Comparison of hourly and daily reference crop evapotranspiration equations across seasons and climate zones in Australia

Agricultural Water Management 148 (2015) 84–96

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Comparison of hourly and daily reference crop evapotranspiration equations across seasons and climate zones in Australia Kushan C. Perera a,∗ , Andrew W. Western a,∗ , Bandara Nawarathna b , Biju George a,c a b c

Department of Infrastructure Engineering, The University of Melbourne, Melbourne, Australia Environment and Research Division, The Bureau of Meteorology, Melbourne, Australia International Center for Agricultural Research in the Dry Areas (ICARDA), PO Box 2416, Cairo, Egypt

a r t i c l e

i n f o

Article history: Received 16 May 2014 Accepted 10 September 2014 Keywords: Reference evapotranspiration ET0 FAO-56 ASCE-PM Hourly ET0 Daily ET0

a b s t r a c t Estimates from the FAO Penman–Monteith (FAO-PM) and the standardized ASCE Penman–Monteith (ASCE-PM) hourly and daily reference evapotranspiration (ET0 ) equations were compared at daily scale, based on the hourly climate data collected from forty (40) geographically and climatologically diverse Automatic Weather Stations (AWS) across the Australian continent. These locations represent 23 agricultural irrigation areas in tropical, arid and temperate climates. The aims of this paper are to: compare the effects of different methods of estimating Clear-sky-radiation—(Rso ); compare sum-of-hourly and daily ET0 ; compare the results of aggregation of hourly ET0 over 24 h compared with daylight hours; and examine the impact of seasonality and climate type. At selected AWS locations, the hourly ET0 was calculated using the hourly FAO-PM and the ASCE-PM equations and then summed to derive daily ET0 (reported as ET0,soh ). This was compared against the daily ET0 values, calculated using the corresponding daily equation (reported as ET0,daily ). Using Rso calculated following the “complex” approach improves the agreement between ET0,soh and ET0,daily of both hourly equations, compared with the “simple” approach. Better agreement between ET0,soh and ET0,daily estimates for the FAO-PM and ASCE-PM were found, when the hourly values are aggregated over 24 h rather than over daylight hours. The average ratio between ET0,soh and ET0,daily for the FAO-PM and ASCE-PM equations is 0.95 and 1.00, respectively. The range of the former is 0.90–0.98 and that of the latter is 0.96–1.04. There was very strong correlation between the two hourly equations at the daily time step: on average 0.997, with a range of 0.993–0.998. The results imply that the ASCE-PM hourly equation’s daily ET0 values are higher than those of FAO-PM, which can be explained by the difference in the treatment of surface resistances. Better agreements between ET0,soh and ET0,daily values for winter, spring and autumn were found for the FAO-PM version, while during summer, the ASCE-PM version showed better agreement. The best agreement between the hourly and daily results for the FAO-PM version was found in temperate climates and the ASCE-PM version showed best agreement in the tropical and arid climates. © 2014 Elsevier B.V. All rights reserved.

1. Introduction During the 20th century, the rate of fresh water consumption has increased at more than twice the rate of population growth, (UN-Water, 2006). It is anticipated that in 2025 there will be 50% and 18% growth in fresh water withdrawals in developing and developed countries, respectively (UNEP, 2007). At present, agricultural irrigation consumes 70% of the world’s fresh water withdrawals. Therefore, more efficient irrigation water use is

∗ Corresponding authors. Tel.: +61 3 8344 7305. E-mail addresses: [email protected] (K.C. Perera), [email protected] (A.W. Western). http://dx.doi.org/10.1016/j.agwat.2014.09.016 0378-3774/© 2014 Elsevier B.V. All rights reserved.

essential. Irrigation water requirement depends mainly on evapotranspiration (ET). Quantification of ET assists in carrying out tasks such as water allocation, water resource management and planning, water and energy balance estimation, yield estimation and irrigation scheduling. However, direct measurement of ET is difficult and costly, given that it is a vapour transfer process affected by dynamic factors such as weather parameters, crop characteristics and management and environmental aspects (Allen et al., 1998). Jensen (1968) introduced a conceptual approach to estimate crop-ET using reference evapotranspiration (ET0 ) and a crop coefficient (Kc ), where ET0 is crop-ET from the reference surface and Kc is the ratio between actual crop ET and ET0 . Based on this concept, the Food and Agricultural Organization’s (FAO) Irrigation

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and Drainage Paper no. 24 provided guidelines to calculate ET0 based for a reference crop of 8 to 15 cm tall green grass. They also provided a range of Kc for various crops (Doorenbos and Pruitt, 1977). They recommended four methods to calculate ET0 , namely, Blaney–Criddle, FAO-24 radiation, modified Penman, and pan evaporation, depending on data availability. The modified Penman was the preferred method of the four recommended methods, but it has frequently overestimated ET0 (by up to 20%) in low evaporative conditions, with the over-estimation of ET0 differing with locality (Allen et al., 1998). Subsequently, FAO Irrigation and Drainage Paper no.56 (FAO-56) was published along with hourly and daily FAO Penman–Monteith (FAO-PM) ET0 equations. These are based on a 12 cm high hypothetical reference crop and updated Kc values are supplied (Allen et al., 1998). The daily FAO-PM equation was recommended as the sole standard method for computing daily ET0 and numerous studies were conducted to evaluate its performance against other ET0 equations as well as against measured ET0 (Allen et al., 1989; Amatya et al., 1995; Chen, 2005; Chiew et al., 1995; George et al., 2002; Jensen et al., 1990). However, only a handful of studies have been conducted to evaluate the FAO-PM hourly ET0 equation and its performance at daily and sub-daily time scales (Irmak et al., 2005; Itenfisu et al., 2003; Temesgen et al., 2005). In 1999, the Evapotranspiration in Irrigation and Hydrology Committee of the American Society of Civil Engineers (ASCE) endeavoured to standardize ET0 calculations, and updated the hourly and daily ET0 equations provided in the FAO-56 (Walter et al., 2005). As an alternative to FAO-PM hourly and daily ET0 equations, the ASCE committee proposed a standardized Penman–Monteith equation to calculate both hourly and daily ET0 . The standardized Penman–Monteith (ASCE-PM) ET0 equation is based on two different reference surfaces, a short crop (similar to clipped grass) and a tall crop (similar to full-cover alfalfa). During the standardization process, the ASCE committee used two constants, namely the numerator—Cn (as an alternative to 900 in the FAO-PM) and the denominator—Cd (as an alternative to 0.34 in the FAO-PM). Values of Cn and Cd vary according to the reference surface and time step. The FAO-PM and ASCE-PM ET0 equations for daily time step are identical. However, for a short crop, the ASCE-PM hourly equation Cn values use surface resistances of 50 s m−1 and 200 s m−1 during the day-time and night-time, respectively, compared with the uniform surface resistance of 70 s m−1 throughout 24 h period for the FAO-PM hourly equations. This is due to the fact that several studies have shown that the uniform surface resistance assumption of 70 m s−1 (standard height of 0.12 m) of the FAO-PM hourly version results in day-time hourly ET0 estimates being more than the actual field observations and vice-versa for night-time conditions (Allen, 1996; Allen et al., 2006; Irmak et al., 2005; Ventura et al., 1999; Walter et al., 2005). As part of the ASCE standardization process, (Itenfisu et al., 2003) estimates from hourly (aggregated to daily) and daily ET0 equations for grass and alfalfa reference surfaces across 49 locations in the United State of America (USA) using ASCE-PM were compared with various other ET0 equations including the FAO-PM. Results showed that the ratio between the sum-of-hourly and daily ET0 values for the FAO-PM version ranged from 0.90 to 1.04 and from 0.94 to 1.07 for the ASCE-PM version. In terms of agreement between hourly and daily versions, it was found that the ASCE-PM ET0 equations agreed better than the FAO-PM equations. The study did not examine possible causes of differences between the two versions that were found in terms of location, especially advective and non-advective environments. Irmak et al. (2005) stated that the differences were partially due to the constant daily ratio between soil heat flux density and net radiation at the crop surface. They recommended the ACSE hourly ET0 equation, as opposed to

85

the FAO-PM version, when hourly climate data is available; due to the fact that neither daily equation reflects diurnal changes in wind speed, air temperature, or vapour pressure deficit. Similar conclusions were drawn by Gavilán et al. (2008) for semi-arid climate conditions in Andalusia, Southern Spain. They found that hourly ET0 calculated using the ASCE-PM version was 4% higher on average compared with the FAO-PM version. However, daily ET0 calculated using the ASCE-PM hourly equation was higher than the ASCE daily ET0 equation, and the differences between these two estimates were not dependent on the wind speed or the magnitude of the ET0 values. Studies comparing ET0 estimates with measurements have also been conducted. Berengena and Gavilan (2005) found that hourly ET0 calculated using the ASCE-PM and FAO-PM versions underestimated measured hourly ET0 by 2% and 3%, respectively, in Cordoba, Spain. Contrasting conclusions were derived by Lopez Urrea and López (2006) after evaluating measured and calculated hourly ET0 under the semiarid conditions in Albacete, Spain. They revealed that on an average calculated hourly ET0 using the FAO-PM version was similar to the measured hourly ET0 , but on average the ASCE-PM version was 4% higher. This result was supported by Suleiman and Hoogenboom (2009) using 15 min climate data for eleven representative and well-distributed sites throughout the state of Georgia, USA. They stated that more consistent results were found between hourly and daily FAO-PM ET0 equations in humid climates, and that the hourly ET0 calculated using ASCE-PM were higher than those of FAO-PM during the day and vice-versa during the night, which results from the treatment of surface resistance as 50 s m−1 during the day and 200 s m−1 during the night, respectively. In contrast, Yildirim (2004) calculated daily ET0 using 12-min interval meteorological data for the GAP project, Turkey and found that the FAO-PM hourly equation underestimated daily ET0 by 2 mm day−1 . These results all suggest inconsistencies between daily ET0 calculated using the hourly equation (ASCE-PM or FAO-PM) and the respective daily equation as well as between daily ET0 calculated using the two hourly equations. Previous studies conducted to evaluate the agreement between daily ET0 calculated using hourly and daily equations in the USA and Europe have drawn conflicting conclusions. Therefore, on the global scale, we are unable to distinguish a version (ASCE-PM or FAO-PM), which provides the best agreement between the hourly and daily ET0 equation at daily scale. The degree of agreement respect to ASCE-PM or FAO-PM equations were highly influenced by the locality and the degree of diurnal change. On the other hand, the hourly ET0 equations have often been used to calculate daily ET0 due to the sub-daily reporting frequency of expanded AWS networks and sub-daily temporal scales for numerical weather prediction models and irrigation scheduling tools. For these reasons, it is important to distinguish the agreement between daily ET0 calculated using the hourly and daily equation and to understand whether the degree of agreement is geographically consistent or location dependent. Furthermore, no studies have compared hourly and daily based estimates of ET0 by season to identify whether systematic differences between the methods are seasonally dependent. This paper aims to quantify the estimation performance of daily ET0 calculated using the FAO-PM and ASCE-PM hourly ET0 equations, against the daily ET0 calculated using the corresponding daily ET0 equation over the Australian continent. We calculated daily ET0 using the hourly equations for 40 locations (automatic weather stations), across 23 agricultural irrigation areas from 9 diverse climate zones and assessed the agreement with the daily ET0 calculated using the corresponding daily equation. We also evaluated the temporal, spatial and climatological variation of agreement between the methods. Further, we investigated the possible causes of differences between the methods.

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2. Materials 2.1. Study area This paper uses the same study area and climate stations as the study of ET0 forecasting by Perera et al. (2014).The study area covers a wide range of irrigation areas as well as climates across the Australian Continent. These irrigation areas fall between latitudes 15◦ and 39◦ south and longitudes 116◦ and 153◦ east. Twenty three (23) irrigation districts were included for the evaluation, based on regions where higher densities of irrigation pixels occur on the 2005/2006 Australian land use map (ABARES, 2010). We selected 40 Automatic Weather Stations (AWS) in these irrigation districts and collected a high-quality and complete hourly climate data set, which is important since the quality of climate data influences the agreement between the two daily ET0 estimation approaches, and completeness of the climate data impacts the reliability of evaluations of agreement. Generally, the instrument enclosure area (16 m × 16 m) of these AWSs is in the middle of a 30 m × 30 m buffer area, which is level, free from buildings or trees and aligned in the true North–South direction (BoM, 1997, 2014). The majority of these buffer areas are mostly covered by short grass, but a few are partly covered. The short grass or natural vegetation with in the instrument enclosure area is maintained to a height of no more than 50 mm and buffer area around the enclosure is maintained to a height of no more than 500 mm (BoM, 1997, 2014). Fig. 1 shows the 40 AWSs in these irrigation districts together with the

Köppen climate zones. Table 1 provides the characteristic of these AWSs, which are sorted according to the Köppen climate classification (Table 2). The stations fall in three main climates, namely tropical, arid and temperate, and nine sub-climates (Peel et al., 2007). The elevation of these stations ranges from 4 m to 871 m Australian Height Datum (AHD). Mean annual precipitation and average daily mean temperature ranges from 400 mm to 2400 mm and from 0 ◦ C to 36 ◦ C, respectively. Long-term mean monthly ET0 varies from 1 mm day−1 during mid-winter (July) for the southern stations to 12 mm day−1 during mid-summer (January).

2.2. Climate data The Australian Bureau of Meteorology (BOM) maintains the network of AWSs across the Australian Continent and provides climate data with various reporting frequencies including monthly, daily and sub-daily scales (BOM, undated). The purpose of the AWS is classified according to the observation program and 40 selected stations are classified as synoptic (seasonal, climatological, aeronautical, upper air etc.). These synoptic AWSs measure climate data in compliance with world meteorological standards (WMO, 2010). Commencement dates for the AWSs used here vary between 1989 and 2009 and this determines the data availability. We used a six year study period from 01 January 2007 to 31 December 2012. Five out of the 40 AWSs commenced operation after 01 January 2007 but were included nevertheless since there were no alternates

Fig. 1. Locations of the automatic weather stations fall under Köppen climate map (Peel et al., 2007).

K.C. Perera et al. / Agricultural Water Management 148 (2015) 84–96

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Table 1 Characteristics of automatic weather stations (Sorted as per Köppen climate zone). No. 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 29 30 31 32 33 34 35 36 37 38 39 40

AWS No.

Name

State 1

32040 33307 2056 35264 24024 74037 74258 75041 76031 80128 24048 40082 40922 41359 41522 41525 41529 54038 55202 73151 80091 81049 81124 81125 41175 81123 85072 85279 85280 85296 90035 9994 9538 9617 23373 26021 26091 90182 90194 33002

Townsville Apt. Woolshed Apt.1 Kununurra Apt.1 Emerald Loxton research Ctr.2 Yanco AG Inst.2 Deniliquin Apt.1 Griffith Apt.1 Mildura Apt.1 Charlton Renmark Apt.1 University of QLD Kingaroy Apt.1 Oakey Apt.1 Dalby Apt.1 Warwick Toowoomba Apt.1 Narrabri Apt.1 Gunnedah Apt.1 Temora Apt.1 Kyabram Tatura Inst.3 sus.4 ag Yarrawonga Shepparton Apt.1 Applethorpe Bendigo Apt.1 East sale Apt.1 Bairnsdale Apt.1 Morwell Apt.1 Mount Moornapa Colac Collie east Dwellingup Bridgetown Nuriootpa Mount Gambier Apt.1 Coonawarra Casterton Dartmoor Ayr DPI Ctr.2

QLD QLD WA QLD SA NSW NSW NSW VIC VIC SA QLD QLD QLD QLD QLD QLD NSW NSW NSW VIC VIC VIC VIC QLD VIC VIC VIC VIC VIC VIC WA WA WA SA SA SA VIC VIC QLD

Latitude (◦ ) ◦





−19 14 54 −19◦ 25 00 −15◦ 46 53 −23◦ 34 10 −34◦ 26 20 −34◦ 37 20 −35◦ 33 27 −34◦ 14 55 −34◦ 14 09 −36◦ 17 05 −34◦ 11 54 −27◦ 32 37 −26◦ 34 25 −27◦ 24 12 −27◦ 09 38 −28◦ 12 22 −27◦ 32 33 −30◦ 18 55 −30◦ 57 13 −34◦ 25 45 −36◦ 20 06 −36◦ 26 16 −36◦ 01 46 −36◦ 25 44 −28◦ 37 18 −36◦ 44’22 −38◦ 06’56 −37◦ 52’54 −38◦ 12’34 −37◦ 44’53 −38◦ 14’00 −33◦ 21’39 −32◦ 42’37 −33◦ 56’55 −34◦ 28’34 −37◦ 44’50 −37◦ 17’26 −37◦ 34’59 −37◦ 55 20 −19◦ 37 01

Longitude (◦ )

El. (m)

Climate zone

Nos. days

Irrigation area

146◦ 45 58 146◦ 32 11 128◦ 42 36 148◦ 10 32 140◦ 35 52 146◦ 25 57 144◦ 56 45 146◦ 04 10 142◦ 05 12 143◦ 20 03 140◦ 40 36 152◦ 20 15 151◦ 50 23 151◦ 44 29 151◦ 15 48 152◦ 06 01 151◦ 54 48 149◦ 49 49 150◦ 14 58 147◦ 30 40 145◦ 03 50 145◦ 16 02 146◦ 01 50 145◦ 23 41 151◦ 57 12 144◦ 19’36 147◦ 07’56 147◦ 34’01 146◦ 28’29 147◦ 08’34 143◦ 47’33 116◦ 10’18 116◦ 03’34 116◦ 07’52 139◦ 00’20 140◦ 46’26 140◦ 49’31 141◦ 20’02 141◦ 15 41 147◦ 22 33

4.3 556.0 44.0 189.4 30.1 164.0 94.0 134.0 50.0 131.7 31.5 89.0 433.7 405.7 343.9 475.4 640.9 229.0 262.6 280.5 105.0 114.0 128.9 113.9 871.6 208.0 4.6 49.4 55.7 480.0 261.0 200.0 267.0 178.7 275.0 63.0 57.0 130.6 51.0 17.0

Aw Aw BSh BSh BSk BSk BSk BSk BSk BSk BWk Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfb Cfb Cfb Cfb Cfb Cfb Cfb Csa Csb Csb Csb Csb Csb Csb Csb Cwa

2067 1753 1954 2026 1873 1939 1939 1936 2009 714 522 1968 1955 2043 2075 1910 1973 1845 1930 1892 1982 853 1956 2046 1855 1945 1600 1934 2084 2053 1949 1919 1042 1830 448 1950 1494 1863 1354 608

Burdekin-Haughton Burdekin-Haughton Ord Nogoa-Mackenzie Golden Heights Murrumbidgee Murray Murrumbidgee Sunrays Pyramid-Boort Renmark Logan River Logan River Logan River Condamine Logan River Logan River Namoi Namoi Murray Central-Goulburn Central-Goulburn Shepparton Shepparton Condamine Central-Goulburn West Gippsland Shepparton West Gippsland West Gippsland Gippsland South West South West South West South East South East South East South East South East Burdekin-Haughton

1

Airport. Centre. Institute 4 Sustainable. NSW—New South Wales, QLD—Queensland, SA—South Australia, VIC—Victoria, WA—Western Australia. 2 3

within those irrigation districts. We obtained hourly temperature, dew point temperature, relative humidity and wind speed recorded at the AWSs. Relative humidity was based on measured dry and wet bulb air temperature and wind speed, with a correction for station elevation. The screen height for temperature measurements was 1.2 m and wind speed was measured at 10 m (BoM, 1997). Recorded hourly wind speed was mostly an average over the 10 min Table 2 Description of Köppen climate symbols and defining criteria for the climate zone in the study (Peel et al., 2007). 1st

2nd

3rd

A w B W S h k C s w f a b

Description Tropical -Savannah Arid -Desert -Steppe -Hot -Cold Temperate -Dry summer -Dry winter -Without dry season -Hot summer -Warm summer

prior to the observation time. Solar or shortwave radiation can be measured using ground-based pyranometers or estimated from space-based satellite imagery. Pyranometers require frequent calibration due to changing sensitivity with time and exposure to radiation, which is expensive and time consuming. Therefore, the Bureau’s AWSs are not equipped with pyranometers. For this study, the Bureau’s daily incoming solar radiation product derived from satellite imagery was used (Weymouth and Le Marshall, 2001). This product is tuned with the measured daily solar radiation from the ground-based data collected using pyranometers placed in 9 monitoring sites throughout Australia. The measurement range and accuracy of these observed weather variables were given in Table 3.

Table 3 Measurement range and accuracy of climate variables from AWS (BoM, 2005). Sensor

Range

Accuracy

Unit

Air pressure Air temperature Wet bulb temperature Relative humidity Wind speed Wind direction Rainfall

750 to 1060 −25 to +60 −25 to +60 2 to 100 2 to 180 0 to 359 0 to 999.8

0.3 0.3 0.3 3 2 5 2%

hPa ◦ C ◦ C % knot degree mm

88

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Fig. 13 of Perera et al. (2014) provides a comparison of satellite and ground-based measurements. It is important to note that the measurement conditions for the operational climate data from the AWSs do not reflect the reference conditions for ET0 calculation, which is often the case. Key differences are that soil moisture may be restricting evapotranspiration, the temperature and humidity measurements are at less than 2 m height (rather than 2 m) and the wind measurements are at 10 m (which we corrected to the ET0 standard 2 m). It is unlikely that the differences in measurement conditions significantly influence the agreement between hourly and daily ET0 calculations, as the same data is used irrespective of the time step. The effect of using disaggregated rather than measured hourly radiation is examined later.

in Section 3.3) provided robust results as shown below. This may reflect a high number of clearsky days, as found by Duffie and Beckman (2006). 3.2. ET0 equations All daily ET0 calculations were made according to the guidelines provided in FAO-56 (Allen et al., 1998) or the ASCE Task committee final report (Walter et al., 2005), as appropriate. Both of these estimate daily ET0 for a 12 cm high hypothetical grass surface reference crop (Allen et al., 1998). Eq. (2) denotes the FAO-PM and ASCE-PM hourly and daily ET0 equations.



ET0 = 3. Methodology 3.1. Data processing Automatic weather stations nominally provide continuous measured weather data; however, there were times within the study period when hourly weather data were missing due to various reasons. In those instances, the entire day was removed from the data set. Table 1 provides the number of evaluated days for each AWS and the percentage of missing data. We assessed approximately 180 station-years of data or on average 1727 AWS-days per location, ranging between 448 and 2084 AWS-days, respectively. The mean hourly air temperature was computed using two consecutive hourly readings and the mean daily air temperature was taken as the average of daily maximum and minimum air temperature rather than the mean of the hourly air temperatures for a given day. This was to avoid underestimation of daily ET0 due to the non-linear relationship between the saturation vapour pressure and temperature (Allen et al., 1998). The mean hourly or daily dew point temperature was calculated by taking the average over the given period of time. BOM uses 4 types of anemometers, mounted 10 m above the ground level to measure the wind speed and record hourly wind speed, mostly an average over the 10 min prior to the observation time (BoM, 1997; Huysing and Warne, 1993). Then, the mean hourly or daily wind speed at the standard height of 2 m was calculated by taking the average over the given period of time and converting to 2 m height by multiplying by a factor derived from Eq. (1), in line with the wind profile relationship provided in FAO-56. The starting threshold for these anemometers is 2 knot or 1.03 m s−1 . Across the 40 stations, on average, recorded wind speed exceeded the starting threshold 92.00% of the time. Therefore, a specific threshold correction method was not applied as impact from very low wind speed values for the agreement between hourly and daily ET0 values is minor. Wind speed measurements below the threshold were entered as zero. u2 = u

4.87 ln (67.8z − 5.42)

(1)

where u2 is wind speed at 2 m above ground surface (m s−1 ), uz is measured wind speed at z m above ground surface (m s−1 ), z is height of measurement above ground surface (m). The Bureau does not have sub-daily incoming solar radiation products for the stations studied. Hourly incoming solar radiation values were calculated using daily values. And a daily to hourly incoming solar radiation disaggregation method, which assumed a temporal pattern consistent with a clear-sky day due to the fact that there is no way to determine various circumstances such as intermittent heavy\light clouds or continuous light clouds from the daily totals (Duffie and Beckman, 2006). The incoming solar radiation disaggregation method (described in more detail



0.408 (Rn − G) + y Cn /T + 273 u2 (es − ea )  + y (1 + Cd u2 )

(2)

where; ET0 is the daily or hourly reference crop evapotranspiration (mm day−1 or mm h−1 ),  is the slope of the saturation vapor pressure versus air temperature curve (kPa ◦ C−1 ), Rn is the daily or hourly net radiation at the crop surface (MJ m−2 day−1 or MJ m−2 h−1 ), G is the daily or hourly ground heat flux density at the soil surface (MJ m−2 day−1 or MJ m−2 h−1 ), T is the mean daily or hourly air temperature at 1.5 to 2.5 m height (◦ C), U2 is the mean daily or hourly wind speed at 2 m height (m s−1 ), es is the saturation vapor pressure (kPa), ea is the actual vapor pressure (kPa),  is the psychometric constant (kPa ◦ C−1 ), and 0.408 is a coefficient (m2 mm MJ−1 ) converting energy flux to water flux. 3.2.1. FAO-PM equation The FAO appointed a panel of experts and researchers in 1990 to revise and update the FAO crop water requirement guidelines. The panel adopted the Penman–Monteith (PM) combination method to estimate the ET0 of a 12 cm high hypothetical grass surface. The equations use a surface resistance of 70 s m−1 ; an albedo or canopy reflection coefficient of 0.23, and Stefan–Boltzmann constant of 4.903 × 10−9 MJ K−4 m−2 d−1 . The corresponding values for Cn and Cd of the FAO-PM hourly and daily equations are provided in Table 4. FAO-56 provides three methods to estimate the actual vapor pressure (ea ) depending on climate data availability. No preference is expressed and the choice leads to slight differences in ea values. We calculated ea for hourly and daily periods using the average relative humidity and the saturated vapour pressure for the given period. FAO-56 guidelines also provide the equations to estimate clear-sky solar radiation (Rso ) with or without calibrated values of the fraction of extraterrestrial radiation reaching the earth on clear-sky days. They recommended a “complex” procedure to obtain more accurate Rso by considering the turbidity and vapor effect and using Beer’s law. 3.2.2. ASCE standardized PM equation In 1999, the American Society of Civil Engineers appointed a task committee to standardize the prevailing ET0 equations and crop coefficients. They derived a standardized ET0 equation for two reference surfaces; a short crop of 0.12 m tall grass and a tall crop of 0.5 m tall rougher crop surface like alfalfa. Only the short crop is considered in this study. The ASCE-PM equations use different surface resistances depending on the reference surface (short/tall), temporal scale (daily/hourly) and time of calculation (day/night) (Table 4). Further, the committee updated equations related to the estimation of clear-sky solar radiation (Rso ) by modifying some of the constants when calculating the clearness index for direct beam radiation (KB ) and the corresponding index for diffuse beam radiation (KD ). Moreover, the committee recommended an order

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Table 4 Values for Cn and Cd . Version

Time step

rs (m s−1 )

Cd

Cn

Units for ET0

Units for Rn , G

Short reference (0.12 m high) FAO-PM

Daily Hourly (day and night times)

900 37

0.34 0.34

70 70

mm day−1 mm h−1

MJ m−2 day−1 MJ m−2 h−1

ASCE-PM

Daily Hourly (daytime) Hourly (night-time)

900 37 37

0.34 0.24 0.96

70 50 200

mm day−1 mm h−1 mm h−1

MJ m−2 day−1 MJ m−2 h−1 MJ m−2 h−1

of preference to estimate actual vapor pressure (ea ) depending on climate data availability and to avoid differences in ea values. We followed the same method (used for the FAO-56 version) to calculate ea for hourly and daily periods, to maintain consistency during the comparison. During the standardization, six equations related to the three time steps and two reference surfaces were reduced to a single equation (Eq. (2)) using two constants, Cn and Cd , the values of which are shown in Table 4. 3.3. Calculating ET0 Four daily ET0 values for a given day were calculated using hourly and daily ET0 equations of FAO-PM and ASCE-PM. The daily ET0 calculated using the hourly equations was based on the basis of sum-of-hourly ET0 (SOH) for a 24 h period and 2 daily ET0 estimates were reported as ET0,soh,FAO and ET0,soh,ASCE , respectively. The two daily ET0 estimates calculated using the daily equations were reported as ET0,daily,FAO and ET0,daily,ASCE , respectively. The FAO-PM and ASCE-PM equations use the same procedure to compute hourly and daily Rn , G, u2 , es and ea . The latter three parameters were calculated as described in Section 3.1. Rn is significantly larger than G and the calculation procedures for hourly and daily G for both the FAO-PM and ASCE-PM equations are identical and depend on Rn (Eqs. (3.1)–(3.3)). Gdaily = 0

(3.1)

Ghourly (daytime) = 0.1 × Rn

(3.2)

Ghourly (nighttime) = 0.5 × Rn

(3.3)

Hourly or daily Rn was calculated as the difference between the incoming net shortwave radiation (Rns ) and the outgoing net longwave radiation(Rnl ) (Allen et al., 1998). Hourly or daily Rns was calculated using the incoming shortwave solar radiation (Rs ) and an albedo of 0.23. Daily Rs was taken as the Bureau daily Rs products. Hourly Rs was calculated by disaggregating daily Rs into hourly Rs using the ratio of hourly total to daily total Rs for each hour, rt , which was calculated using Eqs. (4.1)–(4.3), as suggested by Collares-Pereira and Rabl (1979). Although, this method performs best for clear-sky days as daily Rs values do not reflect intermittent cloudiness or turbidity, many studies have evaluated the performance of the disaggregation method using pyranometers and found that it provides accurate hourly Rs across climates and seasons (Ahmad and Tiwari, 2008; Benseman and Cook, 1969; Collares-Pereira and Rabl, 1979; Kumar et al., 2009; Singh et al., 1997). rt =

 cos ω − cos ωs   (a + b cos ω) 24 sin ωs ωs /180 cos ωs

(4.1)

a = 0.4090 + 0.5016 sin (ωs − 60)

(4.2)

b = 0.6609 + 0.4767 sin (ωs − 60)

(4.3)

where; ω and ωs are hourly angle and sunset angle in degrees Daily Rnl was estimated from the daily maximum and minimum air temperature and relative shortwave radiation, calculated using

the collected daily Rs and calculated clear-sky solar radiation (Rso ) (Eq. (5)).



Rnl,daily =  × ×

Tmax,K 4 + Tmin,K 4 2





 √  × 0.34 − 0.14 ea



1.35

Rs − 0.35 Rso

(5)

where; Rnl, daily is the daily net outgoing longwave radiation (MJ m−2 day−1 ),  is the Stefan–Boltzmann constant (4.903 × 10−9 MJ K−4 m−2 day−1 ), Tmax,K and Tmin,K are maximum and minimum absolute temperature during the 24-h period (K = ◦ C + 273.16), Rs /Rso is the relative shortwave radiation(limited to ≤1) Hourly Rnl was estimated from the mean hourly air temperature and relative shortwave radiation, calculated using the hourly Rs and hourly Rso (Eq. (6)).





 √  Rs Rnl,hourly =  × Th,K 4 × 0.34 − 0.14 ea × 1.35 − 0.35 Rso

(6)

where Rnl, hourly is the hourly net outgoing longwave radiation (MJ m−2 h−1 ),  is the Stefan–Boltzmann constant (2.043 × 10−10 MJ K−4 m−2 h−1 ), Th,K mean absolute temperature during the hourly period (K = ◦ C + 273.16), Rs /Rso is the relative shortwave radiation(limited to ≤1) Rso was calculated using both the “simple” and the “complex” approaches described in FAO-56 (Allen et al., 1998) and the ASCE task committee final report (Walter et al., 2005). The daily ET0 resulting from these two approaches were compared given that calculated hourly and daily Rs /Rso depends on the Rso calculation method. First, we calculated Rso as a function of station elevation and extraterrestrial radiation using Eq. (7.1) and this approach is identical for the FAO-PM and ASCE-PM versions. Second, Rso was calculated using “complex” approach (Eq. (7.2)), which is more accurate (Allen et al., 1998; Walter et al., 2005) and considers sun angle, water vapour and turbidity effects. The calculation procedure for the complex approach is identical for FAO-PM and ASCE-PM versions, but constants used during the calculation of the clearness index for direct beam radiation (KB ) and the corresponding index for diffuse beam radiation (KD ) are different.





Rso = 0.75 + 2 × 10−5 z Ra

(7.1)

Rso = (KB + KD ) Ra

(7.2)

where z is the station elevation above the sea level, Ra is the extra-terrestrial radiation (MJ m−2 d−1 ), KB is the clearness index for direct beam radiation and KD is the corresponding index for diffuse beam radiation. We also calculated daily ET0 during the day light hours using the hourly equations. These two daily ET0 estimates were reported as ET0,dlh,FAO and ET0,dlh,ASCE , respectively. The day light period varies with the latitude of AWS and Julian day of the year. First, the sunrise and sunset angles were calculated for each station and day of year. Second, the day light period was taken as the time period between sunrise and sunset. Then, the calculated hourly ET0 was filtered

90

K.C. Perera et al. / Agricultural Water Management 148 (2015) 84–96

Fig. 2. Calculated daily ET0 as indicated by (a) ET0,soh,FAO and ET0,daily,FAO using Rso “simple”, (b) ET0,soh,ASCE and ET0,daily,ASCE using Rso “complex”, (c) ET0,soh,FAO and ET0,daily,FAO using Rso “simple”, (d) ET0,soh,ASCE and ET0,daily,ASCE using Rso “complex” for Shepparton irrigation areas, Victoria.

according to the day light hours and summed to derive daily ET0,dhl for each version. 3.4. Assessing the agreement The FAO-PM and ASCE-PM hourly ET0 equations are intended to apply on an hourly basis rather than a sum-of-hour basis for daily time step. However, in principle, daily ET0 calculated using the hourly ET0 equation and sum-of-hour basis should be equal to that calculated using the respective daily ET0 equation. Scatter between the two daily ET0 estimations reflects a fundamental difference, where former method focusses on diurnal changes and the latter method focuses on average conditions for a given day. The statistical indices used to quantify the agreement between different equations were the root-mean-squared-difference (RMSD) (Eq. (8)), the coefficient of determination (R2 ) (Eq. (9)), the slope and intercept of the linear regression line and the ratio between daily ET0 values. The slope and intercept of the linear regression line between ET0,soh and ET0,daily for each version are indicators of systematic bias. The daily ET0 calculated using the hourly ET0 equations were taken as dependent variable and daily ET0 calculated using the corresponding daily ET0 equation was taken as the explanatory variable. As a result, the daily ET0 calculated using the daily ET0 equation became the “benchmark”, which can be justified as follows. (1) The daily ET0 equations are recognized as the standard method of computing daily ET0 (Allen et al., 1998). (2) Under the standard conditions, daily ET0 values calculated using both daily ET0 equations are identical (Walter et al., 2005). (3) Practically, daily ET0 is a presumed value that is very difficult to measure under the defined context. The ratio of the daily ET0 from the sumof-hourly equation and the daily ET0 was calculated for each day and averaged.

 n  RMSD =

i=1

 1/2

n

n  R2 = 1 −

ET0,soh,x − ET0,daily,x

i=1

n  i=1

ET0,soh,x − ET0,soh,x

(8)

2

ET0,daily,x − ET0,daily,x

2

(9)

In Eqs. (8) and (9), the over bar indicates the mean of the corresponding variable. 4. Results and discussion Our comparison mainly focuses on the over/underestimation of daily ET0,soh compared with the corresponding ET0,daily and probable causes of difference between the daily ET0,soh values estimated from the hourly ET0 equation of ASCE-PM and FAO-PM, since the

two daily ET0 equations are identical. This section is structured into six subsections which address: different methods of estimating Rso ; a comparison of sum-of-hourly and daily ET0 ; a comparison of aggregation of hourly ET0 over 24 h compared with daylight hours; the impact of seasonality; and the impact of climate type. These comparisons enable the probable causes for the difference between two hourly ET0 values to be investigated. Due to the sheer volume of results generated from 69,088 AWS-days at 40 AWS locations, it is not practical to demonstrate these graphically for individual stations. Therefore, to maintain consistency, only the results related to the ASW at Shepparton Airport (81125) in the Shepparton irrigation region are shown graphically, where necessary and plots and tables summarizing performance across all stations are included in each section.

4.1. Impact of Rso calculation method As mentioned above, Rso can be calculated either using the “simple” or the “complex” method. Although, FAO-56 and the ASCE Task committee final report mentioned that the “complex” method is more accurate, it was not practical to verify this with measured Rso for the 40 AWS locations in this study. Therefore, this section investigated which Rso estimation method provide the best agreement between ET0,soh and ET0,daily rather than comparing estimated Rso with measured Rso . Fig. 2 shows four plots of ET0,daily against ET0,soh for all combinations of FAO-PM and ASCE-PM, with the “simple” and “complex” Rso methods at Shepparton, Victoria. Table 5 summarizes the statistical indicators across all 40 AWS locations. For both FAO-PM and ASCE-PM, the best agreement between ET0,soh and ET0,daily was obtained, when Rso was estimated using the “complex” approach. In both versions, the Rso “complex” approach provided slightly lower RMSD and marginally higher R2 values. When Rso was calculated using the “complex” approach, the mean of the daily ratio (ET0,soh /ET0,dail ) reduced by 0.19 and 0.013 for FAOPM and ASCE-PM versions, respectively, compared with the simple method. Both the regression slope and intercept also reduced when moving from the simple to the complex method. The “complex” Rso calculation method results in lower ET0 than the “simple” method for both versions because it increases net outgoing longwave radiation, thus reducing net all-wave radiation and ET0 estimates. The impact is greater on the hourly estimates. Both the hourly and daily Rso values calculated using the “complex” methods from FAO-56 were slightly higher than those using the ASCE task committee final report. These results all show that daily ET0 calculated using the Rso “complex” approach provided a relatively higher agreement between ET0,soh and ET0,daily for both the versions compared to Rso “complex” approach. This further suggests that the representation of air-turbidity, vapour pressure effect

K.C. Perera et al. / Agricultural Water Management 148 (2015) 84–96

91

Table 5 Summary of statistical indices for daily ET0 calculated using Rso “simple” and “complex” procedure. Rso “simple”

Statistics

Rso “complex”

Mean

Max.

Min.

Mean

Max.

Min.

FAO-PM hourly & daily equations

RMSD Daily ratio Regression slope Regression intercept R2

0.260 0.966 0.927 0.150 0.982

0.323 1.004 0.973 0.297 0.990

0.193 0.914 0.873 −0.029 0.960

0.256 0.949 0.920 0.110 0.983

0.316 0.982 0.969 0.246 0.991

0.187 0.899 0.868 −0.072 0.964

ASCE PM hourly & daily equations

RMSD Daily ratio Regression slope Regression intercept R2

0.285 1.011 0.957 0.215 0.980

0.346 1.052 1.024 0.373 0.989

0.211 0.968 0.890 0.013 0.953

0.281 0.998 0.948 0.195 0.981

0.342 1.039 1.019 0.325 0.989

0.203 0.957 0.883 −0.017 0.957

and sun angle on Rso influence the agreement between ET0,soh and ET0,daily estimated values irrespective of the version. 4.2. Comparison of hourly and daily models Table 6 shows the statistical indicators for the comparison between ET0,soh and ET0,daily for the FAO-PM and ASCE-PM versions. The RMSD between the ET0,soh,FAO and ET0,daily,FAO ranges between 0.187 and 0.316 mm day−1 between locations, whereas those for the ASCE-PM version range between 0.203 and 0.342 mm day−1 . At the majority of locations, ASCE-PM RMSD values were 10% greater than FAO-PM. The exceptions are Woolshed (QLD) and

Warwick (NSW). FAO-PM showed smaller systematic differences between ET0,soh and ET0,daily than the ASCE-PM version. On average the ratio between ET0,soh and ET0,daily of the FAO-PM was 0.95 (ranging between 0.90 and 0.98) and that for the ASCEPM versions was 1.00 (ranging between 0.96 and 1.04). That is across sites the FAO-PM hourly equation shows a consistent underestimation of daily ET0 , whereas the ASCE-PM hourly equation did not. The greatest contributor to the difference is the diurnal variation in surface resistance (50 s m−1 and 200 s m−1 ) for the hourly ASCE-PM equation compared with the constant value of surface resistance (70 s m−1 ) used for the FAO-PM hourly equation.

Table 6 Statistical indicators corresponds to daily ET0 calculated between the hourly and daily ET0 equations of FAO-PM and ASCE-PM versions for 40 AWS stations. AWS ID

32040 33307 2056 35264 74037 74258 75041 76031 80128 24024 24048 40082 40922 41359 41522 41525 41529 54038 55202 73151 80091 81049 81124 81125 41175 81123 85072 85279 85280 85296 90035 9994 9538 9617 23373 26021 26091 90182 90194 33002

Site

Townsville Apt. Woolshed Kununurra Apt. Emerald Apt. Yanco agri. Inst. Deniliquin Apt. Griffith Apt. Mildura Apt. Charlton Loxton res. ctr. Renmark Apt. Univ. Qld Gatton Kingaroy Apt. Oakey Apt. Dalby Apt. Warwick Toowoomba Apt. Narrabri Apt. Gunnedah Apt. Temora Apt. Kyabram Tatura Inst. Sus. Yarrawonga Shepparton Apt. Applethorpe Bendigo Apt. East sale Apt. Bairnsdale Apt. Morwell Apt.) Mount Moornapa Colac Collie east Dwellingup Bridgetown Nuriootpa Viti. Mt. Gambier Apt. Coonawarra Casterton Dartmoor Ayr dpi res. stn

FAO-PM version

ASCE-PM version 2

RMSD

Ratio

Slope

Intercept

R

RMSD

Ratio

Slope

Intercept

R2

0.227 0.208 0.273 0.231 0.279 0.258 0.316 0.247 0.260 0.278 0.306 0.199 0.264 0.257 0.257 0.261 0.243 0.285 0.261 0.275 0.236 0.239 0.245 0.259 0.243 0.247 0.260 0.282 0.276 0.213 0.279 0.232 0.259 0.244 0.288 0.266 0.284 0.237 0.261 0.187

0.957 0.948 0.954 0.933 0.949 0.942 0.954 0.953 0.954 0.953 0.934 0.949 0.961 0.946 0.940 0.970 0.921 0.950 0.946 0.954 0.960 0.947 0.947 0.952 0.970 0.954 0.954 0.951 0.938 0.954 0.899 0.982 0.924 0.978 0.944 0.933 0.950 0.943 0.941 0.957

0.926 0.917 0.937 0.936 0.926 0.931 0.928 0.928 0.925 0.914 0.909 0.966 0.923 0.922 0.913 0.942 0.907 0.918 0.931 0.917 0.919 0.923 0.928 0.916 0.941 0.913 0.923 0.923 0.901 0.928 0.868 0.913 0.882 0.913 0.920 0.894 0.918 0.903 0.897 0.969

0.153 0.118 0.107 −0.017 0.104 0.049 0.119 0.118 0.121 0.168 0.124 −0.072 0.146 0.105 0.130 0.109 0.057 0.155 0.070 0.151 0.143 0.092 0.078 0.140 0.099 0.161 0.101 0.089 0.114 0.081 0.105 0.246 0.177 0.216 0.099 0.130 0.127 0.125 0.126 −0.054

0.973 0.972 0.964 0.983 0.989 0.991 0.986 0.991 0.989 0.986 0.984 0.985 0.972 0.980 0.982 0.975 0.979 0.984 0.985 0.988 0.988 0.987 0.991 0.988 0.974 0.989 0.977 0.972 0.977 0.985 0.981 0.987 0.988 0.985 0.985 0.982 0.983 0.986 0.980 0.983

0.264 0.203 0.295 0.233 0.300 0.296 0.334 0.269 0.287 0.306 0.342 0.215 0.263 0.273 0.265 0.248 0.237 0.311 0.286 0.306 0.258 0.276 0.277 0.292 0.245 0.285 0.300 0.320 0.303 0.243 0.314 0.242 0.317 0.255 0.319 0.325 0.342 0.277 0.292 0.210

1.010 1.000 0.986 0.969 0.977 0.982 0.986 0.989 1.001 0.991 0.967 0.995 1.023 0.996 0.981 1.025 0.970 0.976 0.980 1.002 1.014 1.002 0.987 1.003 1.032 1.004 1.022 1.020 1.005 0.986 0.958 1.036 0.957 1.039 0.992 1.006 1.012 1.006 1.024 1.022

0.968 0.960 0.933 0.944 0.932 0.935 0.932 0.940 0.944 0.930 0.921 0.999 0.962 0.948 0.931 0.981 0.940 0.922 0.946 0.936 0.951 0.962 0.944 0.941 0.985 0.942 0.987 0.983 0.951 0.943 0.913 0.943 0.883 0.944 0.944 0.949 0.954 0.945 0.951 1.019

0.201 0.148 0.310 0.129 0.202 0.203 0.249 0.230 0.229 0.260 0.220 −0.017 0.230 0.210 0.233 0.167 0.127 0.254 0.153 0.267 0.217 0.148 0.179 0.233 0.154 0.236 0.107 0.116 0.159 0.127 0.148 0.325 0.313 0.309 0.192 0.188 0.225 0.189 0.200 0.013

0.967 0.975 0.957 0.983 0.987 0.988 0.985 0.989 0.987 0.984 0.981 0.984 0.973 0.978 0.981 0.979 0.981 0.981 0.982 0.985 0.987 0.984 0.989 0.986 0.976 0.986 0.973 0.968 0.975 0.981 0.979 0.986 0.982 0.985 0.982 0.976 0.977 0.982 0.978 0.981

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Comparatively higher variability for daily ratio (ET0,soh /ET0,daily ) was observed for the ASCE-PM version than the FAO-PM version, where, the standard deviation (calculated between days of each site) for the ASCE-PM version was always higher than that of the FAO-PM. The better agreement between values of ET0,soh, ASCE and ET0,daily, ASCE for ASCE-PM than FAO-PM is also evident in the regression line slopes and intercepts (Table 6). In general intercepts are slightly positive and slopes are slightly less than one, suggesting that, the ET0,soh tends to exceed ET0,daily at relatively low daily ET0 values. The lower slopes and intercepts for the FAO-PM indicate larger deviation from the 1:1 line at large ET0 values, compared with the ASCE-PM version. The R2 of both versions exceeds 98% for most sites and the correlation between ET0,soh and ET0,daily values was slightly higher for the FAO-PM version than for the ASCE-PM version (Table 6). The mean R2 between ET0,soh,FAO and ET0,daily,FAO was 98.3% (ranging from 96.4 to 99.1%) where as for ASCE-PM it was 98.1% (ranging from 98.9% to 95.7%). The lowest R2 was obtained for Kununurra Airport (NT) in both the versions. This is the closest location to the equator, has a tropical climate, and is subjected to large diurnal changes. One potential factor that might influence the difference between the hourly and daily based methods is the fact that we disaggregated global radiation rather than using measured hourly radiation, due to lack of data. The radiation disaggregation method (daily into hourly) does not account for diurnal changes in cloudiness or turbidity. The measured hourly RS is available for a few stations and we undertook a preliminary evaluation (not presented) using the limited available data to determine the impact on the agreement between ET0, soh and ET0, daily from the disaggregation. The pairwise correlation coefficients between disaggregation hourly RS and measured hourly RS were more than 0.975 across climates and seasons at Mildura (VIC) and Townsville (QLD). At Mildura the radiation data corresponds in part with the study period. When hourly observed radiation was used the correlation reduced from 0.9914 to 0.9911, the slope changed from 0.9284 to 0.9383 and the mean ratio reduced from 0.9577 to 0.9539, compared with using disaggregated radiation for the FAO method. Similar changes were observed for the ASCE method. This suggests that the use of disaggregated radiation had a minimal impact on the difference between ET0, soh and ET0, daily . Another possible explanation for the difference between hourly and daily estimates is the treatment of ground heat flux. The hourly methods do not assume a zero ground heat flux on average over the day, while the daily methods do assume zero ground heat flux. We examined the possibility of using the aggregated hourly heat flux

in the calculating the net energy availability in the daily equations. Doing this resulted in greater discrepancies between the hourly and daily based estimates because it tended to decrease the ET0 (due to positive average hourly G) on days with high ET0 and decrease it on days with low ET0 . Overall the approach (FAO or ASCE) with the best agreement between the ET0,soh and ET0,daily depends on which statistics are considered. In terms of RMSD and R2 , the FAO-PM version showed best agreement, whereas the ASCE-PM worked better if we use ratio and linear regression as the indicators.

4.3. Seasonal impact for the ET0,soh vs. ET0,daily values This section investigates, how the agreement between the ET0,soh and ET0,daily values changes seasonally (summer, autumn, winter and spring). The statistical indicators were calculated according to the calendar months of each season in the southern hemisphere (i.e. summer: Dec–Feb, autumn: Mar–May, winter: Jun–Aug, & spring: Sep–Nov). Fig. 3 shows the annual and seasonal box plots for various statistical indices for the 40 AWS locations. Seasonal RMSD values reduced from summer through spring and autumn to winter for both FAO-PM and ASCE-PM, in line with overall seasonal ET0 variation. The ASCE-PM version shows higher median RMSD and spread for all four seasons. Fig. 3(b) and (c) shows the daily ratio (ET0,soh /ET0,daily ) and slope of the best fit regression line. In both cases, the ASCE-PM version showed a higher median and spread for all the four seasons. The mean daily ratio indicates that FAO-PM hourly ET0 equation resulted in lower estimates than the daily ET0 with the exception of winter and the ASCE-PM hourly ET0 equation resulted in higher estimates than the daily ET0 with the exception of summer. Both hourly ET0 equations tend to exceed the daily ET0 equation during the winter (0.04% and 8.7%, respectively) and are slightly less than the daily estimates during the summer (7.5% and 3.0%, respectively). During autumn and spring, the ASCE-PM hourly equation exceeds the daily ET0 equation by 3.20% and 0.06%, respectively, but the FAO-PM hourly equation underestimates it by 2.7% and 5.1%, respectively. The seasonal regression slope for both the version was better than that for the annual data for summer and spring and worse for winter and autumn. R2 values were also higher for summer than winter, probably reflecting greater ET0 and greater temporal variance in ET0 in summer compared with winter. R2 values were more than 0.96 in all seasons except winter.

Fig. 3. Annual and seasonal performance between ET0,soh and ET0,daily for FAO-PM and ASCE-PM versions as indicated by (a) RMSD, (b) ratio(ET0,soh /ET0,daily ), (c) regression slope and (d) R2 for 40 AWS locations. Each box shows the lower (25th), middle (50th) and upper (75th) quartile and the bottom and top whiskers represent the 5th and 95th percentiles.

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Table 7 Summary of statistical indices for daily ET0 calculated based on day light hour and sum-of-hour using hourly ET0 equations for winter. Version

Statistics

SOH—24 h

SOH—DLH hours

Mean

Max.

Min.

Mean

Max.

Min.

FAO-PM

RMSD Daily ratio Regression slope Regression intercept R2

0.17 1.00 0.93 0.10 0.93

0.22 1.11 1.04 0.32 0.98

0.14 0.94 0.83 −0.23 0.82

0.26 0.98 0.71 0.41 0.76

0.43 1.23 1.01 1.86 0.91

0.00 0.83 0.55 −0.09 0.55

ASCE-PM

RMSD Daily ratio Regression slope Regression intercept R2

0.19 1.09 0.93 0.21 0.91

0.26 1.22 1.12 0.70 0.97

0.15 0.99 0.81 −0.21 0.82

0.28 1.11 0.78 0.45 0.78

0.44 1.34 1.10 1.85 0.93

0.20 0.94 0.61 −0.08 0.58

The statistical indicators demonstrate that the correspondence between hourly and daily estimates changes with time of year. The seasonal differences in comparison are no doubt driven by the seasonal difference in magnitude of input variables such as air and dew point temperature, short wave radiation and wind speed. Higher daily ET0 values led to greater RMSD and lower ratios between ET0,soh and ET0,daily . One of the reasons for the seasonal difference in sum-of-hourly ET0 compared with daily ET0 relates to nighttime ET0 . During winter night-time ET0 was very small or negative and effectively did not contribute to daily ET0 , whereas in summer night-time ET0 was significant. Considering all these statistical indicators, the agreement between ET0,soh and ET0,daily values were better for the FAO-PM version during winter, spring and autumn, but during summer, the ASCE-PM version showed better agreement.

4.4. Comparison of 24 h and day-time aggregations The ASCE-PM hourly equation exceeded the daily ET0 equation, with the exception of summer and the FAO-PM hourly equation exceeds daily ET0 during winter. Neither the FAO-56 paper not the ASCE Task committee final report provide guidelines for the use of hourly equations at daily time steps, especially their application at night, but they do provide guidance on the use of hourly data (meteorological data averaged over a 24 hourly period) for the daily equations. Although, in principle daily ET0 calculated using the hourly equation is equal to sum-of-hourly ET0 over a period of 24 h, one can rationalize the sum-of-hours basis only for the daylight hours. This could be justified by the facts that photosynthesis is inactive and net radiation is negative at night-time, suggesting zero ET0 at night. A few authors, (McMahon et al., 2012; Stigter, 1980; Van Niel et al., 2011) provide the starting point for this argument and it has not been either fully rejected or fully accepted in the literature. This argument is stronger for winter than for the other seasons, given the low number of daylight hours and dew point temperatures often exceeding nighttime air temperatures resulting in zero or negative estimates of hourly ET0 , which lead to reduce the sum-of-hourly ET0 over a given day in winter. To examine the impact of nighttime ET0 , we tested the above argument for winter, and Table 7 provides the summary of statistical indicators during winter for daily ET0 calculated using the sum-of-hourly ET0 for 24 h periods (ET0,soh ) and daylight hour periods (ET0,dlh ) compared against the daily ET0 calculated using the daily equation (ET0,daily ). Many, if not most, of the ET0,dlh values were lower than ET0,soh over 24 h. When compared with the ET0,daily values, all performance indicators were in favor of the sumof-hour over 24 h period. The ET0,dlh values increased the RMSD values for both FAO-PM and ASCE-PM. The mean daily ratio for the FAO-PM version indicated that SOH basis over 24 h period exceeded daily ET0 (1.004) whereas the same was underestimated (0.982) during daylight-hours. For the ASCE-PM version, the daylight-hour

basis further enlarged the ratio from 1.087 to 1.105. The regression slope and R2 values for both the versions decreased from SOH basis over 24 h period to the daylight-hour basis. All the statistical indices indicate that better agreement is achieved between hourly and daily ET0 estimates when the hourly values are aggregated over 24 h rather than over daylight hours. 4.5. Comparison of hourly ET0 equations The main difference between the FAO-PM and ASCE-PM hourly equations is the surface resistance–(rs ), where the former is based on an rs of 70 s m−1 for all times while the latter is based on an rs of 50 s m−1 for the day-time and 200 s m−1 for the night-time. The diurnal variation of hourly ET0 , energy, bulk and aerodynamic resistances for the two hourly equations for hot and cold days is shown in Fig. 4, and the respective statistical indicators are given in Table 8. The correlation between the daily ET0 calculated using FAO-PM and ASCE-PM hourly ET0 equations (ET0,soh,FAO and ET0,soh,ASCE ) was 0.99 on average. Moreover, the RMSD between ET0,soh,FAO and ET0,soh,ASCE was very small, compared with the RMSD between ET0,soh and ET0,daily of the respective versions. The mean daily ratio between the ET0,soh,FAO and ET0,soh,ASCE values was always less than 1 (i.e. ASCE-PM hourly ET0 > FAO-PM hourly ET0 ). This was mainly due to the difference in rs , since the hourly energy term and bulk surface resistance terms remained almost the same for both versions for all hourly periods (Fig. 4). Therefore, for the ASCE-PM version, the higher hourly ET0 during the day-time outweighed the lower hourly ET0 during the night, resulting in higher overall daily ET0 . This was reflected in the regression slope and intercept for all 40 locations. 4.6. Climatological impacts on the relationship between ET0,soh vs. ET0,daily The agreement between daily ET0 values calculated using the hourly and daily ET0 equations depended on the location and it was not consistent spatially (Table 6). Therefore, this section breaks the comparison down by the nine climate Köppen zones represented by the stations. The most important measure of agreement between two daily ET0 values is the mean daily ratio as this reflects both the over/under-estimation and scatter in the ET0,soh values, relative to ET0,daily . Fig. 5 shows box plots of the daily mean ratio for each location. Fig. 6 shows the mean and standard deviation for each Köppen climate zone. For all climates, the best agreement between ET0,soh and ET0,daily in terms of ratio was found under ASCE-PM equations. The highest underestimation for daily ET0 calculated using the hourly FAO-PM equation was found in arid climates followed by tropical and temperate climates, whereas for the ASCE-PM version, daily ET0 calculated using the hourly equation was overestimated and

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Fig. 4. (a) Hourly ET0 (b) Hourly energy (c) Bulk resistance and (d) Aerodynamic resistance for a warm day in the summer and a cold day in winter, calculated using hourly FAO-PM and ASCE-PM ET0 equations at Shepparton airport AWS, Victoria.

followed the same order. The box plots show that the ratios were positively skewed for most climates, with the exception being “BSh” and “Cwa” climates. The variance for the ratio between ET0,soh and ET0,soh was higher for the ASCE-PM equations than for the FAO-PM equations for all climates and there is greater variation within a climate zone than between the zones. Within the temperate climate, for both the versions, the highest variability and the maximum daily ratio (averaged over the study period) were found in the “Csb” sub-climate, which has a dry and warm

summer. Particularly, daily ET0 calculated using hourly FAO-PM equation found to be overestimated for two AWSs under the temperate climate (Fig. 5). On the other hand, the mean and standard deviation of the daily ratio was lowest for both versions under the “BSh” climate zone (Emerald Airport-QLD). Notably, in “BSh” and “BWk” climate zones both the hourly ET0 equations resulted in lower estimates of ET0 than the daily ET0 . In the tropical climate, the best agreement between the ET0,soh and ET0,daily values were found for the ASCE-PM version, whereas

Table 8 Statistical indicators of the daily ET0 calculated using the FAO-PM and ASCE-PM hourly ET0 equations. AWS ID

Site

Köppen region

Number of observations

RMSD

Avg. ratio

Slope

Intercept

R2

32040 33307 2056 35264 74037 74258 75041 76031 80128 24024 24048 40082 40922 41359 41522 41525 41529 54038 55202 73151 80091 81049 81124 81125 41175 81123 85072 85279 85280 85296 90035 9994 9538 9617 23373 26021 26091 90182 90194 33002

Townsville Apt. Woolshed Kununurra Apt. Emerald Apt. Yanco agri. Inst. Deniliquin Apt. Griffith Apt. Mildura Apt. Charlton Loxton res. ctr. Renmark Apt. Univ. Qld Gatton Kingaroy Apt. Oakey Apt. Dalby Apt. Warwick Toowoomba Apt. Narrabri Apt. Gunnedah Apt. Temora Apt. Kyabram Tatura Inst. Sus. Yarrawonga Shepparton Apt. Applethorpe Bendigo Apt. East sale Apt. Bairnsdale Apt. Morwell Apt.) Mount Moornapa Colac Collie east Dwellingup Bridgetown Nuriootpa Viti. Mt. Gambier Apt. Coonawarra Casterton Dartmoor Ayr dpi res. stn

Aw Aw BSh BSh BSk BSk BSk BSk BSk BSk BWk Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfa Cfb Cfb Cfb Cfb Cfb Cfb Cfb Csa Csb Csb Csb Csb Csb Csb Csb Cwa

2067 1753 1954 2026 1873 1939 1939 1936 2009 714 522 1968 1955 2043 2075 1910 1973 1845 1930 1892 1982 853 1956 2046 1855 1945 1600 1934 2084 2053 1949 1919 1042 1830 448 1950 1494 1863 1354 608

0.10 0.08 0.12 0.11 0.15 0.15 0.15 0.13 0.12 0.12 0.13 0.10 0.08 0.11 0.11 0.10 0.11 0.14 0.11 0.12 0.09 0.10 0.13 0.12 0.07 0.12 0.12 0.11 0.11 0.12 0.17 0.08 0.13 0.08 0.14 0.13 0.14 0.12 0.10 0.06

0.96 0.97 0.99 0.98 0.99 0.98 0.98 0.98 0.97 0.98 0.98 0.97 0.96 0.97 0.98 0.97 0.97 0.99 0.98 0.97 0.97 0.96 0.98 0.97 0.96 0.97 0.95 0.95 0.96 0.99 0.95 0.97 0.98 0.97 0.97 0.95 0.96 0.96 0.94 0.96

0.95 0.96 1.01 1.00 1.00 1.00 1.00 0.99 0.98 0.99 0.99 0.97 0.97 0.98 0.99 0.97 0.97 1.00 0.99 0.98 0.97 0.96 0.99 0.98 0.96 0.97 0.93 0.94 0.95 0.99 0.95 0.97 1.00 0.97 0.98 0.94 0.96 0.96 0.94 0.95

0.06 0.04 −0.11 −0.09 −0.04 −0.10 −0.07 −0.05 −0.04 −0.03 −0.03 0.01 −0.03 −0.05 −0.05 0.01 −0.02 −0.04 −0.02 −0.06 −0.01 0.01 −0.04 −0.03 0.01 −0.01 0.07 0.04 0.02 0.02 0.02 0.00 −0.07 −0.01 −0.03 0.02 −0.02 0.00 0.00 0.03

1.00 1.00 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

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Fig. 5. Box plots for all AWS as indicated by the daily ratio between ET0,soh and ET0,daily (a) FAO-PM and (b) ASCE-PM equations. Each box shows the lower (25th), middle (50th) and upper (75th) quartile and the bottom and top whiskers represent the 5th and 95th percentiles.

Fig. 6. Summary of mean and standard deviation for sub-climate zones of the daily ET0 between the Daily and Hourly ET0 FAO-PM and ASCE-PM equations.

on average mean daily ratio was 1.00 and the variability was moderate. In the temperate climates without a dry season, the FAO-PM hourly ET0 equation underestimated daily ET0 by 3.9%; where else the ASCE-PM hourly ET0 equation overestimated daily ET0 by 2.35%. In the Arid climate both the hourly ET0 equation underestimated the daily ET0 by 4.9% and 0.5%, respectively. Therefore, the best agreement between the ET0,soh,FAO and ET0,daily,FAO values was found in the temperate climate, whereas agreement between ET0,soh, ASCE and ET0,daily, ASCE values was best in tropical and arid climates. 5. Summary and conclusion In this paper, two major ET0 models, namely the FAO-PM and standardized ASCE-PM, were comprehensively compared at hourly and daily time steps using hourly weather data from 40 AWS locations representing diverse climates across Australia. The sumof-hour based daily ET0 calculated using the hourly equation was compared to the respective daily ET0 from the daily equation. The results were quantified using the RMSD, daily ratio between the ET0,soh and ET0,daily , slope/intercept of the best fit linear regression line, and coefficient of determination—R2 . The difference between daily ET0 calculated using the hourly and daily ET0 equations have previously been considered with respect to certain geographical areas only. In fact, this is the first study to compare such differences between two daily ET0 estimations at a continental scale on a broader spectrum of factors, which included seasonality, climate type, different methods of estimating Rso and different aggregation methods(sum-of-hourly and daylight hours). The results showed that the range for the ratio between ET0,soh and ET0,daily was narrower than most previous studies, probably reflecting the quality of the data set and the moderately large study

period. Here, the range of ratio for FAO-PM and ASCE-PM versions were 0.90–0.98 and 0.96–1.04, respectively, compared with 0.90 to 1.04 (FAO-PM) and 0.94 to 1.07 (ASCE-PM) for Itenfisu et al. (2003) study and 0.97–1.09 (ASCE-PM) for Irmak et al. (2005) study. Our results were similar to the studies of Gavilán et al. (2008), who found that hourly ET0 calculated using the ASCE-PM version was higher than the FAO-PM version and resulted higher daily ET0 estimates. Overall, the daily ET0 from the hourly ASCE-PM equation exceeded the corresponding daily equation by 5%, whereas for FAOPM the hourly exceed the daily equation by 2–3% in previous studies (Berengena and Gavilan, 2005; Gavilán et al., 2008). Our results for the averaged RMSD for FAO-PM and ASCE-PM versions were 0.26 mm day−1 and 0.28 mm day−1 were better than similar studies in Turkey using 12-min intervals meteorological data (Silva et al., 2010). The best agreement between ET0,soh and ET0,daily estimates for summer was found in the ASCE-PM version which corresponds closely to similar studies conducted in the USA and Europe (Irmak et al., 2005; Itenfisu et al., 2003; Lopez Urrea and López, 2006). In this study we found that the Rso calculated using the “complex” approach improved the agreement between ET0,soh and ET0,daily for both versions, compared with Rso calculated using the simple approach. The average ratios between the ET0,soh and ET0,daily in the FAO-PM and ASCE-PM versions were 0.95 and 1.00, respectively, and the range was 0.90–0.98 for the FAO-PM version and 0.96–1.04 in the ASCE-PM version. The RMSD difference between the ET0,soh and ET0,daily for FAO-PM and ASCE-PM versions was on average 0.26 mm day−1 and 0.28 mm day−1 , respectively, and suggesting that daily ET0 calculated using hourly and daily ET0 equations agreed more closely for FAO-PM. However, other statistical indices such as the average daily ratio and the regression slope showed closer agreement between the ACSE-PM equations.

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During the winter, spring and autumn, the best agreement between the hourly and daily versions was found for FAO-PM, whereas in the summer, the ASCE-PM version had closer agreement. Since both the hourly versions exceeded the daily ET0 during the winter, the daily ET0 was calculated on a daylight-hour basis and compared with the daily ET0 calculated using the sum-of-hour basis over a 24 h period. The performance indicators favor aggregating over 24 h. There was a very good correlation between both the hourly equations at daily time step, on average 0.997 with a range of 0.993–0.998. The average ratio and range between the ET0,soh,FAO and ET0,soh,ASCE were 0.97 and 0.94–0.99, respectively. The ASCE-PM’s lower rs during the daytime increases the hourly ET0 and vice versa during the night, the day time changes exceed the night-time changes, resulting in a higher overall estimate of ET0 . The best agreement between the hourly and daily result for the FAO-PM version was found in the temperate climate and the ASCE-PM version showed the best agreement in the tropical and arid climates. Acknowledgements The authors wish to express their gratitude to the Bureau of Meteorology, Australia for providing climate data and Kushan C. Perera was supported by an Australian Post-Graduate Award from the University of Melbourne. References ABARES, 2010. In: Australian Bureau of Agricultural and Resource Economics and Sciences (Ed.), Land Use of Australia, Version 4, 2005/2006. Department of Agriculture, Australia. Ahmad, M.J., Tiwari, G.N., 2008. Estimation of hourly global solar radiation for composite climate. Open Environ. J. 2, 34–38. Allen, R.G., 1996. Assessing integrity of weather data for reference evapotranspiration estimation. J. Irrig. Drain. Eng. 122, 97. Allen, R.G., Jensen, M.E., Wright, J.L., Burman, R.D., 1989. Operational estimates of reference evapotranspiration. Agron. J. 81, 650–662. Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop Evapotranspiration— Guidelines for Computing Crop Water Requirements, United Nations Food and Agriculture Organization, Irrigation and Drain, Paper No. 56. Rome, Italy, pp. 300. Allen, R.G., Pruitt, W.O., Wright, J.L., Howell, T.A., Ventura, F., Snyder, R., Itenfisu, D., Steduto, P., Berengena, J., Yrisarry, J.B., Smith, M., Pereira, L.S., Raes, D., Perrier, A., Alves, I., Walter, I., Elliott, R., 2006. A recommendation on standardized surface resistance for hourly calculation of reference ETo by the FAO56 Penman–Monteith method. Agric. Water Manage. 81, 1–22. Amatya, D.M., Skaggs, R.W., Gregory, J.D., 1995. Comparison of methods for estimating ref-et. J. Irrig. Drain. Eng.—ASCE 121, 427–435. Benseman, R.F., Cook, F.W., 1969. Solar radiation in New Zealand—the standard year and radiation on inclined slopes. N.Z. J. Sci. 12, 696–708. Berengena, J., Gavilan, P., 2005. Reference evapotranspiration estimation in a highly advective semiarid environment. J. Irrig. Drain. Eng.—ASCE 131, 147–163. BoM, A., 1997. Guidelines for the siting and exposure of meteorological instruments and observing facilities. In: Bureau of Meteorology, A. (Ed.), Observation Specification No. 2013.1. BoM, Australia. BoM, A., 2014. Meteorological Observations and Reports Instrument Siting Requirements. BoM, Australia. Chen, D.L., 2005. Comparison of the Thornthwaite method and pan data with the standard Penman–Monteith estimates of reference evapotranspiration in China. Clim. Res. 28, 123. Chiew, F.H.S., Kamaladasa, N.N., Malano, H.M., McMahon, T.A., 1995. Penman– Monteith, FAO-24 reference crop evapotranspiration and class-A pan data in Australia. Agric. Water Manage. 28, 9–21. Collares-Pereira, M., Rabl, A., 1979. The average distribution of solar radiationcorrelations between diffuse and hemispherical and between daily and hourly insolation values. Solar Energy 22, 155–164. Doorenbos, J., Pruitt, W.O., 1977. Guidelines for Predicting Crop Water Requirements/by J. Doorenbos and W. O. Pruitt, in Consultation with A. Aboukhaled

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