PET: Computation of potential evapotranspiration.
In SPEI: Calculation of the Standardised Precipitation-Evapotranspiration Index
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
Potential evapotranspiration (PET) is the amount of evaporation and transpiration that would occur if a sufficient water source were available. Reference evapotranspiration (ET0) is the amount of evaporation and transpiration from a reference vegetation of grass. They are usually considered equivalent. This set of functions calculate PET or ET0 accordind to the Thornthwaite, Hargreaves or Penman-Monteith equations.
Usage
1
2
3
4
5
6
7
Arguments
Tave
a numeric vector, matrix or time series of monthly mean temperatures, <c2><ba>C.
lat
a numeric vector with the latitude of the site or sites, in degrees.
na.rm
optional, a logical value indicating whether NA values should be stripped from the computations.
Tmax
a numeric vector, matrix or time series of monthly mean daily maximum temperatures, <c2><ba>C.
Tmin
a numeric vector, matrix or time series of monthly mean daily minimum temperatures, <c2><ba>C.
Ra
optional, a numeric vector, matrix or time series of monthly mean daily external radiation, MJ m-2 d-1.
Pre
optional, a numeric vector, matrix or time series of monthly total precipitation, mm.
U2
a numeric vector, matrix or time series of monthly mean daily wind speeds at 2 m height, m s-1.
Rs
optional, a numeric vector, matrix or time series of monthly mean dialy incoming solar radiation, MJ m-2 d-1.
tsun
optional, a numeric vector, matrix or time series of monthly mean daily bright sunshine hours, h.
CC
optional, numeric a vector, matrix or time series of monthly mean cloud cover, %.
ed
optional, numeric a vector, matrix or time series of monthly mean actual vapour pressure at 2 m height, kPa.
Tdew
optional, a numeric vector, matrix or time series of monthly mean daily dewpoint temperature (used for estimating ed), <c2><ba>C
RH
optional, a numeric vector, matrix or time series of monthly mean relative humidity (used for estimating ed), %.
P
optional, a numeric vector, matrix or time series of monthly mean atmospheric pressure at surface, kPa.
P0
optional, a numeric vector, matrix or time series of monthly mean atmospheric pressure at sea level (used for estimating P), kPa.
z
optional, a numeric vector of the elevation of the site or sites, m above sea level.
crop
optional, character string, type of reference crop. Either one of 'short' (default) or 'tall'.
Details
thornthwaite computes the monthly potential evapotranspiration (PE) according to the Thornthwaite (1948) equation. It is the simplest of the three methods, and can be used when only temperature data are available.
hargreaves computes the monthly reference evapotranspiration (ET0) of a grass crop based on the original Hargreaves equation (1994). However, if precipitation data Pre is provided a modified form due to Droogers and Allen (2002) will be used; this equation corrects ET0 using the amount of rain of each month as a proxy for insolation. The Hargreaves method requires data on the mean external radiation, Ra. If such data are not available it can be estimated from the latitude lat and the month of the year.
penman calculates the monthly reference evapotranspiration (ET0) of a hypothetical reference crop according to the FAO-56 Penman-Monteith equation described in Allen et al. (1994). This is a simplification of the original Penman-Monteith equation, and has found widespread use. By default the original parameterization of Allen et al. (1994) is used, corresponding to a short reference crop of 0.12 m height. Parameterization for a tall reference crop of 0.5 m height due to Walter et al. (2002) can also be used, by setting the crop parameter to 'tall'. The method requires data on the incoming solar radiation, Rs; since this is seldom available, the code will estimate it from data on the bright sunshine duration tsun, or alternatively from data on the percent cloud cover CC. Similarly, if data on the saturation water pressure ed are not available, it is possible to estimate it from the dewpoint temperature Tdew, from the relative humidity RH or even from the minimum temperature Tmin (sorted from least to most uncertain method). Similarly, the atmospheric surface pressure P required for computing the psychrometric constant can be calculated from the atmospheric pressure at sea level P0 and the elevation z, or else it will be assumed to be constant (101.3 kPa). The code will produce an error message if a valid combination of input parameters is not provided.
If the main input object (Tave, Tmin, Tmax) is a vector or a matrix, data will be treated as a sequence of monthly values starting in January. If it is a time series then the function cycle will be used to determine the position of each observation within the year (month), allowing the data to start in a month different than January.
Value
A time series with the values of monthly potential or reference evapotranspiration, in mm. If the input is a matrix or a multivariate time series each column will be treated as independent data (e.g., diferent observatories), and the output will be a multivariate time series.
Author(s)
Santiago Beguer<c3><ad>a
References
Thornthwaite, C. W. (1948). An approach toward a rational classification of climate. Geographical Review 38: 55<e2><80><93>94. doi:10.2307/2107309.
Hargreaves G.H. 1994. Defining and using reference evapotranspiration. Journal of Irrigation and Drainage Engineering 120: 1132<e2><80><93>1139.
Droogers P., Allen R. G., 2002. Estimating reference evapotranspiration under inaccurate data conditions. Irrigation and Drainage Systems 16: 33<e2><80><93>45.
Allen R. G., Smith M., Pereira L. S., Perrier A., 1994. An update for the calculation of reference evapotranspiration. ICID Bulletin of the International Commission on Irrigation and Drainage, 35<e2><80><93>92.
Allen R.G., Pereira L.S.,Raes D., Smith, M. 1998. JCrop evapotranspiration - Guidelines for computing crop water requirements - FAO Irrigation and drainage paper 56. FAO, Rome. ISBN 92-5-104219-5.
Walter I.A. and 14 co-authors, 2002. The ASCE standardized reference evapotranspiration equation. Rep. Task Com. on Standardized Reference Evapotranspiration July 9, 2002, EWRI<e2><80><93>Am. Soc. Civil Engr., Reston, VA, 57 pp.
Examples
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28
# Load data for Tampa, lat=37.6475N, elevation=402.6 m. a.s.l.
# Data consists on monthly values since January 1980
data(wichita)
attach(wichita)
names(wichita)
# PET according to Thornthwaite
tho <- thornthwaite(TMED,37.6475)
# Hargreaves
har <- hargreaves(TMIN,TMAX,lat=37.6475)
# Penman, based on sun hours, ignore NAs
pen <- penman(TMIN,TMAX,AWND,tsun=TSUN,lat=37.6475,z=402.6,na.rm=TRUE)
# Penman, based on cloud cover
pen2 <- penman(TMIN,TMAX,AWND,CC=ACSH,lat=37.6475,z=402.6,na.rm=TRUE)
# Plot them together
plot(cbind(tho,har,pen,pen2))
# Now consider the data started in June 1900
thornthwaite(ts(TMED,start=c(1900,6),frequency=12),37.6475)
# Comparison with example from Allen et al. (1998), p. 69, fig. 18:
# Data from Cabinda, Angola (-5.33S, 12.11E, 20 m a.s.l.)
data(cabinda)
pen.cab <- penman(cabinda$Tmin,cabinda$Tmax,cabinda$U2,
Rs=cabinda$Rs,tsun=cabinda$tsun,RH=cabinda$RH,lat=-5.33,z=20)
plot(cabinda$ET0,pen.cab)
abline(0,1,lt='dashed')
summary(lm(pen.cab~cabinda$ET0))$r.squared
Example output
Loading required package: lmomco
Loading required package: parallel
Loading required package: ggplot2
# Package SPEI (1.7) loaded [try SPEINews()].
[1] "YEAR" "MONTH" "PRCP" "TMAX" "TMIN" "TMED" "AWND" "TSUN" "ACSH"
Jan Feb Mar Apr May
1900
1901 134.82647616 94.93424965 55.05082261 23.64729587 4.59501165
1902 107.69769281 84.09640801 46.06814437 23.73660829 0.29742788
1903 122.15502477 83.91882065 52.63736757 14.63241485 3.53192014
1904 134.11469547 86.59678207 54.24201268 20.26001958 0.00000000
1905 125.26324177 78.82792749 53.38022373 20.26001958 4.99856517
1906 105.34149878 77.15657594 50.76855597 7.79529909 0.00000000
1907 99.85316608 89.36541775 51.33229248 8.74272124 3.06192287
1908 109.74163187 78.94366791 45.68841657 25.59403169 1.99729364
1909 126.02729726 84.21487465 48.53612737 24.95413209 7.19257162
1910 103.71632036 64.36576561 61.55404115 20.17566310 0.00000000
1911 117.57957692 91.98173878 53.78177351 32.75684082 0.00000000
1912 116.36109800 76.35434095 57.32655992 8.09663766 8.31151530
1913 92.41101102 81.03742337 56.33049266 11.15787544 0.63024860
1914 118.53043817 69.49238389 44.28793828 10.28525531 5.98674004
1915 110.93477189 79.11739312 60.89200716 23.11397269 4.91687850
1916 118.12258860 73.06310223 56.33049266 16.51320448 0.69622573
1917 105.21114994 70.37901798 54.01171661 10.28525531 1.10720612
1918 102.55183483 86.17822320 56.33049266 12.76336704 1.74806726
1919 120.71416766 106.68846675 61.85581690 30.28264697 3.24701980
1920 119.27947590 68.49976722 56.68132790 41.18682665 5.84166928
1921 140.20789822 92.22649708 64.59560680 9.15155520 0.00000000
1922 125.05515344 77.67389075 56.21372194 34.12177212 8.08308772
1923 115.75357387 89.97143726 35.82344899 17.26429701 2.83610557
1924 123.46395286 65.49878127 53.32294795 21.02490924 5.08073530
1925 97.87796243 92.16528555 62.09761985 24.18498511 5.95762347
1926 109.87397351 92.53277411 59.04018859 26.00846766 0.22220949
1927 121.12521290 71.15813717 52.29577658 26.79780706 8.14811876
1928 126.09683977 90.88322786 63.73865028 21.62684770 0.00000000
1929 106.64817913 71.15813717 51.61500034 21.79995136 0.42431722
1930 101.13501492 72.95054446 32.93902681 32.55633911 0.00000000
1931 128.04962939 91.73721474 66.94231946 22.49731790 1.28668621
1932 133.68827850 75.61211526 86.63616214
Jun Jul Aug Sep Oct
1900 0.00000000 0.00000000 12.44598034 41.74632976 66.52496016
1901 1.18847543 10.24389195 27.17415732 72.58505131 63.57226248
1902 0.00000000 0.00000000 22.71322831 39.55103422 72.88102514
1903 0.00000000 2.80232207 16.37660078 24.85775415 56.91014950
1904 0.00000000 12.93636244 10.92842823 34.74524893 67.18101047
1905 0.00000000 0.00000000 31.24398939 59.28210347 81.09948347
1906 6.55449465 6.16567160 39.80961223 55.55324495 77.73642607
1907 0.00000000 14.89480027 25.47961865 51.22902680 88.24144190
1908 0.00000000 1.26144041 18.29230856 40.59108803 83.21925232
1909 7.16683617 0.00000000 25.43178224 58.26732457 75.23239374
1910 9.08485466 7.72058232 25.09783476 41.79911767 67.30054121
1911 0.00000000 20.41604704 33.06505298 56.02190603 90.69218711
1912 7.99188466 21.48155174 33.69792932 48.97476427 66.04929014
1913 0.00000000 0.01906945 15.97031200 36.69101112 66.58450528
1914 0.00000000 1.04939263 34.60187407 43.12659751 76.54333065
1915 0.34858780 11.44987326 21.44083382 36.13834621 56.18018058
1916 0.00000000 6.52731935 10.64749092 44.41497613 87.78051117
1917 0.00000000 5.69513343 26.58875211 32.54797348 64.62967084
1918 1.52996545 12.51050091 10.71747815 41.85192960 89.09975923
1919 0.21353107 22.47133394 19.40847915 46.81224192 72.63507915
1920 0.95335112 14.44653414 29.51079995 44.25318287 85.48892914
1921 0.04485900 0.71010910 15.28809841 60.36343358 80.52478852
1922 3.41472405 5.87000806 13.53468020 53.80843261 67.36033527
1923 0.03077476 0.55273247 21.75645345 53.51958332 70.43507506
1924 0.01193617 0.89605195 34.86937646 49.53490250 87.45180734
1925 0.00000000 11.78709538 24.05867849 49.87208497 80.14247663
1926 16.92755936 3.80091433 30.98687953 70.27982177 81.80388432
1927 0.00000000 1.31234389 49.21919222 38.57201736 82.89681056
1928 0.17128674 1.97738225 21.62098459 40.64334551 75.54378174
1929 0.02651650 15.38941696 27.56697139 44.09160230 73.99148033
1930 0.00000000 0.08614925 25.86347330 62.85261095 74.23906830
1931 0.00000000 0.21762580 28.11039655 55.43630129 76.60595941
1932
Nov Dec
1900 113.21751359 152.30164668
1901 105.86022210 125.17073269
1902 80.13527612 117.27028720
1903 83.50646660 117.87141362
1904 105.08253624 117.87141362
1905 92.24340680 118.00514749
1906 108.72934922 122.92365268
1907 100.65108003 112.23842345
1908 108.46737920 115.14192777
1909 85.30078688 108.25747388
1910 120.00349892 118.13893594
1911 110.76731681 126.19696957
1912 82.85199610 107.99823968
1913 93.79191963 118.27277896
1914 110.83328433 103.37044673
1915 86.44427711 112.43554070
1916 103.34030556 108.64674453
1917 91.74984537 109.36171285
1918 107.55227743 118.60762515
1919 88.93042604 120.35431108
1920 89.17433378 113.02763915
1921 96.72815762 135.84922216
1922 100.90609580 117.87141362
1923 87.29035142 127.98291454
1924 90.88840942 102.28845348
1925 104.50062781 111.64781930
1926 101.09751004 125.44410083
1927 91.68821725 110.40467710
1928 101.80047880 112.63278244
1929 109.97681016 105.67522253
1930 116.29052201 121.90710520
1931 119.12209759 147.78061558
1932
[1] 0.9950968
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Description Usage Arguments Details Value Author(s) References Examples
Description
Potential evapotranspiration (PET) is the amount of evaporation and transpiration that would occur if a sufficient water source were available. Reference evapotranspiration (ET0) is the amount of evaporation and transpiration from a reference vegetation of grass. They are usually considered equivalent. This set of functions calculate PET or ET0 accordind to the Thornthwaite, Hargreaves or Penman-Monteith equations.
Usage
1 2 3 4 5 6 7 |
Arguments
Tave |
a numeric vector, matrix or time series of monthly mean temperatures, <c2><ba>C. |
lat |
a numeric vector with the latitude of the site or sites, in degrees. |
na.rm |
optional, a logical value indicating whether NA values should be stripped from the computations. |
Tmax |
a numeric vector, matrix or time series of monthly mean daily maximum temperatures, <c2><ba>C. |
Tmin |
a numeric vector, matrix or time series of monthly mean daily minimum temperatures, <c2><ba>C. |
Ra |
optional, a numeric vector, matrix or time series of monthly mean daily external radiation, MJ m-2 d-1. |
Pre |
optional, a numeric vector, matrix or time series of monthly total precipitation, mm. |
U2 |
a numeric vector, matrix or time series of monthly mean daily wind speeds at 2 m height, m s-1. |
Rs |
optional, a numeric vector, matrix or time series of monthly mean dialy incoming solar radiation, MJ m-2 d-1. |
tsun |
optional, a numeric vector, matrix or time series of monthly mean daily bright sunshine hours, h. |
CC |
optional, numeric a vector, matrix or time series of monthly mean cloud cover, %. |
ed |
optional, numeric a vector, matrix or time series of monthly mean actual vapour pressure at 2 m height, kPa. |
Tdew |
optional, a numeric vector, matrix or time series of monthly mean daily dewpoint temperature (used for estimating ed), <c2><ba>C |
RH |
optional, a numeric vector, matrix or time series of monthly mean relative humidity (used for estimating ed), %. |
P |
optional, a numeric vector, matrix or time series of monthly mean atmospheric pressure at surface, kPa. |
P0 |
optional, a numeric vector, matrix or time series of monthly mean atmospheric pressure at sea level (used for estimating P), kPa. |
z |
optional, a numeric vector of the elevation of the site or sites, m above sea level. |
crop |
optional, character string, type of reference crop. Either one of 'short' (default) or 'tall'. |
Details
thornthwaite computes the monthly potential evapotranspiration (PE) according to the Thornthwaite (1948) equation. It is the simplest of the three methods, and can be used when only temperature data are available.
hargreaves computes the monthly reference evapotranspiration (ET0) of a grass crop based on the original Hargreaves equation (1994). However, if precipitation data Pre is provided a modified form due to Droogers and Allen (2002) will be used; this equation corrects ET0 using the amount of rain of each month as a proxy for insolation. The Hargreaves method requires data on the mean external radiation, Ra. If such data are not available it can be estimated from the latitude lat and the month of the year.
penman calculates the monthly reference evapotranspiration (ET0) of a hypothetical reference crop according to the FAO-56 Penman-Monteith equation described in Allen et al. (1994). This is a simplification of the original Penman-Monteith equation, and has found widespread use. By default the original parameterization of Allen et al. (1994) is used, corresponding to a short reference crop of 0.12 m height. Parameterization for a tall reference crop of 0.5 m height due to Walter et al. (2002) can also be used, by setting the crop parameter to 'tall'. The method requires data on the incoming solar radiation, Rs; since this is seldom available, the code will estimate it from data on the bright sunshine duration tsun, or alternatively from data on the percent cloud cover CC. Similarly, if data on the saturation water pressure ed are not available, it is possible to estimate it from the dewpoint temperature Tdew, from the relative humidity RH or even from the minimum temperature Tmin (sorted from least to most uncertain method). Similarly, the atmospheric surface pressure P required for computing the psychrometric constant can be calculated from the atmospheric pressure at sea level P0 and the elevation z, or else it will be assumed to be constant (101.3 kPa). The code will produce an error message if a valid combination of input parameters is not provided.
If the main input object (Tave, Tmin, Tmax) is a vector or a matrix, data will be treated as a sequence of monthly values starting in January. If it is a time series then the function cycle will be used to determine the position of each observation within the year (month), allowing the data to start in a month different than January.
Value
A time series with the values of monthly potential or reference evapotranspiration, in mm. If the input is a matrix or a multivariate time series each column will be treated as independent data (e.g., diferent observatories), and the output will be a multivariate time series.
Author(s)
Santiago Beguer<c3><ad>a
References
Thornthwaite, C. W. (1948). An approach toward a rational classification of climate. Geographical Review 38: 55<e2><80><93>94. doi:10.2307/2107309.
Hargreaves G.H. 1994. Defining and using reference evapotranspiration. Journal of Irrigation and Drainage Engineering 120: 1132<e2><80><93>1139.
Droogers P., Allen R. G., 2002. Estimating reference evapotranspiration under inaccurate data conditions. Irrigation and Drainage Systems 16: 33<e2><80><93>45.
Allen R. G., Smith M., Pereira L. S., Perrier A., 1994. An update for the calculation of reference evapotranspiration. ICID Bulletin of the International Commission on Irrigation and Drainage, 35<e2><80><93>92.
Allen R.G., Pereira L.S.,Raes D., Smith, M. 1998. JCrop evapotranspiration - Guidelines for computing crop water requirements - FAO Irrigation and drainage paper 56. FAO, Rome. ISBN 92-5-104219-5.
Walter I.A. and 14 co-authors, 2002. The ASCE standardized reference evapotranspiration equation. Rep. Task Com. on Standardized Reference Evapotranspiration July 9, 2002, EWRI<e2><80><93>Am. Soc. Civil Engr., Reston, VA, 57 pp.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | # Load data for Tampa, lat=37.6475N, elevation=402.6 m. a.s.l.
# Data consists on monthly values since January 1980
data(wichita)
attach(wichita)
names(wichita)
# PET according to Thornthwaite
tho <- thornthwaite(TMED,37.6475)
# Hargreaves
har <- hargreaves(TMIN,TMAX,lat=37.6475)
# Penman, based on sun hours, ignore NAs
pen <- penman(TMIN,TMAX,AWND,tsun=TSUN,lat=37.6475,z=402.6,na.rm=TRUE)
# Penman, based on cloud cover
pen2 <- penman(TMIN,TMAX,AWND,CC=ACSH,lat=37.6475,z=402.6,na.rm=TRUE)
# Plot them together
plot(cbind(tho,har,pen,pen2))
# Now consider the data started in June 1900
thornthwaite(ts(TMED,start=c(1900,6),frequency=12),37.6475)
# Comparison with example from Allen et al. (1998), p. 69, fig. 18:
# Data from Cabinda, Angola (-5.33S, 12.11E, 20 m a.s.l.)
data(cabinda)
pen.cab <- penman(cabinda$Tmin,cabinda$Tmax,cabinda$U2,
Rs=cabinda$Rs,tsun=cabinda$tsun,RH=cabinda$RH,lat=-5.33,z=20)
plot(cabinda$ET0,pen.cab)
abline(0,1,lt='dashed')
summary(lm(pen.cab~cabinda$ET0))$r.squared
|
Example output
Loading required package: lmomco
Loading required package: parallel
Loading required package: ggplot2
# Package SPEI (1.7) loaded [try SPEINews()].
[1] "YEAR" "MONTH" "PRCP" "TMAX" "TMIN" "TMED" "AWND" "TSUN" "ACSH"
Jan Feb Mar Apr May
1900
1901 134.82647616 94.93424965 55.05082261 23.64729587 4.59501165
1902 107.69769281 84.09640801 46.06814437 23.73660829 0.29742788
1903 122.15502477 83.91882065 52.63736757 14.63241485 3.53192014
1904 134.11469547 86.59678207 54.24201268 20.26001958 0.00000000
1905 125.26324177 78.82792749 53.38022373 20.26001958 4.99856517
1906 105.34149878 77.15657594 50.76855597 7.79529909 0.00000000
1907 99.85316608 89.36541775 51.33229248 8.74272124 3.06192287
1908 109.74163187 78.94366791 45.68841657 25.59403169 1.99729364
1909 126.02729726 84.21487465 48.53612737 24.95413209 7.19257162
1910 103.71632036 64.36576561 61.55404115 20.17566310 0.00000000
1911 117.57957692 91.98173878 53.78177351 32.75684082 0.00000000
1912 116.36109800 76.35434095 57.32655992 8.09663766 8.31151530
1913 92.41101102 81.03742337 56.33049266 11.15787544 0.63024860
1914 118.53043817 69.49238389 44.28793828 10.28525531 5.98674004
1915 110.93477189 79.11739312 60.89200716 23.11397269 4.91687850
1916 118.12258860 73.06310223 56.33049266 16.51320448 0.69622573
1917 105.21114994 70.37901798 54.01171661 10.28525531 1.10720612
1918 102.55183483 86.17822320 56.33049266 12.76336704 1.74806726
1919 120.71416766 106.68846675 61.85581690 30.28264697 3.24701980
1920 119.27947590 68.49976722 56.68132790 41.18682665 5.84166928
1921 140.20789822 92.22649708 64.59560680 9.15155520 0.00000000
1922 125.05515344 77.67389075 56.21372194 34.12177212 8.08308772
1923 115.75357387 89.97143726 35.82344899 17.26429701 2.83610557
1924 123.46395286 65.49878127 53.32294795 21.02490924 5.08073530
1925 97.87796243 92.16528555 62.09761985 24.18498511 5.95762347
1926 109.87397351 92.53277411 59.04018859 26.00846766 0.22220949
1927 121.12521290 71.15813717 52.29577658 26.79780706 8.14811876
1928 126.09683977 90.88322786 63.73865028 21.62684770 0.00000000
1929 106.64817913 71.15813717 51.61500034 21.79995136 0.42431722
1930 101.13501492 72.95054446 32.93902681 32.55633911 0.00000000
1931 128.04962939 91.73721474 66.94231946 22.49731790 1.28668621
1932 133.68827850 75.61211526 86.63616214
Jun Jul Aug Sep Oct
1900 0.00000000 0.00000000 12.44598034 41.74632976 66.52496016
1901 1.18847543 10.24389195 27.17415732 72.58505131 63.57226248
1902 0.00000000 0.00000000 22.71322831 39.55103422 72.88102514
1903 0.00000000 2.80232207 16.37660078 24.85775415 56.91014950
1904 0.00000000 12.93636244 10.92842823 34.74524893 67.18101047
1905 0.00000000 0.00000000 31.24398939 59.28210347 81.09948347
1906 6.55449465 6.16567160 39.80961223 55.55324495 77.73642607
1907 0.00000000 14.89480027 25.47961865 51.22902680 88.24144190
1908 0.00000000 1.26144041 18.29230856 40.59108803 83.21925232
1909 7.16683617 0.00000000 25.43178224 58.26732457 75.23239374
1910 9.08485466 7.72058232 25.09783476 41.79911767 67.30054121
1911 0.00000000 20.41604704 33.06505298 56.02190603 90.69218711
1912 7.99188466 21.48155174 33.69792932 48.97476427 66.04929014
1913 0.00000000 0.01906945 15.97031200 36.69101112 66.58450528
1914 0.00000000 1.04939263 34.60187407 43.12659751 76.54333065
1915 0.34858780 11.44987326 21.44083382 36.13834621 56.18018058
1916 0.00000000 6.52731935 10.64749092 44.41497613 87.78051117
1917 0.00000000 5.69513343 26.58875211 32.54797348 64.62967084
1918 1.52996545 12.51050091 10.71747815 41.85192960 89.09975923
1919 0.21353107 22.47133394 19.40847915 46.81224192 72.63507915
1920 0.95335112 14.44653414 29.51079995 44.25318287 85.48892914
1921 0.04485900 0.71010910 15.28809841 60.36343358 80.52478852
1922 3.41472405 5.87000806 13.53468020 53.80843261 67.36033527
1923 0.03077476 0.55273247 21.75645345 53.51958332 70.43507506
1924 0.01193617 0.89605195 34.86937646 49.53490250 87.45180734
1925 0.00000000 11.78709538 24.05867849 49.87208497 80.14247663
1926 16.92755936 3.80091433 30.98687953 70.27982177 81.80388432
1927 0.00000000 1.31234389 49.21919222 38.57201736 82.89681056
1928 0.17128674 1.97738225 21.62098459 40.64334551 75.54378174
1929 0.02651650 15.38941696 27.56697139 44.09160230 73.99148033
1930 0.00000000 0.08614925 25.86347330 62.85261095 74.23906830
1931 0.00000000 0.21762580 28.11039655 55.43630129 76.60595941
1932
Nov Dec
1900 113.21751359 152.30164668
1901 105.86022210 125.17073269
1902 80.13527612 117.27028720
1903 83.50646660 117.87141362
1904 105.08253624 117.87141362
1905 92.24340680 118.00514749
1906 108.72934922 122.92365268
1907 100.65108003 112.23842345
1908 108.46737920 115.14192777
1909 85.30078688 108.25747388
1910 120.00349892 118.13893594
1911 110.76731681 126.19696957
1912 82.85199610 107.99823968
1913 93.79191963 118.27277896
1914 110.83328433 103.37044673
1915 86.44427711 112.43554070
1916 103.34030556 108.64674453
1917 91.74984537 109.36171285
1918 107.55227743 118.60762515
1919 88.93042604 120.35431108
1920 89.17433378 113.02763915
1921 96.72815762 135.84922216
1922 100.90609580 117.87141362
1923 87.29035142 127.98291454
1924 90.88840942 102.28845348
1925 104.50062781 111.64781930
1926 101.09751004 125.44410083
1927 91.68821725 110.40467710
1928 101.80047880 112.63278244
1929 109.97681016 105.67522253
1930 116.29052201 121.90710520
1931 119.12209759 147.78061558
1932
[1] 0.9950968
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