 1928 NA NA NA NA NA 1.45501922 NA
## 1929 NA NA NA NA NA 1.01081468 NA
## 1930 NA NA NA 0.5227284 NA 0.05877079 NA
## 1931 NA NA NA 1.2582426 NA 0.47128571 NA
## 1932 NA NA NA 0.9736192 NA 0.03261041 NA
## 1933 NA NA NA 1.1956032 0.85260574 0.19662848 NA
## 1934 NA NA 1.31563027 1.0564542 0.07930056 1.72707270 NA
## 1935 NA NA 0.90943907 0.3764080 0.39164392 2.93620442 NA
## 1936 NA NA 0.75294225 0.5636412 0.08402553 1.69564682 NA
## 1937 NA NA 1.24214292 1.7388803 1.28750196 1.17712900 NA
## 1938 NA 1.1817565 1.68359509 2.0634416 2.16630660 1.53270255 1.1269894
## 1939 NA 1.0104959 1.26340782 1.5217205 2.21575760 1.03366946 0.9165091
## 1940 NA 0.8962603 0.99799498 1.1241821 2.22345456 1.23308788 0.9982532
## 1941 NA 0.6893504 0.70404832 0.7853706 1.48611583 0.07242166 0.6542935
## 1942 NA 0.7478950 0.53339633 0.8441301 0.90984256 1.31078626 0.8593125
## 1943 NA 0.8862646 0.71485286 0.7354338 0.88543568 0.24876438 0.8679350
## 1944 NA 0.1661752 0.04975625 0.8197338 0.98463352 1.18179140 0.1064034
## 1945 NA 1.0791059 1.13786994 0.1137092 0.13858256 0.13580139 0.9454192
## 1946 NA 1.9875559 1.48999082 0.9081541 1.10491627 1.90764471 1.1738959
## 1947 NA 1.8068896 1.51902674 0.8564233 0.73295411 2.21131079 0.2568493
## 1948 NA 0.5096679 0.53264329 1.0208631 0.72645137 0.95094783 1.1879613
## 1949 NA 0.1505164 0.06787324 0.4289927 0.40320900 0.17294717 0.3826112
## 1950 NA 0.6624126 0.76832138 1.0602273 0.90284209 1.47243214 1.0002874
## 1951 0.8539598 1.2398170 1.08594851 0.8485492 1.25728015 1.52268658 1.7579843
## 1952 1.1959223 1.9066170 1.53170730 1.0910513 1.22737575 1.34352731 2.2337972
## 1953 0.9436128 1.1157746 1.06705347 0.9170583 1.05893658 1.17533573 1.3065221
## 1954 0.9263758 0.9590391 0.97220950 1.1245481 0.83205545 1.27049506 0.6967011
## 1955 1.0062430 1.2114750 1.02038168 1.3384466 1.00843405 1.15699668 1.3931124
## 1956 0.9257664 1.0053790 0.78966271 1.4453645 0.93054836 1.04789187 1.1642398
## 1957 0.9417492 1.4273074 0.87141913 1.3681104 0.75040882 0.37670422 1.3154928
## 1958 0.9237739 1.2933908 0.93998329 0.9835174 0.63084424 0.39970480 1.3613430
## 1959 0.8113244 1.3715869 1.39870599 0.8878083 0.66216566 0.58305428 1.7713559
## 1960 1.2946532 1.0513486 1.45084178 1.1492752 1.02076003 0.66644800 1.5138046
## 1961 1.3277630 1.1537585 1.38274740 1.2363454 1.48668351 0.80201432 0.8102404
## 1962 1.0136601 1.0577350 1.38695086 0.8885454 1.38474495 0.75430534 0.7387691
## 1963 0.9181157 0.7876309 1.00032977 0.8600018 0.97581453 0.63749787 0.7402384
## 1964 1.3053121 0.7225927 1.00596260 1.0153249 1.10889618 0.97615178 0.6413125
## 1965 1.0048159 0.5989590 0.83750214 1.0947118 0.98566372 0.87955355 0.5251825
## 1966 1.0490556 0.7920567 1.01420447 1.2138479 1.18410234 0.92908702 0.8226154
## 1967 1.1519466 1.0961390 1.21853176 1.3241474 1.63964702 1.19182912 0.8757776
## 1968 0.9758552 0.8047915 1.26392951 0.8363921 1.21206052 0.96946681 0.9471899
## 1969 0.9811674 0.8456966 1.25599395 0.9388979 1.06765014 1.04700863 0.7122482
## 1970 0.9540569 0.6786464 0.79820125 0.8432474 1.03061635 1.20743486 0.7638651
## 1971 1.0301154 0.9122417 0.79642398 1.1235736 0.96825004 1.05686325 0.6991852
## 1972 1.0515351 0.9149263 0.76851924 0.9028735 0.88546627 1.17192355 0.6887812
## 1973 0.7670101 0.7651153 0.51536593 0.7394983 0.61583208 0.86680162 0.6608061
## 1974 0.9287152 0.7650275 0.52925181 0.9506679 0.70859310 0.89332901 0.8145017
## 1975 0.7858188 0.8623147 0.74778447 0.7727002 0.78278691 1.14463649 0.9142359
## 1976 0.4413137 0.5315180 0.73551288 0.8072124 0.71150467 0.95356838 0.6323886
## 1977 0.8267129 0.6817231 0.72690917 0.9277297 0.97391628 1.00707312 1.1538564
## 1978 0.8945950 0.7726531 0.77450810 1.4407732 1.11989252 0.94423662 1.1833516
## 1979 0.8561938 0.5288356 0.48004277 1.0213629 0.67443062 0.57950332 1.1268877
## 1980 1.3039042 1.0263471 1.17289882 1.3138382 0.90088854 0.76753839 1.5818327
## 1981 0.9279842 0.9061796 1.10042987 1.1441723 0.64988159 0.55880064 1.2018054
## 1982 0.8198411 1.4475326 1.39632997 1.3411781 0.62618985 1.22384118 0.8571504
## 1983 1.0798603 1.2615179 1.00813682 0.8462615 0.93158363 1.18628843 0.9983394
## 1984 1.0774997 1.3542961 1.16929606 0.8691637 1.03367432 1.11804947 0.9654554
## 1985 0.8344282 1.2318552 1.59888290 0.7380030 1.21352681 1.25270055 0.6957474
## 1986 0.7211752 0.7989602 1.00973868 0.6020446 1.08265898 0.96371994 0.9899920
## 1987 1.0738875 0.8450085 0.74933512 0.5823837 1.05943501 1.11245444 1.3239666
## 1988 1.3537070 1.0169480 1.19211480 1.1003696 1.20366214 1.25660177 1.1320003
## 1989 1.3471924 0.7506007 0.91020066 0.8569309 0.97022944 0.89378075 0.8780724
## 1990 1.0828605 0.9732762 1.00551507 0.8207518 0.99211439 0.92798161 0.7426062
## 1991 1.2506185 0.6890310 1.23958740 0.7357664 0.77758538 0.32908284 0.7507913
## 1992 1.2674433 0.8677869 1.66040728 0.9877703 1.17273948 1.12771025 1.0769634
## 1993 1.0688615 1.2328307 1.37443796 1.2393004 1.08209277 1.18094665 0.8910859
## 1994 1.1140309 0.9637138 1.06562356 1.1184612 1.13974048 1.20025788 0.9772802
## 1995 1.0895864 1.0704215 1.09279386 1.0904879 1.07258119 1.34006572 0.8666894
## 1996 0.9779664 1.3761269 1.15323412 1.2672032 1.12035770 1.30681003 1.2564104
## 1997 1.0508162 1.1654770 1.20161790 1.1818457 1.53671918 1.30120678 1.3529615
## 1998 0.9166988 1.2556597 1.05911940 1.2697024 1.41561686 1.18711016 1.3201844
## 1999 0.7865076 1.1618552 0.78313366 0.8651427 1.10078742 1.03420594 1.2499054
## 2000 0.8950304 1.1501606 0.78913506 0.9248841 1.25734389 0.83026925 1.0472109
## 2001 0.7471096 1.1165974 0.71395347 0.7034766 0.87740532 0.80365156 0.8981007
## 2002 0.8193373 1.2121264 0.76744530 0.8214508 1.00598511 0.78326174 0.8192607
## 2003 0.8783154 1.0192794 0.97639867 0.8920649 0.94459121 0.72637706 0.9435991
## 2004 1.2894648 0.9617521 0.96447269 1.0602537 0.89200871 0.82973653 1.0777343
## 2005 0.8051290 0.7264192 0.58145433 1.0109909 0.57289016 1.09072191 0.7687638
## 2006 0.8975946 1.1042695 0.58264314 0.9657655 0.73782405 0.92222138 1.1446563
## 2007 1.2131331 1.3170363 0.96760815 1.7002912 0.89049371 1.21311166 0.8953863
## AR08E AR09W AR09N AR10N AR10NE AR11NE AR11E
## 1921 NA NA NA NA NA NA NA
## 1922 NA NA NA NA NA NA NA
## 1923 NA NA NA NA NA NA NA
## 1924 NA NA NA NA NA NA NA
## 1925 NA NA NA NA NA NA NA
## 1926 NA NA 1.0808951 NA NA NA NA
## 1927 NA NA 1.2329014 NA NA NA NA
## 1928 NA NA 0.9010154 NA NA NA NA
## 1929 NA NA 1.0568369 NA NA NA NA
## 1930 NA NA 1.2705961 NA NA NA NA
## 1931 NA NA 1.0861881 NA NA NA NA
## 1932 NA 0.74347126 1.2016614 NA NA NA NA
## 1933 NA 0.69230629 1.0546348 NA NA NA NA
## 1934 NA 0.81436262 0.8321014 NA NA NA NA
## 1935 NA 0.94061263 0.7586861 NA NA NA NA
## 1936 NA 1.18757860 0.1711064 NA NA NA NA
## 1937 NA 1.22732874 0.7040168 NA NA NA NA
## 1938 NA 1.97856242 0.9273658 NA NA NA NA
## 1939 NA 1.34784396 1.2016352 NA NA NA NA
## 1940 NA 0.97050413 1.6839488 NA NA NA NA
## 1941 NA 1.16521207 0.6928098 NA NA NA NA
## 1942 NA 1.05523113 0.7861759 NA NA NA NA
## 1943 NA 0.94451335 0.7185702 NA NA NA 1.4148537
## 1944 NA 1.07765299 0.9906365 NA 1.4506472 NA 0.2814033
## 1945 NA 0.09983661 1.0234234 NA 1.4976640 NA 1.1664831
## 1946 NA 0.99267608 1.0758156 NA 1.3076946 NA 0.9285916
## 1947 NA 1.09690693 0.8565309 1.5183157 0.9765670 NA 0.1331459
## 1948 NA 1.18700527 1.1604802 0.5977268 0.4020687 1.2942980 1.1499772
## 1949 NA 0.37146691 0.4837636 0.1114835 0.0711414 0.4861813 0.4324493
## 1950 NA 0.59547448 1.5075509 0.7964019 0.5185485 0.9088266 1.6289766
## 1951 NA 0.68133480 1.2061205 0.8557476 0.6311842 1.7087559 1.8217928
## 1952 NA 1.24957936 1.0714756 1.2457164 1.0227322 1.4059584 1.6628024
## 1953 NA 1.11283334 0.8323880 1.2136826 0.9531291 0.4677614 0.6454853
## 1954 NA 0.83591590 0.7453878 1.1403813 0.9987655 0.7654216 0.8486563
## 1955 0.9995221 1.13034488 0.9465495 1.3441626 1.2274540 0.8127801 0.9507553
## 1956 1.2242752 0.94047010 0.9124226 1.7681871 1.7072051 0.9583338 0.9696301
## 1957 0.7843453 1.01788075 1.2370261 1.0302742 1.0367193 1.0918830 0.9105386
## 1958 0.8489788 0.92061412 0.9845689 1.0176412 1.3013850 1.1085352 1.1025108
## 1959 1.0786444 1.07475811 1.4574590 1.1558175 1.2925335 1.0384595 1.4900762
## 1960 1.2981335 0.81960414 1.0550281 1.1249843 1.2995612 0.8734397 0.9284569
## 1961 1.3486758 1.38642721 1.2390693 0.6658986 1.0555553 0.9637561 1.1501658
## 1962 0.7180610 1.08605491 1.1058526 1.1284365 0.8529051 0.9218133 0.9075965
## 1963 0.8879246 1.13201235 0.8523553 0.9166362 0.7143766 0.8816415 0.8547662
## 1964 1.1422190 1.02770847 1.0442803 0.8388537 0.6976941 0.9230369 0.8684364
## 1965 0.6735422 0.84385305 0.8898254 0.8147929 0.7420628 0.7892733 0.7661989
## 1966 1.3165063 1.05313932 1.0670713 0.9266445 0.9482242 1.1591884 1.2836658
## 1967 0.9418802 1.19248905 1.2906107 1.0901870 1.0601682 1.3450142 1.3589726
## 1968 0.7209457 0.88817389 0.9946383 0.9729251 0.8845955 1.1082755 0.8902336
## 1969 1.0341259 1.01714153 1.0545388 1.0095983 1.0865815 1.2448429 1.0640459
## 1970 0.8811351 0.99961730 1.1345855 0.6327466 0.9425460 0.8721578 0.7409017
## 1971 1.0493622 1.02703586 1.1865437 0.7473135 1.0828953 1.2147665 1.0150805
## 1972 0.8798131 1.11844990 1.0494865 0.6328008 1.0238582 0.8026463 0.8370777
## 1973 0.9489034 1.05783496 1.0271162 0.6171782 1.0318001 1.0224135 0.7909584
## 1974 0.8858430 1.12371910 1.0938856 0.9815025 1.2686554 0.9289812 0.7711405
## 1975 0.6707906 1.07562100 0.9963034 1.2368561 0.9946909 1.0245926 0.9009067
## 1976 0.5407412 0.45627889 0.3918445 0.8615622 0.6617864 0.7824843 0.6615369
## 1977 1.0375172 1.35799255 1.5873912 1.3231388 1.0116322 1.1992395 1.0738954
## 1978 1.1815838 1.33028509 1.1454159 1.8052432 1.2365503 0.9281392 0.9543840
## 1979 0.8632628 0.85161946 0.7582840 0.9740535 0.7757732 0.8945456 1.0482911
## 1980 1.5877045 0.96778287 1.1396772 1.1855248 1.1947387 0.9704402 1.2177444
## 1981 0.9039034 0.83919404 0.6670787 0.9800081 1.0059355 0.8505341 0.7484327
## 1982 0.7952037 0.96948846 0.8509959 1.0876355 1.2678164 1.1835721 1.1857603
## 1983 1.0761817 0.86381375 0.7878299 1.1990253 0.9597939 1.1784642 1.0748434
## 1984 1.3378182 1.02290853 0.9466977 1.0479651 0.8260246 1.2730833 0.9350481
## 1985 1.1787959 0.96279716 0.7188456 0.7352820 0.8151794 1.0238935 0.9458070
## 1986 1.1525297 0.86571320 0.6014090 0.6143901 0.7234955 0.7363540 0.9448697
## 1987 1.3904984 0.86044481 0.6329298 0.5475143 0.7492853 0.9233591 0.8894266
## 1988 1.4252459 1.27340744 1.1146875 0.6784098 0.8574076 0.8206781 1.0906299
## 1989 0.7685949 0.84466476 0.5881527 0.6790869 0.8763770 0.7489491 0.8255951
## 1990 0.8638258 1.02800002 0.5994140 0.7890651 1.1685636 1.0736933 1.1687516
## 1991 0.9798777 0.85583372 0.6506032 0.7763425 0.9604470 0.9579700 1.0461393
## 1992 1.0638280 1.27059729 0.9576442 1.1098515 1.2092281 1.1173804 1.0030504
## 1993 0.8612827 1.25791211 1.2828295 1.3307894 1.5045976 0.9892020 0.9873345
## 1994 0.5738163 0.95799736 0.7420794 1.2641841 1.1898034 0.7463089 1.0570450
## 1995 0.5084655 0.90241251 0.8994465 1.5183480 1.1568293 1.2015538 1.6302389
## 1996 0.9711242 0.94722854 1.2031645 1.3054903 0.9501863 1.0993202 1.1419588
## 1997 1.1667359 0.96736330 1.1360593 1.2011156 0.9997695 1.2471929 1.2595318
## 1998 1.7181428 1.26260386 1.4621463 1.2750250 1.1273003 1.1129233 1.1233348
## 1999 0.9834956 0.97363716 1.1375269 1.2395188 0.9781178 1.2638350 1.0835009
## 2000 0.9588326 0.79190200 0.5211471 1.0484325 1.1207516 1.0980140 0.9304774
## 2001 0.4381195 0.67642206 0.6931960 0.8454442 1.2040278 0.8618342 0.8582721
## 2002 0.7656577 0.73065439 0.8489389 0.7229454 0.8066169 0.6918501 0.6133593
## 2003 0.8174420 0.88198649 1.1564613 0.9153334 0.9787628 1.0083538 0.8910241
## 2004 1.3007199 1.43896800 2.2131922 1.1032630 1.2349103 0.8738602 0.9655600
## 2005 0.9338996 0.84364562 0.6774938 0.6975893 0.7077010 0.5511132 0.5339691
## 2006 1.2153433 0.88193760 1.4994845 0.7380527 0.6609806 1.1554221 1.0431135
## 2007 1.2038315 1.70790238 3.8541632 1.0259768 0.8481556 1.3026207 1.1889876
## AR12E AR12SE AR13SE AR13S AR14S AR15E
## 1921 NA NA NA NA NA NA
## 1922 NA NA NA NA NA NA
## 1923 NA NA NA NA NA NA
## 1924 NA NA NA NA NA NA
## 1925 NA NA NA NA NA NA
## 1926 NA NA NA NA NA NA
## 1927 NA NA NA NA NA NA
## 1928 NA NA NA NA NA NA
## 1929 NA NA NA NA NA NA
## 1930 NA NA NA NA NA NA
## 1931 NA NA NA NA NA NA
## 1932 NA NA NA NA NA NA
## 1933 NA NA NA NA NA NA
## 1934 NA NA NA NA NA NA
## 1935 NA NA NA 0.7560844 NA NA
## 1936 NA 0.8398121 NA 0.9434279 NA NA
## 1937 0.0003911708 1.1546384 NA 1.0835949 NA NA
## 1938 2.2746896389 1.3786943 NA 0.9177126 NA NA
## 1939 1.1760577548 1.6355570 NA 0.9905708 NA NA
## 1940 0.6702471887 1.1641816 NA 1.2434689 NA NA
## 1941 1.2534998578 0.6146186 NA 0.8606444 NA NA
## 1942 1.3280343929 1.1610293 NA 0.6473154 NA NA
## 1943 1.2088234687 1.0028738 NA 0.7127874 NA 1.52956832
## 1944 1.0517998290 0.7808078 NA 0.9160783 NA 0.53123588
## 1945 0.9681460811 0.6082650 NA 0.3738689 NA 1.77238409
## 1946 0.9259357968 0.8802506 NA 0.4146348 NA 0.66542555
## 1947 1.0331121429 0.7714830 NA 1.3458000 NA 0.25067621
## 1948 0.4728843691 1.1173906 NA 2.2879592 0.72675976 1.39368229
## 1949 0.5591845222 0.5808614 NA 0.6581544 0.06433202 0.15613334
## 1950 0.2488317252 0.8200788 1.1842050 1.0376713 0.99527834 2.07941394
## 1951 0.7012020488 0.7528478 0.7990773 1.2047092 1.80533066 2.01207208
## 1952 0.8099560025 0.9097992 1.6669000 2.0293783 1.73851391 0.09192864
## 1953 1.7136223537 0.9985312 0.7207483 0.6902354 1.00505482 1.08894510
## 1954 1.4276107153 0.9436805 0.9945521 0.9671674 0.81678339 1.16344401
## 1955 0.8241943924 0.6485783 0.5077440 0.7692404 1.40671885 1.68975963
## 1956 0.4856525167 0.4783622 0.7494912 0.7872793 1.14850827 0.26980989
## 1957 0.7938957146 0.6490491 0.8847201 1.2876445 0.97175112 0.51610819
## 1958 1.1034645477 1.0029898 0.9437571 1.6313743 0.90654370 0.58400390
## 1959 1.4484892476 1.2133532 1.1453624 0.9238662 0.97498631 0.73341890
## 1960 1.2099161017 1.3182656 1.0811182 0.8401524 0.97143743 0.55583693
## 1961 1.2149613834 1.6423930 0.9444501 0.7798037 1.23823725 0.65908619
## 1962 1.0768201888 1.0336688 0.9262171 1.1044750 0.85208653 0.72690069
## 1963 0.7589824849 0.5344573 1.2434501 1.0202090 0.71826001 0.91053956
## 1964 0.6581333795 1.0765188 1.3274194 1.0583150 0.70531161 1.14306556
## 1965 1.0132184296 1.3675668 0.9475698 0.9034122 0.61235869 0.73262113
## 1966 1.4968420731 1.8513033 0.8820649 0.8104347 1.00870691 1.45303521
## 1967 1.1156765736 1.4083062 1.2807493 1.0968643 1.01949538 1.34778298
## 1968 0.9532628001 0.9147732 0.8795533 0.7128036 1.03148779 0.86807729
## 1969 0.8879642262 0.9924382 0.9722687 0.6341678 1.20382269 1.10035966
## 1970 0.9919737564 0.9188901 0.9042119 0.6261625 0.96926793 1.10522998
## 1971 1.0034224751 0.9628992 1.8030815 2.3451667 1.03357996 1.14814152
## 1972 0.6059368671 0.7678009 1.2116855 1.4194453 0.80897127 0.87586567
## 1973 0.5998575235 1.0603429 0.7237650 1.0366612 0.73085820 1.00967893
## 1974 1.0948628549 1.2131562 0.8650791 1.0285950 0.78990390 0.87217676
## 1975 0.8989172586 0.8953216 0.8504837 1.1510812 0.95952521 0.74207317
## 1976 0.8216927595 0.7305996 0.6879123 0.6932537 0.74371896 0.51331392
## 1977 1.9819545862 1.2724879 1.0243579 0.8360630 1.75208291 1.47764877
## 1978 2.0255673742 1.3159341 0.9101324 0.6926711 1.19056345 1.80057136
## 1979 0.9959818793 0.7023060 0.6229350 0.5760954 1.07243870 1.30434739
## 1980 1.1541236801 1.0445516 0.9140926 0.8858790 0.82533969 1.70120002
## 1981 0.7088708739 0.5090844 1.0653691 0.6180344 0.75727501 1.04441852
## 1982 0.9079608597 0.9364303 0.9720831 0.7558837 1.02643766 1.02299146
## 1983 0.9109761458 1.1854760 1.2206963 1.0073650 1.23998570 1.37920907
## 1984 0.8256790154 1.1206505 1.1380003 1.0023629 1.14623047 0.90099501
## 1985 0.8463345141 1.0171814 1.0977622 0.7889109 1.16027630 0.88982598
## 1986 0.8109866988 1.0082063 0.7642188 0.5402439 0.80803228 0.69169788
## 1987 0.7533431945 0.8775229 0.7477743 1.0475006 0.75230384 1.01726030
## 1988 0.9409964489 0.9725233 0.9661959 1.3016695 1.04692301 0.96925751
## 1989 0.5831853360 0.5182062 0.4541775 1.0308924 0.68056078 0.76704809
## 1990 1.0754892543 0.5910967 0.6743672 1.0214330 1.05043972 0.73639752
## 1991 0.9884686044 0.7824417 0.7753171 0.8976138 0.92408374 0.74573622
## 1992 1.1404161292 1.2694936 1.3079843 1.1405881 1.17618850 1.04846718
## 1993 1.2286759472 1.0811643 1.2270711 1.0005854 1.04778860 0.98765500
## 1994 1.2154761133 1.0727614 1.2643421 1.0103377 1.07702102 0.77736342
## 1995 0.9956841092 1.6101709 1.3124730 1.1067843 1.09415206 0.79536974
## 1996 0.9603053174 1.2369163 1.0352235 1.0275190 0.91591733 0.74922344
## 1997 1.0530677557 1.6128805 1.3745243 1.2650477 1.29875568 0.98519162
## 1998 1.2291754666 1.5891710 1.2212040 1.3273317 1.21194402 0.81622055
## 1999 1.0145674513 1.0807502 1.0265849 1.0844242 1.10382294 0.84277538
## 2000 1.0966018712 1.0482856 1.1991952 1.3384383 0.96655550 0.91765579
## 2001 0.6751536618 0.5967024 0.9930798 0.6674051 1.00182971 0.40337062
## 2002 0.7714238471 0.6993962 0.6790952 0.8784130 0.86353607 0.99342231
## 2003 0.9728377028 0.7397033 1.0711323 1.2182036 1.06102930 1.36813972
## 2004 1.2333165712 1.0508710 1.2455341 1.2113293 1.10114349 1.25647492
## 2005 0.7973040251 0.6087965 0.3813473 0.6063414 0.72373578 1.55213166
## 2006 0.7876033382 0.6988984 0.7942970 0.9872878 0.83493017 0.99863318
## 2007 1.3447131885 1.1166781 1.4556218 1.8496329 NA 2.51964589
## AR15N AR16W AR16N AR19S AR20E2 AR21N
## 1921 NA NA NA NA NA NA
## 1922 NA NA NA NA NA NA
## 1923 NA NA NA NA 0.18620276 NA
## 1924 NA NA NA NA 0.15994998 NA
## 1925 NA NA NA NA 0.20411265 NA
## 1926 NA 0.85532487 NA NA 0.43173978 NA
## 1927 NA 0.89557411 1.09486770 NA 0.56219477 NA
## 1928 NA 1.20045001 1.40974932 NA 0.85800196 NA
## 1929 NA 0.92515004 1.32998426 NA 0.96247116 NA
## 1930 NA 1.07606334 1.17038977 NA 0.82325874 NA
## 1931 NA 0.76016409 0.75814637 NA 0.88403406 NA
## 1932 NA 0.80126051 0.81521443 NA 0.74449528 NA
## 1933 NA 0.54767600 0.46475169 NA 0.52038308 NA
## 1934 NA 1.54065156 0.07129174 NA 0.93142387 NA
## 1935 NA 0.88583193 1.51215855 NA 1.65239971 NA
## 1936 NA 0.97886825 0.83324768 1.37010759 1.87442141 NA
## 1937 0.90531824 1.18490414 0.99616575 1.10632325 1.96164317 NA
## 1938 0.78161592 1.73881559 1.08918404 1.27946130 2.62192802 NA
## 1939 0.85422976 0.97503017 1.37740308 1.04482496 2.69611013 NA
## 1940 0.15256660 1.07681997 1.06820721 0.64339259 1.46569554 NA
## 1941 1.58350683 0.75437881 0.92607583 0.51039507 1.42006798 NA
## 1942 1.56360659 1.00706483 0.71170549 0.66104837 1.20820397 NA
## 1943 1.26124323 0.09203469 0.90326415 0.98615193 1.17434456 NA
## 1944 0.56330959 1.32782972 1.13528465 1.48616203 0.84369988 0.8342112
## 1945 1.54432409 0.39412680 0.15146673 1.15258545 0.96571188 0.9042393
## 1946 0.62653000 1.84523968 1.45542090 1.52268480 1.21701984 0.8090892
## 1947 0.18563649 1.62306782 1.22183557 1.42067316 1.19535297 0.8652283
## 1948 0.99154529 1.77878685 1.52259213 0.07407111 0.50768976 0.8350060
## 1949 0.06880214 0.26938785 0.41217651 0.41946417 0.08430473 0.5933435
## 1950 1.92088551 0.79794392 0.76678804 0.29467559 0.33312741 0.4079945
## 1951 2.05695132 1.37996431 1.19352330 0.64987304 0.48450299 1.2505195
## 1952 1.28604080 0.85167942 1.48183850 1.05297264 0.60528887 1.3558282
## 1953 1.13508594 0.70832804 0.97323231 1.27570709 0.55146247 1.0803106
## 1954 1.35645998 0.89452100 0.91240147 1.34099603 0.46093596 0.8860785
## 1955 0.75816995 1.13572058 1.26533686 1.11236956 0.84122230 1.3387840
## 1956 0.10681241 0.67456481 0.67320279 1.08374594 0.52897026 1.1833942
## 1957 0.89763384 0.94344618 1.10343637 1.31143621 0.78769097 0.5935526
## 1958 1.00087571 0.91447590 0.74175973 1.06778819 0.11890569 1.4898783
## 1959 1.64385508 1.24927230 1.55695070 0.89198148 0.80686221 2.0360690
## 1960 1.24646993 0.95474540 1.12652350 1.25913766 0.86125459 1.1424862
## 1961 1.41255994 1.54812160 1.59668924 1.37814396 0.67137006 1.2338519
## 1962 1.06299884 1.06281121 1.18731838 0.96058225 0.85197997 1.1089841
## 1963 0.95438135 1.01044810 1.18490743 0.63535051 0.90349206 0.7677677
## 1964 0.93923295 0.76988524 0.72951734 0.58809778 1.15979688 1.2178024
## 1965 0.61464436 0.61414587 0.74587328 0.66232640 1.04555584 0.9270744
## 1966 1.24044280 1.23140712 0.96921868 1.12273792 1.11627170 0.7847477
## 1967 1.20803720 1.05084240 1.13889122 1.25528703 1.30407952 0.9920453
## 1968 0.92316413 0.96309027 0.93027344 1.33064024 1.01038150 0.7596345
## 1969 1.02875829 1.10104321 1.07953005 1.45915669 0.70166951 0.8622995
## 1970 0.77750163 0.79598685 0.68371677 1.40775871 0.91095634 0.9016811
## 1971 0.78635054 0.90265031 1.21544296 1.62132248 1.30835435 0.9509939
## 1972 0.69009818 0.76521717 0.81257009 1.21931284 1.08311692 1.0220523
## 1973 0.78733213 0.92154617 0.88857528 1.02169119 0.77779337 0.9984501
## 1974 0.69205428 0.73626440 0.90450913 1.05303668 1.38804743 0.9959912
## 1975 0.64265058 0.78507701 0.78021679 0.79859001 1.01537242 1.0510097
## 1976 0.54919324 0.63627084 0.45636981 0.36281658 0.66375214 0.6246972
## 1977 0.59244012 1.35948229 1.14083908 0.79811189 0.86600632 0.8719540
## 1978 1.13927997 0.95796024 1.27212404 0.95559295 0.83410017 0.8693913
## 1979 1.19515984 0.99869476 1.15773965 0.50117564 0.72967535 0.5655863
## 1980 1.65056611 1.03863487 1.33237481 0.45884617 0.73435165 1.0352574
## 1981 0.90128980 0.99954816 0.84677179 0.41448461 0.56543318 0.7849193
## 1982 0.88358970 1.07979057 1.09074975 0.76135542 0.64073943 0.9117100
## 1983 1.27235504 1.41998052 0.89788483 1.39593836 1.12717778 1.3278576
## 1984 1.14843300 1.17680736 0.84683606 1.65594206 1.04400374 1.2046367
## 1985 0.97066306 1.07654318 0.80659811 1.30064365 1.01004115 0.6974564
## 1986 0.79262542 0.83013906 0.53411810 0.67632834 1.07591125 0.1628248
## 1987 0.91503270 0.98821214 0.74438584 0.60016555 0.80161910 0.5389673
## 1988 1.19163597 0.96196208 0.95216285 0.57295064 2.08310336 0.9831994
## 1989 1.16964395 0.90138928 0.95487340 0.52290270 0.87801731 0.7315669
## 1990 1.05000693 1.07910313 1.01190541 0.50585311 0.86076420 1.1742868
## 1991 1.01361943 0.78262953 0.81631697 0.86321152 0.89763356 1.0799273
## 1992 1.24561565 1.18967280 1.17068217 0.80725370 0.98427937 1.2687361
## 1993 0.83630009 1.19060865 1.04036704 0.88208979 1.24040051 1.5951739
## 1994 0.90466509 0.87708538 0.70472674 0.86783333 1.43650064 1.1979857
## 1995 1.05343869 0.95392791 1.04220392 1.30020443 2.13253392 1.2650170
## 1996 1.05590430 0.97018325 0.95423538 1.57081100 1.18387506 1.2938533
## 1997 1.14728869 1.11026879 1.21712960 1.85931637 1.30410719 1.2130083
## 1998 0.84681437 1.57467461 1.33465572 1.67559958 1.19540640 1.1116366
## 1999 0.99361743 0.82051866 0.88815357 1.13472324 1.29453586 0.9807479
## 2000 0.89547306 0.87323232 0.76122807 0.84389652 0.80974006 0.9840621
## 2001 1.01778135 1.07792856 1.11083674 0.93884511 0.94743300 0.8753517
## 2002 0.97052018 1.06358811 0.96959879 0.58758802 0.33757294 0.9826424
## 2003 0.80147326 0.68907461 1.04725455 0.68655766 0.74964304 0.8750390
## 2004 1.11511792 1.26615817 1.42757183 1.15343596 1.17469044 0.9209848
## 2005 0.79399795 0.77421303 0.95125117 0.86049684 0.83230419 0.7708781
## 2006 1.23248919 0.79199891 0.92811232 1.06079879 0.93408235 0.9531021
## 2007 1.16277745 1.11009754 1.21976216 1.21343635 0.60545903 1.15973736) Identificación de árboles con múltiples series
jt.ids <- read.ids (jt, stc = ("auto"))stats<-rwi.stats(detr_jt, jt.ids, prewhiten=TRUE)7) Construcción de la cronología estandar (con los datos estandarizados)
chron.detr <- chron(detr_jt, biweight = TRUE, prewhiten = TRUE)- Prewhiten se refiere a un proceso utilizado para eliminar o reducir la autocorrelación en una serie de datos dendrocronológicos antes de realizar análisis posteriores, como la detección de cambios temporales o la modelización del crecimiento de los árboles.
Garantiza la validez de análisis posteriores (porque muchos métodos asumen independencia de los datos)
La autocorrelación es la correlación de una serie de datos consigo misma a medida que se desplaza en el tiempo. En dendrocronología, puede haber autocorrelación en las series de ancho de anillos de los árboles debido a factores como el clima o las condiciones ambientales
El biweight es utilizado en dplR para el cálculo de estadísticas como la media del ancho de anillos y la desviación estándar, con el fin de reducir la influencia de valores anómalos o atípicos y obtener estimaciones más robustas de los parámetros dendrocronológicos
plot.detrend <- plot.crn(chron.detr,
xlab="Años",
crn.line.col = 'seagreen',
samp.depth.col = 'lightyellow')
- El eje de la izquierda junto a a la línea verde indican la media de las medidas de los datos estandarizados mientras que la línea amarilla.
- El eje de la derecha junto a la línea amarilla indican el número de muestras en cada año para realizar la media
- La gráfica de arriba está construida a partir de los datos estandarizados
- La gráfica de abajo está construida a partir de los residuos, en la que se elimina la autocorrelación (relación que hay entre un año y el siguiente)
8) Generación de datos a partir de la serie AR12SE del grupo 2 de Arlanza
A continuación se indican los scripts usados para la generación de datos sin autocorrelación:
df=read.csv("ARLANZA_serieprueba.csv",sep=";",header=T)
#simulate option 1: it maintains AR structure
df$AR=c(NA,df$AR12SE[1:(nrow(df)-1)])
###
# Load the necessary packages
library(gam)## Warning: package 'gam' was built under R version 4.2.3## Loading required package: splines## Loading required package: foreach## Warning: package 'foreach' was built under R version 4.2.3## Loaded gam 1.22-2#Do a gam model with autocorrelation
modelo=gam(formula = AR12SE~Year+AR,data = df)
performan=summary(modelo)
1-performan$deviance/performan$null.deviance #around 0.7. PseudoR2## [1] 0.7159286####second option: Same model, simple shufflig residuals
sim.mdl2=function(mdl=modelo,n=nrow(mdl$data)){
simulated_data=mdl$data
simulated_data$AR12SE[2:n]=mdl$fitted.values+sample(mdl$residuals,n-1,replace = T)
simulated_data$AR12SE[simulated_data$AR12SE<=0]=0.001
return(simulated_data)
}
mysim=sim.mdl2(modelo)También se indicó la correlación que tenía la muestra generada con la muestra orignal, usando para ello la siguiente función:
cor(df$AR12SE,mysim$AR12SE) #cor of this is basicaly the same as performance of the model## [1] 0.7889335datrwlBt<-mysim9) Modificación de los datos de un formato rwl a un formato FASTA
Se conviertieron los datos estandarizados en secuencias de repeticiones de las letras A y T.
Para ello se multiplicó las medidas de los datos estandarizados por 100, por lo que un valor de 0.5 mm de medida de un anillo se transforma en 50 repeticiones de la letra correspondiente.
Para dicho proceso se usó el siguiente script:
datos<-read.table(file="datos_detrend.csv",sep=";",header=T)
for (i in 2:ncol(datos))
{
write.table(file="FakeSeqs.fasta",paste(">",colnames(datos)[i],collapse=""),append=ifelse(i==2,F,T),quote=F,row.names=F,col.names=F)
this.col<-na.omit(datos[,i])
write.table(file="FakeSeqs.fasta",paste(unlist(mapply(x=rep(c("A","T"),length=length(this.col)), y= unlist(round(this.col*100)), function(x,y) rep(x,y))),collapse=""),append=T,quote=F,row.names=F,col.names=F)
}10) Inducción de errores en las dataciones
Inducción de anillos ausentes
Se eliminaron algunos años de determinadas series simulando anillos ausentes y se correlacionaron con el resto de series para comprobrobar si dplR podía detectar dichos errores.
La eliminación de series se hizo directamente sobre el formato rwl, eliminando a mano un año y desplazando la serie un año.
Primero se cargaron los datos:
Maestra es la serie maestra que se forma a partir de los datos en los que no se ha inducido el error
Serie es el grupo que dataciones que contiene una muestra a la que se ha inducido un error, eliminando una medida de un año conocido. En nuestro caso, se ha elegido la serie AR01N y se ha eliminado la medida correspondiente al año 1973, generando un anillo falso en dicho año.
Marcada indica la serie en la que se ha inducido el error y se selecciona para la correlación. Por último se elimina la serie marcada de la cronología maestra, para evitar correlacionar la serie con ella misma
maestra<-read.rwl("MARLANZA.rwl")## Attempting to automatically detect format.
## Assuming a Tucson format file.## Warning in readLines(con): incomplete final line found on 'MARLANZA.rwl'## There does not appear to be a header in the rwl file
## There are 33 series
## 1 AR01N 1940 2007 0.001
## 2 AR01S2 1938 2007 0.001
## 3 AR01SW 1925 2007 0.001
## 4 AR02SW 1940 2007 0.001
## 5 AR02SW2 1933 2007 0.001
## 6 AR03SW 1947 2007 0.001
## 7 AR03SE 1957 2007 0.001
## 8 AR04NE 1951 2007 0.001
## 9 AR06SW 1938 2007 0.001
## 10 AR06W 1934 2007 0.001
## 11 AR07SE 1930 2007 0.001
## 12 AR07E 1933 2007 0.001
## 13 AR07NW 1921 2007 0.001
## 14 AR08S 1938 2007 0.001
## 15 AR08E 1955 2007 0.001
## 16 AR09W 1932 2007 0.001
## 17 AR09N 1926 2007 0.001
## 18 AR10N 1947 2007 0.001
## 19 AR10NE 1944 2007 0.001
## 20 AR11NE 1948 2007 0.001
## 21 AR11E 1943 2007 0.001
## 22 AR12E 1937 2007 0.001
## 23 AR12SE 1936 2007 0.001
## 24 AR13SE 1950 2007 0.001
## 25 AR13S 1935 2007 0.001
## 26 AR14S 1948 2006 0.001
## 27 AR15E 1943 2007 0.001
## 28 AR15N 1937 2007 0.001
## 29 AR16W 1926 2007 0.001
## 30 AR16N 1927 2007 0.001
## 31 AR19S 1936 2007 0.001
## 32 AR20E2 1923 2007 0.001
## 33 AR21N 1944 2007 0.001serie<-read.rwl("MARLANZAERROR73AR1N.rwl")## Attempting to automatically detect format.
## Assuming a Tucson format file.## Warning in readLines(con): incomplete final line found on
## 'MARLANZAERROR73AR1N.rwl'## There does not appear to be a header in the rwl file
## There are 33 series
## 1 AR01N 1941 2007 0.001
## 2 AR01S2 1938 2007 0.001
## 3 AR01SW 1925 2007 0.001
## 4 AR02SW 1940 2007 0.001
## 5 AR02SW2 1933 2007 0.001
## 6 AR03SW 1947 2007 0.001
## 7 AR03SE 1957 2007 0.001
## 8 AR04NE 1951 2007 0.001
## 9 AR06SW 1938 2007 0.001
## 10 AR06W 1934 2007 0.001
## 11 AR07SE 1930 2007 0.001
## 12 AR07E 1933 2007 0.001
## 13 AR07NW 1921 2007 0.001
## 14 AR08S 1938 2007 0.001
## 15 AR08E 1955 2007 0.001
## 16 AR09W 1932 2007 0.001
## 17 AR09N 1926 2007 0.001
## 18 AR10N 1947 2007 0.001
## 19 AR10NE 1944 2007 0.001
## 20 AR11NE 1948 2007 0.001
## 21 AR11E 1943 2007 0.001
## 22 AR12E 1937 2007 0.001
## 23 AR12SE 1936 2007 0.001
## 24 AR13SE 1950 2007 0.001
## 25 AR13S 1935 2007 0.001
## 26 AR14S 1948 2006 0.001
## 27 AR15E 1943 2007 0.001
## 28 AR15N 1937 2007 0.001
## 29 AR16W 1926 2007 0.001
## 30 AR16N 1927 2007 0.001
## 31 AR19S 1936 2007 0.001
## 32 AR20E2 1923 2007 0.001
## 33 AR21N 1944 2007 0.001marcada<-serie$AR01N
names(marcada)<-rownames(serie)
maestra$AR01N<-NULLY se usó la siguiente función:
correlación<-corr.series.seg(rwl=maestra, series=marcada,
seg.length = 16, bin.floor = 20, n = NULL,
prewhiten = TRUE, biweight = TRUE,
method = c("pearson"),
pcrit = 0.05,
make.plot = TRUE, floor.plus1 = FALSE)
En el periodo temporal del 1968-1984 se observa una brusca disminución de la sincronía de la serie problema con la cronología maestra. En dicho periodo se encuentra el error.
Inducción de dobles anillos
Se dividieron determinados anillos y ambas medicidiones se añadieron a la muestra como si fueran independientes, generando así dos anillos en lugar de uno.
En el caso ejemplo, se dividió la medida correspondiente al anillo del año 1972 de la muestra AR01N, generando dos anillos independientes.
En primer lugar se cargaron los datos
maestra<-read.rwl("MARLANZA.rwl")## Attempting to automatically detect format.
## Assuming a Tucson format file.## Warning in readLines(con): incomplete final line found on 'MARLANZA.rwl'## There does not appear to be a header in the rwl file
## There are 33 series
## 1 AR01N 1940 2007 0.001
## 2 AR01S2 1938 2007 0.001
## 3 AR01SW 1925 2007 0.001
## 4 AR02SW 1940 2007 0.001
## 5 AR02SW2 1933 2007 0.001
## 6 AR03SW 1947 2007 0.001
## 7 AR03SE 1957 2007 0.001
## 8 AR04NE 1951 2007 0.001
## 9 AR06SW 1938 2007 0.001
## 10 AR06W 1934 2007 0.001
## 11 AR07SE 1930 2007 0.001
## 12 AR07E 1933 2007 0.001
## 13 AR07NW 1921 2007 0.001
## 14 AR08S 1938 2007 0.001
## 15 AR08E 1955 2007 0.001
## 16 AR09W 1932 2007 0.001
## 17 AR09N 1926 2007 0.001
## 18 AR10N 1947 2007 0.001
## 19 AR10NE 1944 2007 0.001
## 20 AR11NE 1948 2007 0.001
## 21 AR11E 1943 2007 0.001
## 22 AR12E 1937 2007 0.001
## 23 AR12SE 1936 2007 0.001
## 24 AR13SE 1950 2007 0.001
## 25 AR13S 1935 2007 0.001
## 26 AR14S 1948 2006 0.001
## 27 AR15E 1943 2007 0.001
## 28 AR15N 1937 2007 0.001
## 29 AR16W 1926 2007 0.001
## 30 AR16N 1927 2007 0.001
## 31 AR19S 1936 2007 0.001
## 32 AR20E2 1923 2007 0.001
## 33 AR21N 1944 2007 0.001serie<-read.rwl("MARLANZAdoble1972AR01N.rwl")## Attempting to automatically detect format.
## Assuming a Tucson format file.## Warning in readLines(con): incomplete final line found on
## 'MARLANZAdoble1972AR01N.rwl'## There does not appear to be a header in the rwl file
## There are 33 series
## 1 AR01N 1939 2007 0.001
## 2 AR01S2 1938 2007 0.001
## 3 AR01SW 1925 2007 0.001
## 4 AR02SW 1940 2007 0.001
## 5 AR02SW2 1933 2007 0.001
## 6 AR03SW 1947 2007 0.001
## 7 AR03SE 1957 2007 0.001
## 8 AR04NE 1951 2007 0.001
## 9 AR06SW 1938 2007 0.001
## 10 AR06W 1934 2007 0.001
## 11 AR07SE 1930 2007 0.001
## 12 AR07E 1933 2007 0.001
## 13 AR07NW 1921 2007 0.001
## 14 AR08S 1938 2007 0.001
## 15 AR08E 1955 2007 0.001
## 16 AR09W 1932 2007 0.001
## 17 AR09N 1926 2007 0.001
## 18 AR10N 1947 2007 0.001
## 19 AR10NE 1944 2007 0.001
## 20 AR11NE 1948 2007 0.001
## 21 AR11E 1943 2007 0.001
## 22 AR12E 1937 2007 0.001
## 23 AR12SE 1936 2007 0.001
## 24 AR13SE 1950 2007 0.001
## 25 AR13S 1935 2007 0.001
## 26 AR14S 1948 2006 0.001
## 27 AR15E 1943 2007 0.001
## 28 AR15N 1937 2007 0.001
## 29 AR16W 1926 2007 0.001
## 30 AR16N 1927 2007 0.001
## 31 AR19S 1936 2007 0.001
## 32 AR20E2 1923 2007 0.001
## 33 AR21N 1944 2007 0.001marcada<-serie$AR01N
names(marcada)<-rownames(serie)
maestra$AR01N<-NULLY se usó la siguiente función para co-datar las muestras:
correlación<-corr.series.seg(rwl=maestra, series=marcada,
seg.length = 16, bin.floor = 20, n = NULL,
prewhiten = TRUE, biweight = TRUE,
method = c("pearson"),
pcrit = 0.05,
make.plot = TRUE, floor.plus1 = FALSE)
De nuevo, en el periodo del 1968-1984 se muestra una brusaca disminución de la sincronía, que se corresponde con el periodo en el que se ha inducido el error.