# PET: Computation of potential evapotranspiration. In SPEI: Calculation of the Standardised Precipitation-Evapotranspiration Index

## 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``` ```thornthwaite(Tave, lat, na.rm = FALSE) hargreaves(Tmin, Tmax, Ra = NA, lat = NA, Pre = NA, na.rm = FALSE) penman(Tmin, Tmax, U2, Ra = NA, lat = NA, Rs = NA, tsun = NA, CC = NA, ed = NA, Tdew = NA, RH = NA, P = NA, P0 = NA, z = NA, crop='short', na.rm = FALSE) ```

## Arguments

 `Tave` a numeric vector, matrix or time series of monthly mean temperatures, 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, C. `Tmin` a numeric vector, matrix or time series of monthly mean daily minimum temperatures, 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), 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.

## 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
# 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
```

SPEI documentation built on May 2, 2019, 11:05 a.m.