REFERENCE EVAPOTRANSPIRATION CALCULATIONS: COMPARISONS OF SUM OF HOURLY AND DAILY TIME STEPS
Boštjan NAGLIČ23
UDC / UDK 556.13:551.5(045) original scientific article / izvirni znanstveni članek received / prispelo: 12th October 2014 accepted / sprejeto: 25 th November 2014
Abstract
Comparisons among FAO-56-PM and standardized ASCE-PM (sASCE-PM) equations for reference evapotranspiration (ETo) calculations were made with a purpose to assess differences between using a daily (24 h) time step equations (FAO-56-PM and sASCE-PM-daily) and sum of hourly ETo (sASCE-PM) equation. Calculations were performed for grass reference crop using weather data from Celje-Medlog (Slovenia)agrometeorological station. The mean ETo values for investigated period of 23 successive days resulted in ETo of 3.13 mm/day for daily time step FAO-56-PM and sum of hourly sASCE-PM equations. Mean of 3.01 mm/day was observed for sASCE-PM daily time step equation. The paired /-test showed that mean ETo value for entire period calculated with sASCE-PM (based on daily and hourly calculations) equation were not significantly different (P < 0.05) from the ETo values observed with FAO-56-PM equation. This suggests that the daily and hourly time step form of standardized ASCE-PM method for ETo calculations is comparable to FAO-56-PM method for given location and time period.
Key words: evapotranspiration, reference evapotranspiration, Penman-Monteith method, FAO-56-PM equation, standardized ASCE-PM equation, hourly ETo, agrometeorology
IZRAČUNI REFERENČNE EVAPOTRANSPIRACIJE: PRIMERJAVA VSOTE URNIH PROTI DNEVNIM IZRAČUNOM
Izvleček
Narejena je bila primerjava med FAO-56-PM in standardizirano ASCE-PM enačbo za izračun referenčne evapotranspiracije z namenom, da bi ocenili razlike med uporabo dnevnega (24 h) časovnega koraka (FAO-56-PM in sASCE-PM-dnevno) in vsoto urnih vrednosti (sASCE-PM). Izračuni so bili opravljeni za referenčno površino trave ob uporabi vremenskih podatkov, zabeleženih na agrometeorološki postaji Celje-Medlog (Slovenija). Povprečne vrednosti ETo za preiskovano obdobje 23 zaporednih dni so znašale 3,13 mm/dan za metodi FAO-56-PM-dnevno in sASCE-PM-vsoto urnih vrednosti. Povprečna vrednost za sASCE PM metodo za dnevni časovni korak je znašala 3,01 mm/dan. Parni t-test je pokazal, da se povprečna ETo vrednost za celotno preučeno obdobje, izračunano z
23 Dr., univ. dipl. inž. agr., Inštitut za hmeljarstvo in pivovarstvo Slovenije, Cesta Žalskega tabora 2, 3310 Žalec, Slovenia, e-pošta: bostjan.naglic@ihps.si
sASCE-PM (na podlagi dnevnih in umih izračunov), ni pomembno razlikovala (p < 0,05) od vrednosti ETo, opaženih z uporabo FAO-56-PM metode. To kaže, da je dnevna in urna časovna oblika standardizirane ASCE-PM metode za izračune ETo primerljiva s FAO-56-PM metodo za dano lokacijo in za dano časovno obdobje.
Ključne besede: evapotranspiracija, referenčna evapotranspiracija, Penman-Monteith metoda, FAO-56-PM enačba, standardizirana ASCE-PM enačba, urna ETo, agrometeorologija
1 INTRODUCTION
Reference evapotranspiration (ETo) is defined as the rate at which water, if readily available, would be removed from specified soil and plant surfaces (Jensen et al. 1990 cited in Itenfisu et al., 2003). When calculating crop irrigation water requirements the ETc (crop evapotranspiration) has to be calculated by multiplying ETo (reference crop evapotranspiration) with crop coefficient (Kc). About nine major ETo methodologies (1963 Penman, FAO-24 Penman, Kimberly Penman, CIMIS Penman, ASCE Penman-Monteith, FAO-56 Penman Monteith, Hargreaves, Jensen-Haise and pan evaporation) have been traditionally used over the last fifty years for ETo calculations. ETo equations range in sophistication from emprical solar radiation or temperature based equations (i.e. Hargreaves equation) to complex resistance based equations. The most widely used ETo equations are of combination type and most commonly include different versions of the original Penman Monteith (PM) equations (Dorenbos and Pruitt, 1977; Itenfisu et al., 2003). Because so many ETo calculation methods have been introduced this caused some confusion among researchers, growers and consultants about which method to use for ETo estimation.
In recent years advances in research and science resulted in the development of more accurate methods for assessing crop water use. Consequently it was revealed that the different ETo calculation methods did not behave the same way in different locations around the world which presented their major weakness. This unveiled the need for derivation of a standard and more consistent method for ETo calculations. For that reason in 1990 Food and Agricultural Organisation (FAO) organized a conference with scientists, experts and researchers. An outcome of this meeting was the new FAO-56 Penman-Monteith method (FAO-56-PM) which is now recommended as the standard method for calculation of the ETo. This method has a good probability of correctly predicting ETo for a wide range of climates and even in the case of missing meteorological data (Allen et al., 1998; FAO, 2002).
However, when the weather stations collect or summarize hourly weather data the users sometimes need or want to calculate ET for hourly time steps. It is important that hourly summed ETo calculations closely agree with calculations made with
daily time-step calculations. Hourly ETo data is important where substantial shifts in wind speed, humidity and dewpoint occur hourly. On the other hand, hourly evapotranspiration data is sometimes necessary as an input data for some numerical or analytical models that simulate water flow and root-water uptake. One such model is for instance the numerical model Hydrus (Šimunek et al., 2006). The model has been in recent years, for instance, extensively used to simulate water distribution under surface and subsurface drip irrigation systems under cropped conditions (e.g. Aussaline, 2002; Gardenas et al., 2005; Bufon et al., 2011; Phogat et al., 2011). The FAO-56-PM equation can be also applied on an hourly basis as well, but the most accurate results can be obtained when it is used with 24-hour data (Allen et al., 1998). The equation parameters are the same in both cases.
With a reason to standardize the computation of ETo and to facilitate the use and transfer of Kc's now in use, scientists were looking for equation that can be readily modified to be equally accurate at predicting ETo for hourly and for daily time steps for particular region and climate. In response to this in 2005 the American Society of Civil Engineers (ASCE) and the Environmental and Water Resources Institute (EWRI) (ASCE-EWRI, 2005) recommended the use of standardized ASCE-Penman-Monteith method (sASCE-PM) as the representative equation for calculation of ETo. This equation is derived from the full form of ASCE-PM in a very similar manner as FAO-56-PM equation was derived. Parameters in the sASCE-PM equation are different for hourly and 24 h time steps. They have also included parameters for (1) short crop (similar to 0.12 m high clipped grass) and (2) a tall crop (similar to 0.5 m high full cover alfa-alfa) which were embodied in a single equation. Itenfisu et al. (2003) analysed hourly and daily ETo data at numerous sites across USA. He compared most commonly used ETo equations for tall and short reference surfaces and the sASCE-PM equations. The sASCE-PM equation based on surface resistance of 50 s m-1 during daytime and 200 s m-1 during night time provided the best agreement with the full form of the ASCE-PM equation applied on a daily basis.
Accurately estimated ETo data will in irrigated agriculture become of great importance because it represents the basis for more efficient use of water and for better irrigation scheduling. Above mentioned becomes even more important by considering that a 14 % increase in irrigation water withdrawal for countries in development is expected by 2030 without taking into account impacts of climate change (Bruinsma, 2003).
In this study the daily and sum of hourly ETo values (SOH) calculated with standardized ASCE Penman-Monteith equation are compared to daily ETo values calculated with FAO-56 Penman-Monteith equation which is used by Slovenian Environmental Agency (ARSO). The ETo data is compared for one specific site located in Celje-Medlog, Slovenia. The purpose is to investigate if and how sum of
hourly ETo values calculated with sASCE-PM equation for short reference crop (grass) applies to Slovenian climate conditions.
2 MATERIALS AND METHODS 2.1 Study site and climate data source
The study site was located at the Celje-Medlog, Slovenia, with coordinates 46°15'N, 15°15'W and elevation of 240 m above sea level. The site is characterised by interaction of alpine and continental climate with mild to hot summers and cold winters. The monthly average rainfall and temperatures for period 1991 - 2000 for Celje-Medlog station are presented in Table 1 (ARSO, 30.8.2013). Meteorological data needed for calculation of hourly ETo was collected for a small test dataset of 23 successive days, from 22nd of August to 13th of September 2012.
Table 1: Average monthly temperatures (°C) and rainfall (mm) for period 1971 to 2000 and for 2012 for agrometeorological station Celje-Medlog Preglednica 1: Povprečne mesečne temperature (°C) in padavine (mm) za obdobje od 1971 do 2000 in za leto 2012 za agrometeorološko postajo Celje-Medlog
Average temp. (°C) Average precipitation (mm)
Average temp. for 2012 (°C) Monthly sum of precipitation for
2012 (mm)_
Average monthly reference evapotranspiration values for 30 years period compared to average monthly values for 2012, for station Celje-Medlog, are given on Figure 1.
Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	Year
-0,7	1.0	5.1	9.4	14.6	17.9	19.6	18.9	14.8	9.6	4.1	0.3	9.6
49	52	70	77	90	134	132	123	109	117	102	76	1129
0.7	-3.1	7.8	10.8	15.2	20.3	21.4	20.8	16	10.6	8.1	0.2	10.7
16.1	31.5	7.4	97.6	143.3	79.8	95.7	47.4	200.2	205.3	109.0	72.6	1105.9
Figure 1: Average monthly reference evapotranspiration (ETo) calculated with FAO-56-PM method for 30-years period (1982-2012) and 2012 for agrometeorological station Celje-Medlog
Slika 1: Povprečna mesečna referenčna evapotranspiracija (ETo), izračunana z metodo FAO-56-PM za 30-letno obdobje (1982-2012) in za leto 2012 (za agrometeorološko postajo Celje-Medlog)
Daily reference evapotranspiration data for reference surface were collected and computed by ARSO using FAO-56-PM equation for daily time step. In FAO-56-PM method ETo is defined for a hypothetical grass reference crop which is not short of water, with an assumed crop height of 0.12 m, a fixed surface resistance of 70 sec/m and an albedo of 0.23 (Dorenbos and Pruitt, 1977; FAO, 2002). FAO-56-PM equation for daily time step is given as:
where ETo is reference evapotranspiration (mm day-1), Rn is net radiation at the crop surface (MJ m-2 day-1), G is soil heat flux density [MJ m-2 day-1], T is mean air temperature at 2 m height (°C), U2 is mean wind speed at 2 m height (m s-1), es is saturation vapour pressure (kPa), ea is actual vapour pressure (kPa), es-ea is saturation vapour pressure deficit (kPa), A is slope vapour pressure curve (kPa°C-1), Y is psychrometric constant (kPa °C-1).
Hourly meteorological data needed as an input for calculation of hourly ET o using sASCE-PM equation was collected at the same site. sASCE-PM is given as:
where Cn is numerator constant that changes with reference surface and calculation time step (900°C mm s3 Mg-1 d-1 for 24 h time steps, and 37°C mm s3 Mg-1 h-1 for hourly time steps for the grass-reference surface, Cd is denominator constant that changes with reference surface and calculation time step (0.34 s m-1 for 24 h time steps, 0.24 s m-1 for hourly time steps during daytime, and 0.96 s m-1 for hourly night time for the grass-reference surface).
The sASCE-PM with Cn and Cd for daily time steps is exactly the same as the FAO-56-PM equation. However, for hourly time steps, the sASCE-PM uses a smaller value for surface resistance of vegetation per unit leaf area (r^ (s m-1)) during daytime (50 s m-1) and a larger value for rs during night time (200 s m-1). FAO 56-PM presumes constant rs of 70 s m-1 during all periods (Allen et al., 1998). However, later, in 2005, FAO has recommended applying the FAO-56-PM for hourly or shorter periods using the same rs coefficients as for the ASCE-PM (Allen et al., 2006).
The calculation approach to calculate hourly ETo values, following the approach described in the ASCE-EWRI report, was developed by Snyder and Eching (2006). Required data for ETo calculations using sASCE-PM approach included data about site characteristics (latitude and elevation) and weather data, as hourly solar radiation (Rs) (MJ m-2 h-1), mean air temperature (T) (°C), mean wind speed (u2) (m s-1) and mean dew point temperature (td) (°C). Td was calculated using equation 3-11 in Allen et al. (1998). Actual vapour pressure (ea (kPa)) was calculated from mean saturation vapour pressure (es (kPa) and relative humidity (RH (%)).
3 RESULTS WITH DISCUSSION
3.1 Comparison of FAO-56-PM (daily time step) and sASCE-PM (SOH and daily time steps) ETo calculations
Sum of hourly (for 24 h) ETo and daily ETo values calculated with sASCE PM equation were compared to daily ETo values computed with FAO-56-PM method. The results are presented in Figure 2. It has to be noted that sASCE-PM equation for short crop similar to grass was used to calculate the ETo values.
Figure 2: Comparison of reference evapotranspiration (ETo (mm/day)) values and sum of hourly and daily ETo (mm/day) values for short canopy obtained at agrometeorological station Celje-Medlog for period from 22. 8. 2012 to 13. 9. 2012 Slika 2: Primerjava dnevne referenčne evapotranspiracije (ETo (mm/dan)) in vsot urnih ETo (mm/dan) za kratko krošnjo, pridobljenih na agrometeorološki postaji Celje-Medlog za obdobje od 22. 8. 2012 do 13. 9. 2012
It can be visually observed from the Figure 2 that SOH and daily ETo values calculated with sASCE-PM equation fitted closely to daily ETo values calculated with FAO-56-PM equation. However, some discrepancy occurred for day 2 and for days, where ETo was generally low.
Table 2 shows calculated daily ETo and ETo differences between FAO-56-PM and sASCE-PM equations for location Celje-Medlog for period of 23 days (from 22nd of August 2012 to 13th of September 2012). Calculated ETo values using FAO-56-PM equation are presented as daily (24 h) time steps. ETo values calculated with sASCE-PM equation are presented as SOH time steps and, the same as with FAO-56-PM, as daily time steps.
Table 2: Daily and sum of hourly ETo and ETo differences for FAO 56-PM and sASCE-PM equations for location Celje-Medlog for period of from 22nd of August 2012 to 13 th of September 2012.
Preglednica 2: Vsota urnih in dnevnih ETo vrednosti in njihove razlike za FAO 56-PM in sASCE-PM enačbi za lokacijo Celje-Medlog za obdobje od 22. 8. do 13. 9. 2012
	A	B	C		
	FAO 56-	Standardized	Standardized		
Date	PM daily	ASCE PM	ASCE PM	Difference	Difference
	time step (mm/day)	daily time step (mm/day)	SOH time step (mm/day)	(A-B)	(A-C)
22/08/2012	4.7	4.62	4.78	0.08	-0.08
23/08/2012	4.4	3.08	3.26	1.32	1.14
24/08/2012	5.8	5.64	5.77	0.16	0.03
25/08/2012	4.5	5.00	5.17	-0.50	-0.67
26/08/2012	1.8	0.89	0.98	0.91	0.82
27/08/2012	4	4.20	4.3	-0.20	-0.30
28/08/2012	4.3	3.83	4.03	0.47	0.27
29/08/2012	3.8	3.90	4.06	-0.10	-0.26
30/08/2012	3.8	3.84	3.97	-0.04	-0.17
31/08/2012	1.5	0.73	0.78	0.77	0.72
01/09/2012	1.3	0.41	0.41	0.89	0.89
02/09/2012	2.6	3.13	3.19	-0.53	-0.59
03/09/2012	2.9	2.93	3.01	-0.03	-0.11
04/09/2012	3.2	3.24	3.31	-0.04	-0.11
05/09/2012	2.5	2.25	2.34	0.25	0.16
06/09/2012	2.5	2.42	2.42	0.08	0.08
07/09/2012	3.1	3.22	3.33	-0.12	-0.23
08/09/2012	3.1	3.51	3.71	-0.41	-0.61
09/09/2012	3.1	3.43	3.63	-0.33	-0.53
10/09/2012	3.3	3.29	3.5	0.01	-0.20
11/09/2012	2.9	3.28	3.48	-0.38	-0.58
12/09/2012	1.9	1.84	1.95	0.06	-0.05
13/09/2012	1.1	0.52	0.52	0.58	0.58
Mean	3.13	3.01	3.13		
Comparisons made in Table 2 showed that the mean ETo value of 3.13 mm/day for investigated period was observed for FAO-56-PM and sASCE-PM SOH equations. Average ETo of 3.01 mm/day was observed for sASCE-PM equation for daily time step. When SOH and daily ETo values calculated with sASCE-PM equation were compared to FAO-56-PM equation, the biggest difference was observed for 23rd of August (1.32 and 1.14 mm/day) and the smallest one for 12th of August (0.06 and -0.05 mm/day). Sum of hourly ETo calculated with sASCE-PM equation were,
when averaged, in better agreement with values observed with FAO-56-PM equation.
The paired ^-test was used to compare the difference between each pair of results given by the two sASCE-PM ETo calculation methods. The null hypothesis was adopted saying that there is no significant difference in the mean ETo calculations given by all calculation methods. With other words, we have tested if the mean of the ETo differences differs significantly from zero. The results are presented in Table 3, showing that the ETo values calculated with sASCE-PM (daily and hourly) equation were not significantly different from the ETo values observed with FAO-56-PM equation. Therefore the null hypothesis was retained meaning that the applied methods of ETo calculations do not give significantly different values for the mean ETo value.
Table 3: Results of statistics of paired ^-tests for the ETo calculated with sASCE-PM (daily) versus FAO-56 PM daily and sASCE-PM (SOH) versus FAO-56-PM daily values for selected period of 23 days
Preglednica 3: Statistični rezultati in parni ^-test za ETo izračunano s sASCE-PM (dnevno) in FAO-56 PM dnevno metodo in vsoto urnih vrednosti, izračunanih s sASCE-PM proti FAO-56-PM dnevni metodi za preučevano obdobje 23 dni
Mean difference
Location
ETo for FAO-56-
PM -sASCE-PM (daily time step)
Standard deviation (SD) of the differences
ETo for FAO-56-
PM -sASCE-PM (SOH time step)
ETo for FAO-56-
PM -sASCE-PM (daily time step)
f-test (paired) computed*
ETo for FAO-56-
PM -sASCE-PM (SOH time step)
ETo for FAO-56-
PM -sASCE-PM (daily time step)
ETo for FAO-56-
PM -sASCE-PM (SOH time step)
f
critical
Celje-Medlog
0.13
0.01
0.48
0.5
1.26
0.08
2.07
*Degrees of freedom (n-1), P = 0.05 (5 % significance level)
It is important to mention that, when calculating SOH ETo, some negative values were set to zero before summed over the 24-hours (SOH). This caused some minor differences in ETo daily calculations between sASCE-PM methods used in this research. Additional analysis showed that if negative hourly ETo values calculated with sASCE-PM method were left as negative, the SOH ETo values was identical to daily ETo values calculated with sASCE-PM. As mentioned in ASCE-EVRI (2005), the negative hourly ETo values may indicate the condensation of vapour during time of morning dew. However, the impact of SOH ETo values over daily periods using negative hourly values was, when compared to daily ETo values, less than 4 %.
4	CONCLUSIONS
In this paper the standardized sASCE-PM equation was evaluated against FAO-56-PM equation with a purpose to assess discrepancies between using a daily (24 h) time step equations (FAO-56-PM and sASCE-PM-daily) and sum of hourly (SOH) ETo (sASCE-PM-SOH) equation. Daily and hourly ETo computation time steps are in common use and it is important that hourly computations, when summed over a day (24 h) closely agree with daily time step calculations. Results revealed that SOH ETo values, calculated with sASCE-PM equation when compared to daily ETo values with FAO 56-PM and sASCE-PM, closely agree for most of investigated days. Comparisons showed that the mean ETo values for entire investigated period added up to 3.13 mm/day for FAO56-PM and sASCE-PM SOH equations and 3.01 mm/day for sASCE-PM daily time step equation. Also, the paired ^-test showed that mean ETo value for entire period calculated with sASCE-PM (daily and hourly) equation were not significantly different (P<0.05) from the ETo values observed with FAO-56-PM equation. However, some discrepancy occurred for day 2 and for days, where ETo was generally low. The reason for these differences stays unknown. It has to be noted, however, that further research is needed to investigate the behaviour of those equations under given climate characteristics for longer time scales (e.g. 1 year or 1 growing season).
Acknowledgements
The author would like to thank to dr. Andreja Sušnik and dr. Gregor Gregorič from Slovenian Environment Agency for provided weather data.
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