# Thornthwaite and Mather's water balance Calculates Thornthwaite and Mather's water balance from monthly series of precipitation and temperature. Aimed at a classification of a site's climate according to its water balance features. ```r thornthwaite( series, latitude, clim_norm = NULL, first.yr = NULL, last.yr = NULL, quant = c(0, 0.1, 0.25, 0.5, 0.75, 0.9, 1), snow.init = 20, Tsnow = -1, TAW = 100, fr.sn.acc = 0.95, snow_melt_coeff = 1 ) ``` ## Arguments - `series`: the monthly series of temperature and precipitation. - `latitude`: latitude of the station in degrees. - `clim_norm`: climatic normals. - `first.yr`: first year of the period over which water balance is calculated. Default is `NULL` (calculations start with the first year of the series). - `last.yr`: last year of the period over which water balance is calculated. Default is `NULL` (calculations stop with the last year of the series). - `quant`: vector of quantiles for which water balance has to be assessed. Default is: min, 10th, 25th 50th, 75th, 90th, max. - `snow.init`: initial water equivalent for snowpack (mm). Default is 20. - `Tsnow`: maximum temperature (monthly mean) for precipitation to be treated as snowfall. Default is -1 degree C. - `TAW`: maximum (field capacity) for soil water retention, and initial soil water content (mm). Default is 100. - `fr.sn.acc`: fraction of snow that contributes to snowpack (0-1). 1 - fr.sn.acc is treated as liquid monthly precipitation Default is 0.95. - `snow_melt_coeff`: monthly coefficient(s) for snowmelt. Default is 1. ## Returns A `thornthwaite` S3 object, consisting on a list of two lists. The first (name: W_balance) is a list of data frames containing the monthly series of all indices, the second (name: quantiles) the relevant quantiles. See details for meanings of single variables. ## Details The algorithm for the calculation of water balance is adapted from Thornthwaite, 1948; Thornthwaite and Mather, 1955; Thornthwaite and Mather, 1957. `series` is a data frame with years, months, temperature and precipitation values. Names in series columns must include: year, month, Tn and Tx (minimum and maximum temperatures, respectively) or, as an alternative, Tm (mean temperatures), and P (mandatory). `clim_norm` is a monthly data frame of climate normals, with column names: "P", "Tn", "Tx", "Tm" (precipitation, minimum, maximum and mean temperature, respectively). It can be the output of function `climate`. If `clim_norm` is not NULL, any missing value in the monthly series is substituted by the corresponding climatic value in `clim_norm`. At any winter season, the maximum monthly snowpack height is attained in the last month before "spring" conditions (`Tm` >= `Tsnow`), even if a month with Tm < Tsnow may occur later. `snow_melt_coeff` is (are) the coefficient(s) for snow melt fraction(s) at any month where the condition for melting exists. If `snow_melt_coeff` = 1 (default), all the melting occurs in the first month when `Tm >= Tsnow`; if it is a vector, melting is spread over more than one month. If the sum of coefficients is less than 1, the residual melting occurs in one further month. The output function is a list of two lists of data frames (balance and quantile). In both lists, data frame (and names) are the following (all variables in mm): `Precipitation` (repeats input values); `Et0` (potential evapotranspiration); `Storage` (water stored in soil); `Prec. - Evap.` (difference between precipitation and potential evapotranspiration); `Deficit` (difference between potential and real evapotranspiration, due to water unavailability in soil); `Surplus` (water surplus in soil, routed to runoff). Please, refer to the quoted references for details. This function requires the function `daylength` from the `geosphere` package. ## Examples ```r data(Trent_climate) # lista_cli is a list of data frames of the type "series", # each one referring to one station - see function "climate". # clima_81_10 is a list of data frames having climatic means # of temperature and precipitation, each one referring to one station. # It can be the output of function "climate". library(geosphere) # required for function daylength thornt_lst<-NULL lista_cli <- lista_cli[1:3] ## lista_cli is reduced to diminish elapsed time of execution! for(k in 1 : length(lista_cli[1:3])) { thornt_lst[[k]]<-thornthwaite(series=lista_cli[[k]], clim_norm=clima_81_10[[k]], latitude = 46, first.yr=1981, last.yr=2010, snow_melt_coeff=c(0.5,0.5 ) ) } names(thornt_lst)<-names(lista_cli) # splits list into two lists W_balance<-NULL; quantiles<-NULL for(k in 1 : length(lista_cli)) { W_balance[[k]]<-thornt_lst[[k]]$W_balance quantiles[[k]]<-thornt_lst[[k]]$quantiles } names(W_balance)<-names(thornt_lst); names(quantiles)<-names(thornt_lst) ``` ## References Thornthwaite, C. W., 1948: An Approach toward a Rational Classification of Climate. Geographical Review, Vol. 38, No. 1(Jan.):55-94. Thornthwaite, C. W., and Mather, J.R., 1955: The water balance. Publications in Climatology, Volume 8(1), Laboratory of Climatology Thornthwaite, C. W., and Mather, J.R., 1957: Instructions and tables for computing potential evapotranspiration and the water balance. Publications in climatology, Volume 10(3), Laboratory of Climatology ## See Also `climate`, `ExAtRa`, `plot.thornthwaite` ## Author(s) Giambattista Toller and Emanuele Eccel

thornthwaite function