Oct 2, 2002 - The program has been written to calculate daily reference crop (potential) evapotranspiration (ETo) from data collected by an automatic ...
POTENTIAL EVAPOTRANSPIRATION PROGRAM FOR AUTOMATIC WEATHER STATIONS Version 3.0
POTENTIAL EVAPOTRANSPIRATION PROGRAM FOR AUTOMATIC WEATHER STATIONS
Dr Tim Hess Institute of Water and Environment Cranfield University Silsoe Bedford MK45 4DT UK tel. fax
+44 (0)1525 863292 +44 (0)1525 863344
POTENTIAL EVAPOTRANSPIRATION FOR AUTOMATIC WEATHER STATIONS The program has been written to calculate daily reference crop (potential) evapotranspiration (ETo) from data collected by an automatic weather station. The software allows the calculation of daily evapotranspiration by two approaches; •
Daily: Weather data, recorded hourly (or at any other time step), are aggregated into daily means and totals which are used to calculated daily evapotranspiration (in mm/d).
•
Evapotranspiration is calculated for each time step of the weather data and aggregated into a daily total.
The results are written to data files that can be printed, loaded into a spreadsheet or used as input to other programs (such as the Silsoe soil water balance). Additionally a daily summary of the input, and derived, weather data is generated. The software may be installed on computers based on a single site within the department or section of a company, institute or organisation purchasing the software. Copies may be made for backup purposes only. It may not be copied for distribution, resale, hire or rental or any purpose other than the legitimate purposes above without the prior approval of Cranfield University. Whilst every effort has been made to ensure the validity of the algorithms used in the calculation equations, the accuracy of the calculated evapotranspiration depends upon the accuracy of the input data measurement, siting of the weather station and relevance of the chosen evapotranspiration calculation method. Cranfield University takes no responsibility for matters arising from the application of the results of this program. AWSET Version 3 © Cranfield University (2002)
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Contents 1.
Introduction _____________________________________________________ 1
1.1
Calculation methods _____________________________________________ 1
1.1.1 1.1.2 1.1.3 1.1.4 1.1.5
Penman-Monteith Method ________________________________________________ FAO Modified Penman Method ____________________________________________ Penman Method _______________________________________________________ Penman-Monteith (time step method)________________________________________ Penman Open Water Method______________________________________________
1 1 1 1 2
2.
Installation______________________________________________________ 3
3.
Running the program _____________________________________________ 4
3.1
Configure _____________________________________________________ 4
3.1.1 3.1.2 3.1.3
3.2
File __________________________________________________________ 8
3.2.1 3.2.2 3.2.3
3.3
4.
Options ______________________________________________________________ 4 Data File Format________________________________________________________ 6 Station Parameters ______________________________________________________ 7 Single data file _________________________________________________________ 8 One file per day ________________________________________________________ 9 Calculation __________________________________________________________ 10
View ________________________________________________________ 10
Daily Calculation Methods ________________________________________ 11
4.1
Humidity variables _____________________________________________ 11
4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6
Mean vapour pressure __________________________________________________ Relative humidity______________________________________________________ Wet and dry bulb temperature ____________________________________________ Saturation vapour pressure ______________________________________________ Mean air pressure _____________________________________________________ Wind speed at 2 m_____________________________________________________
11 12 12 12 12 12
4.2
Convert wind speed to 2m equivalent ______________________________ 12
4.3
Radiation variables _____________________________________________ 14
4.3.1 4.3.2 4.3.3 4.3.4 4.3.5
4.4
14 14 14 14 14
Evapotranspiration calculation methods ____________________________ 15
4.4.1 4.4.2 4.4.3 4.4.4
5.
Maximum solar radiation ________________________________________________ Day length___________________________________________________________ Incoming solar radiation_________________________________________________ Actual sunshine duration________________________________________________ Soil heat flux _________________________________________________________ Penman-Monteith _____________________________________________________ Penman (1967) ________________________________________________________ FAO Modified Penman _________________________________________________ Penman open water ____________________________________________________
15 18 20 22
Time step calculation Method______________________________________ 23
5.1 5.1.1 5.1.2 5.1.3 5.1.4
5.2
Net radiation__________________________________________________ 23 Net long wave radiation _________________________________________________ Clear sky solar radiation_________________________________________________ Hour angle___________________________________________________________ Net radiation _________________________________________________________
23 23 23 23
Soil heat flux __________________________________________________ 23
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5.2.1 5.2.2
5.3
Potential evapotranspiration _____________________________________ 23
5.3.1 5.3.2
5.4
6.
Daytime _____________________________________________________________ 23 Night time ___________________________________________________________ 23 Aerodynamic term _____________________________________________________ 24 Radiation term ________________________________________________________ 24
Surface parameters and resistance factors __________________________ 26
References _____________________________________________________ 29
List of figures Figure 1. Main screen ____________________________________________________________ 4 Figure 2 Options screen __________________________________________________________ 5 Figure 3 Data file format configuration ______________________________________________ 7 Figure 4 Station parameter configuration ____________________________________________ 7 Figure 5 File Open dialog box for single data files ______________________________________ 9 Figure 6 File Open dialog box for 'one file per day' option.________________________________ 9 Figure 7 Example view of daily summary ____________________________________________ 10
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1. INTRODUCTION 1.1 Calculation methods The program offers the user alternative methods of evaporation / evapotranspiration calculation by combination equations from various sources. Three of the methods calculate daily evapotranspiration only, using hourly (or shorter time step) data to calculate daily totals, means, maxima and minima and then calculate daily reference evapotranspiration (ETo) from the daily weather parameters. One method calculates the evapotranspiration for each time step of the weather data and aggregates those into a daily total. With this method, resistance factors for other surfaces can be used and the evapotranspiration flux (mm/h) for each time step can be calculated. One method is provided for estimating daily open water evaporation, Eo. 1.1.1 Penman-Monteith Method This is based on the original form of the Penman-Monteith equation (Monteith, 1965 & 1981). The equations used for ET0 are those recommended by the Food and Agriculture Organisation of the United Nations (FAO) using factors for a reference surface1 (Allen et al., 1999). The method should be appropriate in all parts of the world and is identical to the ETsz recommended for the USA by the ASCE-EWRI (ASCE, 2001). 1.1.2 FAO Modified Penman Method This uses the method of Doorenbos and Pruitt (1976). The equations used are those presented by Smith (1988) for a grass reference crop. The equation has widely used outside of UK, but has a tendency to overestimate ETo in temperate climates and is not generally recommended for use in the UK. 1.1.3 Penman Method This uses the version of the Penman equation (Penman, 1948) for grass presented by MAFF (1967). The look-up tables used in that publication are substituted by equations presented by Mason (1978). The method is primarily intended for UK conditions. A spreadsheet version of the equations used can be found in Hess and Stephens (1993). 1.1.4 Penman-Monteith (time step method) The Penman-Monteith method can be used to calculate the evapotranspiration flux on an hourly, or other, timestep. The methods used are as presented in Allen et al. (1999). By selecting the
1 Defined as ‘the rate of evapotranspiration from a hypothetical crop with an assumed height of 12cm, a fixed
canopy resistance of 70 s m-1, and an albedo of 0.23, closely resembling the evapotranspiration from an extensive surface of green grass of uniform height, actively growing, completely shading the ground and not short of water’. AWSET3.DOC
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appropriate resistance factors the method can be used to calculate the FAO reference ETo (Allen et al., 1999) or the ASCE-EWRI reference ETsz (ASCE, 2001)2 . Resistance factors can also be entered for any other surface and the potential evapotranspiration can be calculated. 1.1.5 Penman Open Water Method This uses the version of the Penman equation (Penman, 1948) for open water presented by Penman (1963).
2 The FAO ETo uses a daytime surface resistance of 70 s/m whereas the ASCE method uses 50 s/m. AWSET3.DOC
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2. INSTALLATION The AWSET program is supplied on two 3.5” disks and must be installed on the hard disk. • Insert the 3.5” disk labelled ‘Disk 1’ in the computer’s disk drive • Run SETUP.EXE. • This will create a folder called \AWSET3 on your hard disk with the program file in it. It will also create a program group on your start menu. DO NOT INSTALL AWSET3 IN THE ROOT DIRECTORY OF YOUR HARD DISK, ALWAYS INSTALL IT TO A FOLDER.
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3. RUNNING THE PROGRAM The main screen shows four menu options that are used to control the program.
Figure 1. Main screen Each of the menus can be activated by ‘clicking’ with the mouse pointer or typing the letter that is underlined whilst holding down the key. Additionally, the main functions also have short-cut keys to allow them to be accessed directly using the keys. The status bar shows the currently selected evapotranspiration calculation method and the station and data-file format filenames (see 3.1 below). 3.1 Configure The configuration options allow description of the ET calculation method, output requirements, input data file format and the weather station parameters. 3.1.1 Options 3.1.1.1 ET method The options screen (Figure 2) is used to define the ET calculation method and output requirements. If the Penman-Monteith (time step) method is chosen, then the reference surface should be selected. In addition, the method for calculating aerodynamic resistance can be set. If the ‘resistance for trees’ box is not checked, then the resistance is calculated from equation 22 (Allen et al., 1981). For tress, equation 71 can be used (Thompson et al. 1981).
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Figure 2 Options screen 3.1.1.2 Synoptic hour The synoptic hour is the hour at which evapotranspiration will be calculated for the previous 24 hours. Conventional (manual) weather stations are only read at certain times of the day, therefore readings are usually summarised at a particular synoptic hour (e.g. 0900GMT in the UK). Alternatively, with automatic weather stations, evapotranspiration may be calculated for calendar days (midnight to midnight) by setting the synoptic hour to zero. 3.1.1.3 Output requirements Three output files may be selected; þ Summary writes a daily summary of the input weather data and derived values (including ETo) to a file with the name filename.SUM. þ ETo and rainfall only writes the date, daily ETo and daily rainfall to a file with the name filename.ETO. þ ET flux writes the date, time and ET rate in mm/h to a file with the name filename.ETF. (only available for the time step method) Where filename is the name of the weather data file. Each of the output files is written in ASCII format and can be loaded into a word processor or spreadsheet. The options are saved when you click on OK. Clicking on Cancel will revert to the previous options. NB. The option settings are preserved between sessions and therefore do not need to be reset each time the program is run.
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3.1.2 Data File Format The data file format screen (Figure 3) allows the user to specify the format of the data file containing the automatic weather station data. The data file should be ASCII (i.e. not binary) and data should be in columns with one row for each time step of the data. Number of columns
Defines the number of columns of data in the data file.
Separator
Defines the way the columns are separated. There are three options; • Space(multiple spaces are treated as a single separator) • Comma • Tab
Time step (hrs)
The time step (in hours) of the data should be set. This allows integration of rates (e.g. conversion of radiation in W/m2 to MJ/m2). The time step cannot be varied within one data file. The minimum time interval allowed is 5 minutes.
One file per day
Some weather stations record each day’s data in a separate data file, rather than a single data file for all the data. If this is the case then the ‘one file per day’ box must be checked. NB. If the data are stored in separate data files for each day, then the first record for 00:00:00 relates to the last timestep of the previous day, therefore, to calculate values for a single day requires the data files for that day and the previous day to be selected.
The following check boxes allow specification of what sensors are used, the units in which data are recorded and the column in which the data are stored. If the date is recorded in the form DD MM YY (i.e. separated by spaces) then you need only specify the column of the day and it is assumed that month and year are in the next two columns. The DD/MM/YY format can accept two- or four-digit years. If two-digit years are used, then a value greater than 50 implies 19xx (twentieth-century) and a value equal to or less than 50 implies 20xx (twenty-first century) as specified by BSI DISC PD2000-1:1998.
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Figure 3 Data file format configuration The data file configuration may be saved (using Save or Save As from the File menu) and loaded using Load. By this means, a library of data file configurations can be created. 3.1.3 Station Parameters Before calculations can be made, it is necessary to set a number of station parameters (Figure 4). Each item on the form can be accessed using the mouse pointer and left mouse button, or pressing the letter underlined whilst holding down the Alt key.
Figure 4 Station parameter configuration AWSET3.DOC
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3.1.3.1 Station Name This is not used in calculations but is written to identify the station. 3.1.3.2 Latitude, Longitude & Altitude The latitude and longitude3 of the station (in degrees and minutes) and altitude (in metres) can be set using the scroll bar. The scroll bar can be set using the mouse or the arrow keys on keyboard. 3.1.3.3 Time zone The time zone is used along with the longitude, in the calculation of potential solar radiation if the time step method is used. This should be the time zone that the weather station clock is set to. Stations east of Greenwich will be positive and those west of Greenwich will be negative. 3.1.3.4 Anemometer The calculations of evapotranspiration as based on wind speed at 2.0 m above ground level. Wind speeds measured at different heights are adjusted to an equivalent wind speed at 2.0, using equation 4, therefore the height of the anemometer (above ground level) should be entered. 3.1.3.5 Ångström constants These are the constants used to estimate sunshine hours (if not measured) from solar radiation (see 4.3.3 below). The default values are a = 0.25 and b = 0.50 (Allen et al., 1998). Locally applicable values may be calibrated based on observations of sunshine duration and measured solar radiation. Doorenbos and Pruitt (1976, Appendix VI) and Martínez-Lozano, et al. (1984) present experimentally determined values of a and b for a range of locations world-wide. The station configuration may be saved (using Save or Save As from the file menu) and loaded using Load. By this means, a library of station configurations can be created. 3.2 File Once the data file and station parameters have been set you will see the names of the currently selected configurations appear in the status bar at the bottom of the AWSET screen. You may then proceed to calculate evapotranspiration. 3.2.1 Single data file Select the data file to be processed by selecting Open from the File menu.
3 Only required if the time step ET method is used AWSET3.DOC
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Figure 5 File Open dialog box for single data files A dialog box will be displayed that allows you to browse directories to locate the required file. By default only files with the extension ‘.DAT’ will be displayed. Other filters may be applied by selecting from the ‘List of file type’ menu. To display all files type ‘*.*’ in the File Name box (or any other extension filter). 3.2.2 One file per day
Figure 6 File Open dialog box for 'one file per day' option. If the data is stored in one file per day, then a different dialog box will be displayed. Select the folder containing the data files in the right hand box and all files in that folder with the extension *.DAT will be shown in the left hand box. • To select a ‘block’ of files, click on the first file, then, whilst holding the key, click on the last file. • To select several files, click on each file in turn whilst holding down the key.
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3.2.3 Calculation Once the input file(s) has been selected, the calculation commences. As the calculations are being done, the current date and daily evapotranspiration (mm/day) are shown on the form. The calculation can be stopped at any time by pressing the key. 3.3 View When the calculation is complete, a summary of the daily weather data (Figure 7) can be viewed by selecting from the View menu. This option will not be available until calculations have been completed. •
Parameters that have been estimated by the program are shown in blue.
•
Any days for which there was an incomplete record will be left blank.
Figure 7 Example view of daily summary Selecting Close from the View menu will clear the display.
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4. DAILY CALCULATION METHODS Evapotranspiration is calculated on a daily basis from; • • • • •
maximum air temperature, °C minimum air temperature, °C mean daily vapour pressure, kPa net radiation, MJ m-2 d-1 wind run, km d-1
The following input data required by the Penman equation for each time step; þ Maximum and minimum (or mean) air temperature (required) þ Mean vapour pressure (calculated from relative humidity or wet & dry4 bulb temperatures). If no humidity measurements are available, daily mean vapour pressure is estimated from the saturation vapour pressure at the minimum air temperature. þ Mean wind speed (required). þ One of net radiation, solar (global) radiation or sunshine ratio (required). If net radiation is not available, longwave radiation is estimated from air temperature, sunshine ratio and humidity. If solar radiation is not available, it is estimated from the sunshine duration, time of year and latitude. If sunshine ratio (actual sunshine / potential sunshine duration) is not available, it is estimated from the solar radiation, time of year and latitude. The following data are optional and will be used if present, if not they will be estimated; o
Barometric pressure. If not available, this is estimated from the altitude (m) of the station.
o
Soil heat flux. If soil heat flux is not available, it is estimated as a fraction of net radiation.
o
Rainfall. This is not used in the calculation, but if available it is written to the output file for subsequent use.
4.1 Humidity variables 4.1.1 Mean vapour pressure If vapour pressure for each time step is given, this is averaged and used as input to the evapotranspiration equation.
4 If a wet and dry bulb psychrometer is present, the ambient air temperature will be used for the dry bulb
temperature. AWSET3.DOC
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4.1.2 Relative humidity If relative humidity for each time step is given, then for each timestep, ed =
RH 100
eaT max + eaT min 2
(Allen at al., 1998) (19)
4.1.3 Wet and dry bulb temperature If wet and dry bulb temperatures for each time step are given, then for each timestep. ed = eaTwet − γ (Tdry − Twet )P
(1)
4.1.4 Saturation vapour pressure ea = 0.61078e
17.27 T T + 237.3
(Tetens, 1930) (2)
4.1.5 Mean air pressure g ηR
T − η ( A − A0 ) P = P0 k 0 T k0
(Burman et al., 1987) (3)
4.1.6 Wind speed at 2 m The wind speed measured at height z, m, is converted to an equivalent 2 m wind speed (assuming that wind speed is measured above a reference grass surface) using 4.2 Convert wind speed to 2m equivalent
U2 4.87 = U z ln (67.8 z − 5.42 )
AWSET3.DOC
(Allen et al. 1989) (4)
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Symbol γ η A A0 eaT ed g P P0 R RH Tdry Tk0 Twet
Description psychrometric constant for natural ventilation constant lapse rate altitude altitude at sea level saturation vapour pressure at temperature T actual vapour pressure gravitational acceleration atmospheric pressure atmospheric pressure at sea level specific gas constant relative humidity dry bulb temperature reference temperature at sea level wet bulb temperature
AWSET3.DOC
Unit kPa °C -1
Value 0.0008
K m-1 m m kPa
0.0065K m-1
kPa m s-2 kPa kPa J kg-1 K-1 % °C K °C
13
0m
9.8 m s-2 101.3kPa 287 J kg-1 K-1
293.16K
2 October, 2002
4.3 Radiation variables 4.3.1 Maximum solar radiation 2π δ = 0.4093Sin J − 1.405 365
(5)
ω = arccos (− Tan(L ) * Tan(δ ))
(Duffie & Beckman, 1980) (6)
2π d r = 1 + 0.033 cos J 365
(Duffie & Beckman, 1980) (7)
Ra =
G sc d r [ω sin ( L) sin (δ ) + cos (L ) cos (δ ) sin (ω )] π
(Duffie & Beckman, 1980) (8)
4.3.2 Day length N =
24 ω π
(Duffie & Beckman, 1980) (9)
4.3.3 Incoming solar radiation If no solar radiation data are available, then Rs = Ra (a s + bs
n N
)
(10)
4.3.4 Actual sunshine duration If no sunshine data are available, then
n=
1 Rs − a s bs Ra
(11)
4.3.5 Soil heat flux G = 0.38(Ti − Ti −1 )
AWSET3.DOC
(Wright & Jensen, 1972) (12)
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Symbol δ ω as bs G Gsc J L n N Ra Rs Ti
Description solar declination sunset hour angle Ångström constant Ångström constant soil heat flux solar constant Julian day number (Jan 1 = 1) latitude daylight hours maximum daylight hours extra-terrestrial radiation incoming shortwave radiation mean air temperature on day I
Unit rad rad MJ m-2 d-1 MJ m-2 d-1 rad h d-1 h d-1 MJ m-2 d-1 MJ m-2 d-1 °C
Value
118.08 MJ m-2 d-1
4.4 Evapotranspiration calculation methods 4.4.1 Penman-Monteith5 4.4.1.1 Net radiation If net radiation is not measured it is estimated from; Rns = (1 − α )Rs
(13)
bs n as + bc + f = ac ac as + bs as + bs N
(14)
ε ′ = al + bl ed
(15)
Tk 4 + Tk min 4 Rnl = − fε ′σ max 2
(16)
Rn = Rns + Rnl
(17)
4.4.1.2 Evapotranspiration T + Tmin T = max 2
(18)
5 Methods are taken from Smith (1991). AWSET3.DOC
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λ = 2.501 − 0.002361T ea =
∆=
(19)
eaTmax + ea Tmin
(20)
2
4098ea (T + 237. 3)2
(21)
Zw − d Zs − d ln x ln Zom Zoh ra = κ 2U z
(22)
cpP × 10− 3 ελ
(23)
rc * γ = γ 1 + ra
(24)
γ =
ed Tkv = Tk 1 − 0.378 P
ρ=
−1
(25)
P
(26)
R Tkv 1000
ETaero =
86.4 1 ρcp (ea − ed ) λ ∆ + γ * ra
(27)
ETrad =
∆ (R n − G) ∆ +γ* λ
(28)
ETo = ETrad + ETareo
Symbol λ ∆ γ ρ α κ ε σ ε‘
(29)
Description latent heat of vapourisation slope of vapour pressure curve psychrometric constant atmospheric density albedo von Karman constant ratio of molecular weight of water to dry air Stefan Boltzman constant net emissivity
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Unit MJ kg-1 kPa °C -1 kPa °C -1 kg m-3 -
Value
MJ m-2 K-4 d-1 -
4.903 x 10-9 MJ m-2 K-4 d-1
0.23 for grass 0.41 0.622
2 October, 2002
γ* ac al as bc bl bs cp d ea ed ETaero ETo ETrad f G n P R ra rc Rn Rn Rnl Rns Rs Ti Tk Tkv Tmax Tmin Uz Zoh Zom Zs Zw
kPa °C -1 kJ kg-1 °C-1 m
modified psychrometric constant empirical constant empirical constant Ångström constant empirical constant empirical constant Ångström constant specific heat of moist air zero plane displacement of wind profile mean saturation vapour pressure actual vapour pressure aerodynamic term reference crop evapotranspiration radiation term cloudiness factor Soil heat flux bright sunshine hours atmospheric pressure specific gas constant aerodynamic resistance bulk surface resistance net radiation net radiation net longwave radiation net shortwave radiation incoming solar radiation mean air temperature for day i mean air temperature virtual temperature maximum air temperature minimum air temperature windspeed at height z roughness parameter for heat and water vapour roughness parameter for momentum screen height height of windspeed measurement
AWSET3.DOC
kPa kPa mm d-1 mm d-1 mm d-1 MJ m-2 d-1 h d-1 kPa J kg-1 K-1 s m-1 s m-1 MJ m-2 d-1 MJ m-2 d-1 MJ m-2 d-1 MJ m-2 d-1 MJ m-2 d-1 °C K K °C °C m s-1 m m m m
17
1.35 0.34 -0.35 -0.14 1.013 kJ kg-1 °C-1 0.08m for grass
287 J kg-1 K-1 70 s m-1 for reference grass
0.0015m for grass 0.01476m for grass 1.2m 2m
2 October, 2002
4.4.2 Penman (1967)6 4.4.2.1 Net radiation λ = 4.1868(597.31 − 0.565T ) Rns = (1 − α )
f (T ) = σTk
(Mason, 1978) (30)
100Rs 10λ
(31)
4
(32)
f (ed ) = 0.47 − 0.075 0.75(10ed ) f (n ) = 0.17 + 0.83
(33)
n N
(34)
Rnl = f (T ). f (ed ). f (n )
(35)
Rn = Rns − Rnl
(36)
4.4.2.2 Evapotranspiration T + Tmin T = max 2
(37)
U f (U ) = 0.262521561 + 0.01 1.609334
(Mason, 1978) (38)
Ea = f (U )10(ea − ed ) ∆=
10ea 6970 − 5.028 Tk Tk
γ =
2.4 P 0.62196λ
Rn ETo =
(39) (40)
(Mason, 1978) (41)
∆ + Ea γ ∆ +1 γ
(42)
6 Methods are based on Hess and Stephens, 1993. AWSET3.DOC
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Symbol λ α σ ∆ γ λ ea ed Ea ETo f(ed) f(n) f(T) f(U) n N P Rn Rns Rs T Tk Tmax Tmin U
Description latent heat of vapourisation albedo Stefan Boltzman constant slope of vapour pressure curve psychrometric constant latent heat of vapourisation mean saturation vapour pressure actual vapour pressure aerodynamic term reference crop evapotranspiration humidity factor cloudiness factor temperature term wind function bright sunshine hours maximum daylight hours atmospheric pressure net radiation net shortwave radiation incoming solar radiation mean air temperature mean air temperature maximum air temperature minimum air temperature wind speed
AWSET3.DOC
Unit J g-1 mm K-4 d-1 mb °C-1 mb °C-1 J g-1 kPa kPa mm d-1 mm d-1 mm d-1 mm mb-1 d-1 h d-1 h d-1 kPa mm d-1 mm d-1 MJ m-2 d-1 °C K °C °C km d-1
19
Value 0.25 for grass 1.9885 x 10-9 mm K-4 d-1
2 October, 2002
4.4.3 FAO Modified Penman7 4.4.3.1 Net radiation R Rns = (1 − α ) s 2.45
(
(43)
)
Rnl = σTk 7.723 − 10ed (0.1 + 0.9 Nn )
(44)
Rn = Rns − Rnl
(45)
4
4.4.3.2 Evapotranspiration U f (U ) = 0.271 + 100
(46)
γ = 0.006595P
(47)
∆=
10ea 6790 Tk Tk − 5.028
(48)
W =
∆ ∆+γ
(49)
Ud =
U 1 1 1 + k 43.2
(50)
ed x100% RH max = eaT min
(51)
c = a0 + a1 RH max + a2 Rs + a3U d + a4k + a5U d k + a 6 RH max RsU d + a7 RH max Rs k (Frevert et al., 1983) (52) ETo = c[WRn + (1 − W ) f (U )10(ea − ed )]
(53)
7 Methods are based on Smith (1988). AWSET3.DOC
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Symbol α σ
Description albedo Stefan Boltzman constant
Unit mm K-4 d-1
∆ γ a0 a1 a2 a3 a4 a5 a6 a7 ea ed ETo f(U) k n N P RHmax Rn Rnl Rns Rs Tk U Ud W
slope of vapour pressure curve psychrometric constant constant in estimation of c constant in estimation of c constant in estimation of c constant in estimation of c constant in estimation of c constant in estimation of c constant in estimation of c constant in estimation of c mean saturation vapour pressure actual vapour pressure reference crop evapotranspiration wind function day - night wind ratio bright sunshine hours maximum daylight hours atmospheric pressure maximum relative humidity net radiation net longwave radiation net shortwave radiation incoming solar radiation mean air temperature wind speed daytime wind speed weighting factor
mb °C-1 mb °C-1 kPa kPa mm d-1 mm mb-1 h d-1 h d-1 kPa % mm d-1 mm d-1 mm d-1 MJ m-2 d-1 K m s-1 km d-1 -
AWSET3.DOC
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Value 0.25 for grass 8.727 x 10-12 mm K-4 d-1
0.6817 0.0027864 0.0181768 -0.0682501 0.0126514 0.0097297 0.43025 E-4 -0.92118 E-7
2 October, 2002
4.4.4 Penman open water 4.4.4.1 Net radiation Net radiation, Rn, is calculated as in section 4.4.1.1 above except that an albedo, α, of 0.05 is used for open water. 4.4.4.2 Evaporation 0.621375 U Ea = 0.35 0.5 + 7.500638 (ea − ed ) 100 Rn Eo =
(Penman, 1963) (54)
∆ λ γ + Ea ∆ +1 γ
(55)
λ, ∆ and γ are calculated as in section 4.4.1.2 above. Symbol λ ∆ γ α ea ed Ea Eo Rn
Description latent heat of vapourisation slope of vapour pressure curve psychrometric constant albedo mean saturation vapour pressure actual vapour pressure aerodynamic term open water evaporation net radiation
AWSET3.DOC
Unit MJ kg-1 kPa °C -1 kPa °C -1 kPa kPa mm d-1 mm d-1 MJ m-2 d-1
22
Value
0.05 for open water
2 October, 2002
5. TIME STEP CALCULATION METHOD Methods for the calculation of evapotranspiration for each time step are as for the Penman-Monteith method (section 4.4.1) except the following (Allen et al., 1998) 5.1 Net radiation 5.1.1 Net long wave radiation
(
)
Rs 4 Rnl = σTk 0.34 − 0.14 e d 1.35 − 0.35 Rso
(56)
5.1.2 Clear sky solar radiation Rso = (a s + bs )Ra
(57)
12 xtimestep G sc d r [(ω 2 − ω1) sin ( L )sin (δ ) + cos (L ) cos(δ )(sin (ω1) − sin (ω 2 ))] π (Duffie & Beckman, 1980) (58) Ra =
5.1.3 Hour angle ω=
π [(t + 0.06667( Lz − Lm ) + S c ) − 12] 12
(59)
S c = 0.1645 sin (2b) − 0.1255 cos(b ) − 0.025 sin (b) b=
2π ( J − 81) 364
(60) (61)
5.1.4 Net radiation
Rn = Rs (1 − α ) + Rnl
(62)
5.2 Soil heat flux 5.2.1 Daytime G = 0.1 Rn
(63)
5.2.2 Night time G = 0.5 Rn
(64)
5.3 Potential evapotranspiration ETp = ETrad + ETareo
AWSET3.DOC
(65)
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2 October, 2002
5.3.1 Aerodynamic term ETaero =
0.001 1 ρcp (ea − ed ) λ ∆ + γ * ra
(66)
5.3.1.1 Aerodynamic resistance d = 23 hc
(67)
Zom = 0.123 hc
(68)
Zoh = 0.1 * Zom
(69)
For vegetation other than trees; Zw − d Zs − d x ln ln Z Z ra = om 2 oh κ Uz
(70)
For trees ra =
94 U 10
(Thompson et al. 1981) (71)
5.3.2 Radiation term ETrad =
∆ Rn − G ∆ + γ * λ × 1E 6
AWSET3.DOC
(72)
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Symbol δ η λ ∆ γ γ* ρ σ α κ ε ω1 ω2 as bs A A0 cp d ea ed ETaero ETp ETrad G g h h0 hc J Lm Lz LT P P0 R ra rc Rn Rnl Rs Rso T
Description solar declination constant lapse rate latent heat of vapourisation slope of vapour pressure curve psychrometric constant modified psychrometric constant atmospheric density Steffan-Boltzman constant albedo von Karman constant ratio of molecular weight of water to dry air Solar time at time h – timestep (hours) Solar time at time h Ångström constant Ångström constant altitude altitude at sea level specific heat of moist air zero plane displacement of wind profile mean saturation vapour pressure actual vapour pressure aerodynamic term potential crop evapotranspiration radiation term soil heat flux gravitational acceleration local time local time of solar noon crop height Julian day number (Jan 1 = 1) Longitude of measurement site longitude of standard meridian latitude atmospheric pressure atmospheric pressure at sea level specific gas constant aerodynamic resistance canopy resistance net radiation net longwave radiation incoming shortwave radiation Clear sky shortwave radiation mean air temperature
AWSET3.DOC
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Unit rad K m-1 MJ kg-1 kPa °C -1 kPa °C -1 kPa °C -1 kg m-3 MJ m-2 h-1 rad rad m m kJ kg-1 °C-1 m kPa kPa mm d-1 mm d-1 mm d-1 MJ m-2 d-1 m s-2
m ° ° rad kPa kPa J kg-1 K-1 s m-1 s m-1 W m-2 W m-2 W m-2 W m-2 °C
Value 0.0065K m-1
2.043 10-10 MJ m-2 h-1 0.41 0.622
0m 1.013 kJ kg-1 °C-1 0.08m for grass
9.8 m s-2
101.3kPa 287 J kg-1 K-1
2 October, 2002
Tk Tk0 Tkv Uz Zoh Zom Zs Zw
mean air temperature reference temperature at sea level virtual temperature windspeed at height z roughness parameter for heat and water vapour roughness parameter for momentum screen height height of windspeed measurement
K K K km timestep-1 m m m m
293.16K
1.2m 2m
5.4 Surface parameters and resistance factors By default, the program calculates Evapotranspiration for a reference grass surface, defined as ‘a hypothetical crop with an assumed height of 12cm, a fixed canopy resistance of 70 s m-1, and an albedo of 0.23’8 . Potential evapotranspiration for different land covers can be determined by selecting the land cover from the drop-down list under the station configuration option. Resistance and crop height data for different land covers are stored in a comma separated ASCII data file called ‘CROPFAC.TXT’. The format of this file is described below. Further land covers can be added to this file and they will automatically appear on the list when the program is run. The first line is a heading and is ignored by the program. Then, for each cover type; 1. The first line contains the cover name, followed by the albedo. In the case of incomplete covers, this refers to the albedo at full cover. This is adjusted for incomplete cover within the program according to the leaf area index. If the leaf area index is zero (or blank), as in the case of bare soil or water, then the albedo for full cover is used. 2. The second line contains the label ‘hc’ followed by the crop height (m) in each month of the year (i.e. 12 values). 3. The third line contains the label ‘rc(d)’ followed by the canopy resistance (s m-1) during the daytime for each month of the year. 4. The fourth line contains the label ‘rc(n)’ followed by the canopy resistance (s m-1) during the night-time for each month of the year. 5. The fifth line is contains the label ‘LAI’ followed by the average leaf area index for each month of the year. If no LAI is given, complete ground cover is assumed.
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2 October, 2002
Table 1 Contents of CROPFAC.TXT Reference Grass hc rc(d) rc(n) LAI MORECS Grass hc rc(d) rc(n) LAI Bare Soil hc rc(d) rc(n) LAI Water hc rc(d) rc(n) LAI ASCE Reference Grass hc rc(d) rc(n) LAI
AWSET3.DOC
January 0.23 0.12 69.4 200 2.88 0.25 0.15 89.8 1350 2 0.2 0.001 100 100
February
March
April
May
June
July
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.12 69.4 200 2.88
0.15 89.8 1350 2
0.15 73.7 933.3 3
0.15 62 725 4
0.15 50.1 600 5
0.15 66.7 600 5
0.15 66.7 600 5
0.15 75 600 5
0.15 77.2 725 4
0.15 80.3 933.3 3
0.15 88.2 1100 2.5
0.15 89.8 1350 2
0.001 100 100
0 100 100
0.001 100 100
0.001 100 100
0.001 100 100
0.001 100 100
0.001 100 100
0.001 100 100
0.001 100 100
0.001 100 100
0.001 100 100
0.05 0.001 0 0
0.001 0 0
0 0 0
0.001 0 0
0.001 0 0
0.001 0 0
0.001 0 0
0.001 0 0
0.001 0 0
0.001 0 0
0.001 0 0
0.001 0 0
0.23 0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
0.12 50 200 2.88
28
August September October
2 October, 2002
November December
6. REFERENCES Allen, R. G., Jensen, M. E., Wright, J. L. and Burman, R. D., (1989) Operational estimates of evapotranspiration. Agronomy Journal 81:650-662. Allen, R. G., Pereira, L.S., Raes, D. and Smith, M. (1998) Crop evapotranspiration. Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56. Rome. 300pp. ASCE (2001) The ASCE standardized reference evapotranspiration equation. Environmental and Water Resource Institute of the American Society of Civil Engineers, standardized reference evapotranspiration committee. Draft. December 2001. Doorenbos, J. and Pruitt, W. O. (1976) Guidelines for predicting crop water requirements. FAO Irrigation and Drainage Paper 24, 2nd ed. Rome. 156pp. Duffie, J. A. and Beckman, W. A. (1980) Solar engineering of thermal processes. John Wiley & Sons, New York. pp1-109. Frevert, D. K., Hill, R. W. and Braaten, B. C. (1983) Estimation of FAO evapotranspiration coefficients. J. of Irrig. and Drainage Eng. 109:265-270 Hess, T. M. and William Stephens (1993) The Penman equation. In Spreadsheets in Agriculture, Eds. D. H. Noble and C. P. Course. Longman Scientific and Technical, pp184-194. Martínez-Lozano J. A., Tena, F., Onrubia, J. E. and De La Rubia, J., (1984) The historical evolution of the Ångström formula and its modifications: review and bibliography. Agricultural and Forest Meteorology, 33:109-128. Mason, D. J. (1978) Input parameters for combination equation. MSc thesis, Silsoe College, Silsoe, Bedford. Unpubl. Monteith, J. L. (1965) Evaporation and the environment. In: The state and movement of water in living organisms. XIXth Symposium. Soc for xp. Biol., Swansea. Cambridge University Press. pp. 205-234. Monteith, J. L. (1981) Evaporation and temperature. Q. J. Royal Meteo. Soc. 107:1-27. Penman, H. L. (1948) Natural evaporation from open water, bare soil and grass. Proc. Royal Soc., London, Series (A) 193:120-145. Penman, H. L. (1963) Vegetation and hydrology. Tech. Comm. no. 53. CAB, Farnham, England. pp124 Smith, M. (1988) Calculation procedures of modified Penman equation for computers and calculators. FAO, Land and Water Development Division, Rome. Smith, M. (1991) Expert consultation on revision of FAO methodologies for crop water requirements. FAO, Land and Water Development Division, Rome. Thompson, N., Barrie, I. A. and Ayles, M. (1981). The meteorological office rainfall and evaporation calculation system: (MORECS). Hydrological Memorandum No. 45. The Met Office. Bracknell, UK. Tetens, O. (1930) Uber einige meteorologische Begriffe. Z. Geophys. 6:297-309 Wright, J. L. and Jensen M. E. (1972) Peak water requirements of crops in Southern Idaho. J. Irrig. and Drain. Div., ASCE. 96(IR1):193-201.
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2 October, 2002
Software for the calculation of reference evapotranspiration from automatic weather stations AWSET V3
Year 2000 Conformity This document describes how the AWSET V3 software conforms to the requirements for Year 2000 conformity as specified in BSI DISC PD2000-1:1998. General: The AWSET V3 software uses the Gregorian Calendar and is applicable for dates after 1 January 1900. Rule 1. General integrity. The AWSET V3 software will successfully cope with roll-over of dates. Rule 2. Date integrity. The AWSET V3 software will correctly calculate, manipulate and represent dates for the purpose for which it is intended. Rule 3. Explicit / implicit century. Where the original data file contains explicit representation of the year (i.e. four-digits), this is used in the AWSET V3 software. If the original data file contains two-digit years, then a value greater than 50 implies 19xx (twentieth-century) and a value equal to or less than 50 implies 20xx (twenty-first century). Rule 4. Leap years . The AWSET V3 software successfully identifies leap years (as defined by ISO 8601:1998) and correctly identifies 2000 as a leap year. Cranfield University Monday, 12 April 1999
AWSET3.DOC
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2 October, 2002
Cranfield University Software Licence Agreement Terms and Conditions 1. Cranfield University (hereinafter referred to as "the Owner") hereby grants to you the user, and you accept, a personal non-exclusive, non-transferable licence to use the enclosed disk, Program documentation and any related materials (hereinafter referred to as "the Software") on the terms and conditions set out herein. 2. The Software is the Owner's proprietary product and is protected by Copyright Law. The Owner reserves all rights of ownership and copyright in the Software as recorded on the diskette, and all subsequent copies thereof. You the user own only the diskette on which the Software is recorded. 3. The Software is distributed on the basis that they shall not be copied for further distribution or resale without the written permission of the Owner. 4.
You may:
4.1
Install and use the Software on a computer.
4.2
Transfer the Software onto another computer.
4.3 Make full or partial copies of the Software for backup and archive purposes only, provided you label such copies clearly with our name, the name of the program and the date of this licence. 4.4 Transfer the Software and the licence permanently to another party but only if you obtain our prior written approval and provided the other party agrees to these terms and conditions. Any such transfer terminates your licence agreement. 5.
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5.1 Transfer, assign, rent, lease, sub-licence, sell, give or otherwise dispose of this Software except as stated in these Terms and Conditions. 5.2
Reverse compile, disassemble, or otherwise reverse engineer the whole or part of the Software.
5.3
Modify, adapt or translate the Software in any way.
5.4 Merge the whole or part of the Software with any other software other than that strictly required by the operating system stated in these Terms and Conditions. 5.5
Reproduce, distribute or alter the Software documentation.
6.
Your responsibilities:
6.1 You are responsible for installing and commissioning the Software onto your computer system(s) unless the Owner has agreed in writing to do so. 6.2 You must ensure that proper security precautions are followed to secure backup copies of the Software, and that an effective control is kept on the number of copies of the Software. 6.3 You must train the staff that run this Software to understand its purpose, operations and limitations. You are responsible for how you use the Software.
AWSET3.DOC
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2 October, 2002
6.4
You are responsible for the interpretation of the results produced by the Software.
6.5 You must treat this Software and its documentation as confidential. You must not disclose any part of it to another party without the Owner's permission. 7.
Term
7.1.
You are licensed to use the Program indefinitely.
7.2 You may terminate your licence and this Agreement at any time by returning it to us together with the original media and user documentation of the Software. 7.3
This Licence will terminate immediately if you fail to comply with any term or condition of this Agreement.
In the event of any termination you must destroy all full or partial copies of the Software resident on your computer system(s) in any form and you agree to provide to the Owner on request a written certificate of such destruction. 8.
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The Owner warrants that it has the right to licence the Software and that for a period of ninety (90) days from the date of purchase the diskette on which the Software is supplied will be free from all defects. If a diskette or other media of the Software is defective the Owner will replace it at no charge provided that the defective item is returned to the Owner within ninety (90) days from the date of purchase. The Owner warrants that the Software will perform substantially in accordance with the accompanying documentation. EXCEPT FOR THE LIMITED WARRANTY DESCRIBED IN THIS PARAGRAPH THERE ARE NO WARRANTIES EITHER EXPRESSED OR IMPLIED BY THIS AGREEMENT. NO WARRANTY IS GIVEN AS TO THE COMPLETENESS OR ACCURACY OF THE SOFTWARE NOR THAT IT IS ERROR-FREE OR OF A SATISFACTORY QUALITY OR APPEAR PRECISELY AS DESCRIBED IN ANY DOCUMENTATION IN RESPECT OF THE SOFTWARE. ALL OTHER SUCH WARRANTIES ARE EXPRESSLY DISCLAIMED. 9.
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You shall use the Software at your own risk and you agree that regardless of the form of any claim you have, the liability of the Owner and their authorised distributor shall not exceed the value of the Licence fee you have paid for the Software. THE OWNER AND THEIR AUTHORISED DISTRIBUTOR ACCEPT NO LIABILITY FOR ANY LOSS OR DAMAGE, LOSS OF PROFIT, LOSS OF CONTRACTS, ANTICIPATED SAVINGS OR ANY OTHER DIRECT OR INDIRECT CONSEQUENTIAL LOSS OR DAMAGES HOWSOEVER CAUSED EXCEPT THAT WHICH IS UNLAWFUL TO EXCLUDE. Notwithstanding the above, nothing herein shall exclude any liability for death or personal injury which arises as a result of the negligence of the Owner and/or their authorised distributor, their employees, servants or authorised representatives. 10.
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This Agreement shall be governed by and construed in accordance with the law of England and Wales and shall be subject to the jurisdiction of the Courts of England. AWSET3.DOC
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2 October, 2002
