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Comparison of Reference Evapotranspiration Calculations for Southeastern North Dakota | OMICS International
ISSN: 2168-9768
Irrigation & Drainage Systems Engineering
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Comparison of Reference Evapotranspiration Calculations for Southeastern North Dakota

Xinhua Jia1*, Thomas Scherer1, Dongqing Lin1, Xiaodong Zhang2 and Ishara Rijal3

1Department of Agricultural and Biosystems Engineering, North Dakota State University, Fargo, North Dakota-58108, USA

2Department of Earth System Science and Policy, University of North Dakota, Grand Forks, North Dakota-58202, USA

3Department of Geography, MichiganStateUniversity, East Lansing, Michigan-48824, USA

*Corresponding Author:
Xinhua Jia
Department of Agricultural and Biosystems
Engineering, North Dakota State University
Fargo, North Dakota, USA
Tel: 1-701-231-6453
Fax: 1-701-231-1008
Email: [email protected]

Received October 24, 2013; Accepted November 25, 2013; Published December 02, 2013

Citation: Jia X, Scherer T, Lin D, Zhang X, Rijal I (2013) Comparison of Reference Evapotranspiration Calculations for Southeastern North Dakota. Irrigat Drainage Sys Eng 2:112. doi:10.4172/2168-9768.1000112

Copyright: © 2013 Jia X, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Abstract

Potential water consumption for irrigation scheduling in North Dakota was typically calculated from a reference Evapotranspiration (ETref) using the Jensen-Haise method and its associated crop coefficient (Kc) curves developed in the 1970’s and 1980’s. The ETref method proposed by the American Society of Civil Engineers, Environmental and Water Research Institute (ASCE-EWRI) reference evapotranspiration task force has shown to be more accurate and therefore more widely used than any other methods. However, to apply the ASCE-EWRI method for irrigation scheduling requires a corresponding change of the Kc curves associated with the Jensen-Haise method. In this paper, a comparison of ETref estimates for 11 methods, including the ASCE-EWRI and the Jensen-Haise methods, was conducted using 18 years of data collected in southeastern North Dakota. The results show that the annual ETref by the Jensen-Haise method was nearly the same as the ASCE-EWRI grass ETref, but with a higher Root Mean Square Deviation (RMSD), 0.903 mm d-1, and a lower coefficient of determination (R2) 0.8659. The ETref comparison for the growing season only shows an RMSD of 1.007 mm d-1, R2 of 0.7996 and 8.13% overestimation. The ETref by the Jensen-Haisemethod has a higher monthly ETref than the ASCE-EWRI in June, July, and August, and a lower monthly ETref for all other months in an 18 year period. The ETref comparisons also show that the modified Penman method used by the High Plains Regional Climate Center (HPRCC Penman) has the best accuracy and correlation with the ASCE-EWRI ETref method. Indeed, all alfalfa based ETref methods, including Kimberly Penman and HPRCC Penman, show better performance than the grass based ETref methods, including FAO24 Penman, FAO24 Radiation, FAO24 Blaney-Criddle, Priestley-Taylor, Hargreaves, and the Jensen-Haise methods.

Keywords

Reference evapotranspiration; Jensen-Haise; ASCE standardized reference ET

Introduction

Evapotranspiration (ET) is defined as evaporation of water from land and water surfaces [1] and transpiration by vegetation [2]. Knowledge of ET is important for water resource planning, efficient water management, and water permitting application. Direct measurement of ET is time consuming and costly [3]. Therefore, ET is normally determined indirectlyby relating to a reference evapotranspiration (ETref) to a crop coefficient (Kc), namely, ET = Kc×ETref [3]. ETref is defined as the ET rate from a uniform surface of dense, actively growing vegetation having specified height and surface resistance, not short of soil water, and representing an expanse of at least 100 m of the same or similar vegetation [1]. It represents the evaporative power of the atmosphere at a specific location and time of the year, but does not consider the crop characteristics and soil factors [4]. ETref can be calculated from weather data collected by weather stations. The Kc curve represents crop growth characteristic for a growing season. Both ET and Kc are influenced by crop characteristics, such as crop variety and cultivar, growth stage, crop height, and surface roughness. ET can also be affected by soil characteristics, including soil salinity, fertility, impenetrable soil layers, and plant residue [4]. The Kc curve for a specific crop is normally developed from research data for a specific region.

Many methods have been developed to estimate ETref. These can be categorized into four basic groups: combination, radiation, temperature, and pan evaporation methods [3]. The combination method, accounting for radiation (energy balance) and aerodynamic (heat and mass transfer) terms [2], was first proposed in 1948 by Penman [5]. The Penman equation was subsequently modified as the FAO24 Penman method [3], the Kimberly Penman [6], the Penman- Monteith [7], the FAO Penman-Monteith [4] and the American Society of Civil Engineers, Environmental and Water Resources Institute (ASCE-EWRI) Penman-Monteith [1] equation. Radiation based ETref equations include the Priestley-Taylor [8] and FAO24 radiation methods [3]. Temperature based ETref equations include the Thornthwaite [9], Jensen-Haise [10], FAO24 Blaney-Criddle [3], and Hargreaves [11]. The pan evaporation methods are termed FAO class-A Pan [3] and Christiansen Pan [12]. While the availability of reliable weather data is limited, temperature methods (e.g. Jensen- Haise method) have been shown to provide reasonable ETref estimates. Among all the methods, the one that was developed by the ASCE EWRI standardized reference evapotranspiration task committee [1] was recommended as the standardized reference ET method [13-15]. Application of this method requires solar radiation, air temperature, relative humidity and wind speed as the input parameters.

Weather data used for estimating ETref are normally collected from a reference crop surface, either a tall crop similar to a full-cover alfalfa or a short crop similar to a clipped, cool-season grass. While most ETref methods are only applicable for one reference surface, the ASCEEWRI method [1] can be applied to both full cover crops of alfalfa and grass. The ETref on an alfalfa reference surface is abbreviated as ETr, and the ETref on a grass reference surface as ETo. Most methods, such as the FAO24 Penman [3] and the Penman-Monteith [7], are based on the grass reference surface, but some, such as the Kimberly Penman [6] and the modified Penman methods [16] used by the High Plains Regional Climate Center (HPRCC, http://www.HPRCC.unl.edu) are based on an alfalfa reference surface.

In North Dakota, the Jensen-Haise equation is used to calculate the ETref [17-19]. The Jensen-Haise method only requires temperature and solar radiation as the input parameters. It was originally developed from data collected in the western United States over 35 years using 15 field and orchard crops [10,20].The North Dakota Agricultural Weather Network (NDAWN, http://ndawn.ndsu.nodak.edu/) calculates ETref values using the Jensen-Haise method and the modified Penman (or HPRCC Penman) method for each weather station on the network. North Dakota is part of the High Plains Regional Climate Center. As indicated by Irmak et al. [21], the HPRCC Penman method applies when vapor pressure deficit (VPD) and wind speed do not exceed 2.3 kPa and 5.1 ms-1, respectively. Weather records from the Oakes NDAWN weather station indicate that higher values for wind speeds and VPD are not rare. For the period of record from 1991 to 2008 (6575 days), there are 12 days with VPD over 2.3 kPa, and 724 days (or 40 days per year) with wind speed above 5.1 m s-1. Irmak et al. [21] found that at the higher end of the ETr values, the HPRCC Penman method provided consistently lower ETr values than those using the ASCEEWRI method, which was attributed to the upper limits of applicability by the HPRCC Penman method.

The standardized ETref method [1] has not been widely used in North Dakota. Most crop coefficient curves were developed using the Jensen-Haise method for this region [22-25]. As indicated by Snyder et al. [26], Kc values are developed specifically for a region, and are highly dependent on the methods used for actual ET measurement and reference ET calculations. This indicates that all Kc curves were bonded specifically to the ET and ETref methods used to develop them because Kc values were derived as ET/ETref. The variable ET would only need to be figured initially before ETref and Kc could be applied. Applications of the ASCE EWRI method will require sequential changes to the Kc curves developed using other methods, such as the Jensen-Haise method.

Most irrigation research studies in North Dakota were conducted near Oakes in the southeast area of the state [17,27,28]. There hasn’t been much research in the west part of the ND state where it’s drier and research is needed. Irmak et al. [21] categorized the Jensen-Haise method as an alfalfa reference based method, but Jia et al. [29] found that the ETref by the Jensen-Haise method is closer to a grass reference based method. Jensen and Haise [10] stated they developed the method based on data collected during the growing season over 35 years from 15 field and orchard crops in different regions of the Western US. The Oakes area does not have the most typical climate to represent the whole state and may not be the best place for irrigation based on its above average precipitation [29], but the sandy soil conditions, available water resources, and financial assistance from Garrison Division Conservancy District made the Oakes area one of the most irrigated areas in ND [30,31].

In this study, using weather data collected at the Oakes NDAWN station from 1991 to 2008, the daily ETref was calculated using 11 methods. The differences between the ASCE-EWRI ETo method [1] and the Jensen-Haise ETo method [10] as well as other 9 methods were compared on a daily, monthly, and yearly basis for the entire year and the growing season for the period of May 1 to September 30.

Materials and Methods

Study site

The study site is located in Oakes, North Dakota. The weather station, surrounded by agricultural land, is located south of Oakes at latitude 46.07oN, longitude 98.09oW, and an elevation of 392 m. The soil at the weather station is Embden fine sandy loam (coarse-loamy, mixed Pachic Udic Haploborolls), and Maddock fine sandy loam (sandy, mixed Udorthentic Haploborolls) [32].

Weather conditions

The weather conditions at Oakes are typical continental; cold in the winter and semi-humid in the summer. The weather data recorded during the past 18 years showed that the average annual temperature was about 6oC, with the minimum in January and the maximum in July and August. Rainfall amounts ranged from 346 mm to 637 mm from May to September, with the highest rainfall amounts generally in June. The average ETr during the growing season was 842 mm, which was 471 mm higher than the average precipitation amount. Wind speed averaged 3.3 m s-1 at 2 meter above the ground, with the highest average monthly wind speed of 4.0 m s-1 in May, and the lowest monthly average wind speed of 2.4 m s-1 in August. The average annual maximal wind speed was 8.8 m s-1. The longest day time at Oakes is 16 hours in June and the shortest day time of 9 hours is in December [3]. There are 137 frost free days at Oakes, with the last killing frost in May and the first killing frost in October [33]. Monthly average, maximum, and minimum daily values for temperature, relative humidity, rainfall, and solar radiation over the 18 years at Oakes are listed in Table 1.

Month Tmax (°C) Tmin (°C) Tavg (°C) Uavg (m d-1) RH (%) Rs (MJ m-2) Day time (h) PET (mm) Rain (mm)
Jan -7 -18 -12 3.4 75 5.9 9 18  
Feb -3 -14 -9 3.6 74 9.4 10 27  
Mar 3 -7 -2 3.7 71 13.4 12 60  
Apr 13 0 6 3.9 57 17.4 14 131 35
May 20 7 14 4.0 56 20.1 15 187 73
Jun 25 13 19 3.4 65 22.1 16 186 102
Jul 28 15 21 2.6 70 23.1 15 183 79
Aug 27 14 20 2.4 68 19.9 14 160 51
Sep 22 8 15 2.8 63 14.9 13 126 66
Oct 14 1 8 3.1 61 9.4 11 84 51
Nov 4 -7 -2 3.3 70 5.8 10 36  
Dec -3 -14 -8 3.4 75 4.7 9 19  
Annual 12 0 6 3.3 67 14 12 1217 457

Table 1: Monthly average maximal temperature (Tmax), minimal temperature (Tmin), daily temperature (Tavg), wind speed (Uavg) at 2 m height, incoming solar radiation (Rs), day time length (hour), monthly total potential evapotranspiration (PET) by Hprcc Penman method (mm), and monthly total rainfall (Rain) during the study period from 1991 to 2008 at Oakes, North Dakota. All parameters were obtained from the NDAWN website, except day time hours were calculated from Doorenbos and Pruitt (1977) using Oakesâ latitude.

Data quality

“Data quality has the highest priority in the operation of the North Dakota Agricultural Weather Network (NDAWN) because erroneous data are worse than no data” [34]. Two procedures are performed daily for ensuring data quality control: locate missing and erroneous values and provide estimates using data from nearby stations. The data retrieved from NDAWN are further checked following the weather data integrity assessment procedures recommended by Allen [35] and ASCE-EWRI [1] for solar radiation, humidity, temperature, and wind speed to ensure that all data used in the calculation and analysis are good quality.

Weather parameters

Daily weather data, including maximal temperature (Tmax), minimal temperature (Tmin), wind speed (U), maximal wind speed (Umax), dew point temperature (Tdew), and shortwave incoming radiation (Rs) were downloaded from the NDAWN website for the period of 01/01/1991 to 12/31/2008. All the other required information, such as latitude, elevation, height of wind speed measurement and grass height were obtained either from the NDAWN website or from personal communications [34].

NDAWN measures wind speed at a height of 3 m immediately adjacent to the weather station, the grass in an area of about 40 m2 has been maintained at a height of about 8-10 cm. However, to accommodate the fully mature crop heights typically taller than 0.5 m [34], equation 47 in FAO56 [4] was used to convert the wind speed at 3 m height to 2 m height:

equation                                            (1)

where u2 is the wind speed at 2 m above the ground surface in m s-1, uz is the measured wind speed at z m above ground surface in m s-1, and z is the height of measurement above the ground surface in m, which is 3 m for this study.

The relative humidity is calculated from equation 6 to 8 of ASCEEWRI method [1] using measured Tmax, Tmin, and Tdew from NDAWN weather data via saturated (es) and actual vapor pressure (ea):

equation                                           (2)

equation                             (3)

equation          (4)

where the T in equation (3) can be either Tmax in °C or Tmin in °C to be used in equation (2) to calculate the es and ea in kPa. The relative humidity (RH) is calculated as the ratio of ea to es. Details of sensor types, layout, and data quality control are detailed on the NDAWN website.

Reference ET calculations

The daily Jensen-Haise and HPRCC Penman ETref values are available on the NDAWN website. The ETref by these two methods will be directly used in the comparison. The ETref by the ASCE-EWRI method for grass and alfalfa references were calculated [1] using:

equation          ( 5)

Where ETref is the reference crop evapotranspiration for short grass (ETo) or tall alfalfa (ETr) [mm day-1], Rn is net radiation at the crop surface [MJ m-2 day-1], G is soil heat flux [MJ m-2 day-1], T is mean daily air temperature at 2 m height [°C], u2 is wind speed at 2 m height [m s-1], Δ is slope vapor pressure curve [kPa °C-1], and γ is the psychrometric constant [kPa °C-1]. For a 24 hour time step, soil heat flux, G, is presumed to be 0. The values of Cn and Cd vary depending on the reference crops, and are 900 and 0.34 for the grass reference and 1600 and 0.38 for the alfalfa reference, respectively.

The downloaded weather data were arranged in the correct format for the REFET software [36], so that daily ETref by FAO24 Penman, FAO24 Radiation, FAO24 Blaney-Criddle, Priestley-Taylor, Hargreaves ,Kimberly Penman 1982 and Kimberly Penman 1972 methods could be calculated.

A total of eleven methods were used to calculate the ETref; four methods are alfalfa based methods (ASCE-EWRI ETr, HPRCC Penman, Kimberly Penman 1982 and Kimberly Penman 1972) and seven methods are grass based reference methods (ASCE-EWRI ETo, FAO24 Penman, FAO24 Radiation, FAO24 Blaney-Criddle, Priestley- Taylor, Hargreaves, and Jensen-Haise).

Statistics analysis

The daily ETref values calculated from each method were compared to the ASCE-EWRI ETr or ETo values, depending on whether it was grass or alfalfa reference surface method. The root mean square deviation (RMSD) between the ASCE-EWRI ETref (method x, in Eq. (6)) and the compared method (method y, in Eq. (6)) was used to determine the difference:

equation                                        (6)

where xi is the ETref calculated by method x on day i; yi is the ETref calculated by method y on day i; and n is the total number of days used in the calculation.

Since the ASCE-EWRI ETref is considered a standard value for comparison, the RMSD values between ETref values using the ASCEEWRI and the compared method are considered a quantitative measure of all other methods. A smaller RMSD means a better comparison between the other method and the ASCE-EWRI ETref method. The slope and coefficient of determination (R2) values are used to assess the bias of each method. The intercept of the regression line between the ASCE-EWRI ETref and the compared ETref values were forced to zero for an equal comparison among all methods. However, when forcing the regression curve to zero, it also assumes that at zero ET values, there is no atmosphere demand for water for all methods and the resulting slope can be used to indicate the error regardless of the magnitude of the readings. It also biases the results by placing heavier weight on points farthest from the origin. The purpose of this paper is to determine how widely the ETref values were different from the standardized ASCE-EWRI ETref values and the RMSD and R2 values should be reasonable sufficient.

Results and Discussions

Daily ETo and ETr comparison

Comparison of daily ETo and ETr values between the ASCE-EWRI ETo or ETr method and the targeted method are shown in Figure 1a-1j. The slope of the fitting and coefficient of determination for each pair are also shown in the graph and in Table 2. In addition, the RMSD and the rank of all methods are also shown in Table 2. The rank is made according to the average of the R2 and the RMSD ranks. For example, the R2 ranks 9 and the RMSD ranks 7 between the Prestley-Taylor and ASCE-EWRI ETo methods, the overall rank is the average, 8.

ID Method y Method x Slope R2 Rank-R2 RMSD Rank-RMSD Overall Rank
(a) ASCE-EWRI ETo ASCE-EWRI ETr 0.7488 0.9804   1.103    
(b) FAO24 Penman ASCE-EWRI ETo 1.5464 0.9735 2 1.827 9 6
(c ) FAO24 Radiation ASCE-EWRI ETo 1.1133 0.9358 6 0.717 5 5
(d) FAO24 Blaney-Criddle ASCE-EWRI ETo 1.1578 0.9566 4 0.746 6 4
(e) Hargreaves 1985 ASCE-EWRI ETo 0.9706 0.8794 7 0.707 4 5
(f) Prestley-Taylor ASCE-EWRI ETo 0.8701 0.8588 9 0.854 7 7
(g) Jensen-Haise ASCE-EWRI ETo 0.9961 0.8659 8 0.903 8 7
(h) Hprcc Penman ASCE-EWRI ETr 1.0071 0.9754 1 0.429 1 1
(i) Kimberly Penman 1972 ASCE-EWRI ETr 0.9532 0.9496 5 0.624 3 3
(j) Kimberly Penman 1982 ASCE-EWRI ETr 1.0261 0.9652 3 0.522 2 2

Table 2: Comparison of daily reference evapotranspiration (ETref), Root Mean Square Deviation (RMSD), and coefficient of determination (R2) from 1991 to 2008 at Oakes, North Dakota. ETo is grass based reference surface and ETr denotes alfalfa based reference surface. The overall rank is based on average ranks from RMSD and R2 for annual ETref

irrigation-drainage-daily-reference-evapotranspiration

Figure 1: Daily reference evapotranspiration comparisons between (a) ASCEEWRI ETo and ASCE-EWRI ETr; (b) FAO24 Penman and ASCE-EWRI ETo; (c) FAO24 Radiation and ASCE-EWRI ETo; (d) FAO24 Blaney-Criddle and ASCEEWRI ETo; (e) Hargreaves 1985 and ASCE-EWRI ETo; (f) Prestley-Taylor and ASCE-EWRI ETo; (g) Jensen-Haise and ASCE-EWRI ETo; (h) Hprcc Penman and ASCE-EWRI ETr; (i) Kimberly Penman 1972 and ASCE-EWRI ETr; and (j) Kimberly Penman 1982 and ASCE-EWRI ETr methods for Oakes, North Dakota in 1991-2008.

From 1991 to 2008, the HPRCC Penman method results were most similar to the ASCE-EWRI ETr values using R2 and RMSD. Even with limitations on high wind speed and high VPD, the HPRCC Penman method performed the best among all methods. It overestimated the ASCE-EWRI ETr by a mere 1%; much better compared to reports by Irmak et al. [21] with a 5% underestimation. The Jensen-Haise method provided very close ETo values when compared to the ASCE-EWRI ETo values with less than 0.2% difference. However, the R2 was only 0.87 and the RMSD was 0.903 mm d-1. If one argues that forcing the equation to zero has caused the problem, the R2 was only 0.89 without forcing the equation to zero. This proves that the Jensen-Haise method is not strongly correlated to the ASCE-EWRI ETo values.

Winter in North Dakota extends from late November to early April. During this time period, average air temperature is normally less than 0 °C, while the ground is frozen, plants are dead or dormant, and most of the state is covered with snow. Under these conditions, no water evaporates from the soil surface or transpired by plants. Thus, these conditions seem to violate the definition of ET. There may be some water loss through sublimation, a phase change from solid ice or snow to vapor [37,38]. The calculation of ET during this time period is for comparison purposed only, and does not represent any actual ET lost. Evaluation of ET values during the growing season in North Dakota is more important.

Growing season ETo and ETr

Because the Jensen-Haise method was originally developed using data during the growing season, the ETref comparisons are performed using weather data from May 1 to September 30 over an 18-year period (Figure 2a-2j).

After changing the comparison days from 6575 days for the 18 years to 2966 days for the growing season only, the relationship between the ETref by ASCE-EWRI method and other methods did not change significantly. The HPRCC Penman method still performed the best among all the methods with the higher R2 and smallest RMSD value. The Priestley-Taylor method performed better for the growing season than for the entire year. The FAO24 Blaney-Criddle method had the highest correlation (R2) with the ASCE-EWRI ETo values, but with 20.76% overestimation, and therefore, a higher RMSD value than that in Figure 1. The Blaney-Criddle method required mean daily temperature, mean daily percentage of total annual daytime hours, and an adjustment factor depending on minimum relative humidity, sunshine hours, and daytime wind estimates as the input parameters, which are similar to the ASCE-EWRI method, but without considering the crop factors, and thus do not strongly correlated. The Jensen-Haise method remained about the same rank with the ASCE-EWRI ETo either for the growing season or for the entire year. For the growing season, it overestimated the ETo by 8.35% from the ASCE-EWRI ETo method with a lower R2 and a higher RMSD value. Considering the relationship between the ASCE-EWRI ETo and ETr, this might indicate more than 10% underestimation from the ETr as others have reported [21,30]. Jensen [20] and Burman et al. [39] stated that the Jensen-Haise method is better suited for time intervals of five days to one month rather than for daily estimates. The daily estimated ETref by the Jensen- Haise method was used in the analysis for Figures 1 and 2. Therefore, a growing season comparison of ETref didn’t improve the correlation between the Jensen-Haise method to the ASCE-EWRI method than for an entire year.

irrigation-drainage-daily-reference-evapotranspiration-asce

Figure 2: Daily reference evapotranspiration comparisons between (a) ASCEEWRI ETo and ASCE-EWRI ETr; (b) FAO24 Penman and ASCE-EWRI ETo; (c) FAO24 Radiation and ASCE-EWRI ETo; (d) FAO24 Blaney-Criddle and ASCEEWRI ETo; (e) Hargreaves 1985 and ASCE-EWRI ETo; (f) Prestley-Taylor and ASCE-EWRI ETo; (g) Jensen-Haise and ASCE-EWRI ETo; (h) Hprcc Penman and ASCE-EWRI ETr; (i) Kimberly 1972 and ASCE-EWRI ETr; and (j) Kimberly 1982 and ASCE-EWRI ETr methods for Oakes, North Dakota for the growing season (May 1 â September 30) of 1991-2008.

Monthly ETref

As shown in Table 3 and Figures 1 and 2, the total ETref by the Jensen-Haise method was very close to the ASCE-EWRI ETo values both for annual or seasonal time scale, but with a poor correlation (R2) and less accuracy (RMSD). Figure 3a-3c shows the monthly average ETref of the 11 methods over the 18 years. Most methods showed a similar trend as the ASCE-EWRI standardized equation; higher in the summer and lower in the winter. A higher difference was observed between winter and summer, but not between spring and fall. All combination methods showed similar trends for all seasons while comparing the ASCE-EWRI ETref methods. In Figure 4a, the FAO24 Penman method showed a comparable annual curve to the ASCEEWRI ETo method, while in Figure 4c, all the ETr values were very similar to each other with less than 5% difference and followed the ASCE-EWRI ETr curve. This is probably due to the fact that the ASCEEWRI ETr was developed using data at Kimberly, or originated from the Kimberly Penman methods [2]. The HPRCC Penman method also gave more similar results to the ASCE-EWRI ETr method for all month. The local-adjusted HPRCC Penman method proved to be the best fit for the Oakes area in southeastern North Dakota. The temperature and radiation based methods were quite different from the monthly ASCEEWRI ETo values. The FAO24 Radiation, FAO24 Blaney-Criddle and Prestley-Taylor methods showed underestimation in the winter and overestimation in the summer compared to the ASCE-EWRI ETo values. The Jensen-Haise method had the greatest deviation from the ASCE-EWRI ETo method with lower ETo values from January to May and from September to December, and higher ETo values from June to August. Though the annual ETo values were close to the ASCE-EWRI ETo values, the month to month difference was higher.

ID Method y Method x Slope R2 Rank-R2 RMSD Rank-RMSD Overall Rank
(a) ASCE-EWRI ETo ASCE-EWRI ETr 0.7671 0.9543   1.395    
(b) FAO24 Penman ASCE-EWRI ETo 1.5697 0.9529 3 2.624 9 6
(c ) FAO24 Radiation ASCE-EWRI ETo 1.1387 0.8915 6 0.916 6 5
(d) FAO24 Blaney-Criddle ASCE-EWRI ETo 1.2054 0.9625 1 1.001 8 3
(e) Hargreaves 1985 ASCE-EWRI ETo 1.0026 0.4373 9 0.901 5 7
(f) Prestley-Taylor ASCE-EWRI ETo 0.9251 0.7272 8 0.858 4 5
(g) Jensen-Haise ASCE-EWRI ETo 1.0813 0.7996 7 1.007 7 7
(h) Hprcc Penman ASCE-EWRI ETr 1.0108 0.9541 2 0.483 1 1
(i) Kimberly Penman 1972 ASCE-EWRI ETr 0.9905 0.9148 5 0.588 2 2
(j) Kimberly Penman 1982 ASCE-EWRI ETr 1.0324 0.9316 4 0.586 3 2

Table 3: Comparison of daily reference evapotranspiration (ETref), Root Mean Square Deviation (RMSD), and coefficient of determination (R2) from May to September in 1991-2008 at Oakes, North Dakota. ETo is grass based reference surface and ETr denotes alfalfa based reference surface. The overall rank is based on average ranks from RMSD and R2 for seasonal ETref.

irrigation-drainage-monthly-reference-evapotranspiration

Figure 3: Comparison of monthly total reference evapotranspiration (ETref) among different methods: (a) ASCE-EWRI ETo, FAO24 Penman, FAO24 Radiation, and FAO24 Blaney-Criddle methods; (b) ASCE-EWRI ETo, Hargreaves 1985, Prestley-Taylor, and Jensen-Haise methods; and (c) ASCEEWRI ETr, Hprcc Penman, Kimberly Penman 1972, and Kimberly Penman 1982 methods.

irrigation-drainage-average-daily-reference-evapotranspiration

Figure 4: Comparison of average daily reference evapotranspiration (ETAref) for 18 years using ASCE-EWRI ETr, ASCE-EWRI ETo and Jensen-Haise ETref methods at Oakes, North Dakota.

Figure 4 shows the average daily ETref for the ASCE-EWRI ETr, ASCE-EWRI ETo, and the Jensen-Haise ETref. The ASCE-EWRI ETr peaked on May 21. Actually, the month of May has the highest ETr, mainly due to the higher wind speed (Table 1). The Jensen-Haise method only accounts for temperature and solar radiation and does not include the effect of wind speed. This may be the reason that noncombination ETref methods do not have the same ETref pattern and peaked at different times than the combination methods. Also notice that the higher wind speed shifted the peak of alfalfa based ASCE-EWRI equation, but not the grass based equation. The grass based method peaked at the same time as the Jensen-Haise method. The difference between the grass and alfalfa based equation is the surface resistance, defined by Allen et al. [4] as “the resistance of vapor flow through stomata openings, total leaf area and soil surface”. For the alfalfa reference surface, a constant surface resistance of 70 s m-1 was used, and for the grass reference surface, 45 s m-1 was used as the constant surface resistance for the standardized reference ET calculations [1].

A direct replacement of Jensen-Haise method by the ASCEEWRI ETo method may result in underestimation of ETo during the growing season. Use of ASCE-EWRI ETo values combined with the Kc curve developed using the Jensen-Haise method would result in lower calculated crop ET, thus applying less irrigation than the crop actually needed. The Kc curve is tied to a particular ETref method and a replacement of the current ETref method used for irrigation scheduling will require changes to the Kc curves as well.

Annual ETref

Average annual ETref values are shown in Figure 5, with error bars indicating the standard deviation across 18 years of data. Almost all grass based ETref values showed lower annual ETref than the alfalfa based methods. However, the FAO24 Penman method showed a similar total ETo as the alfalfa based method. The ETo showed lower standard deviation than the ETr values. Again, the HPRCC Penman method was the closest to the ASCE-EWRI ETr value, with only 12.4 mm or 1% annual difference. The Hargreaves method has a 0.5 mm, or 0.1% difference from the ASCE-EWRI ETr method.

irrigation-drainage-annual-reference-evapotranspiration

Figure 5: Comparison of annual reference evapotranspiration values (ETref) for all methods. The dark color bars indicate the grass reference based methods and the light color bars indicate the alfalfa reference based methods. The error bars indicate the standard deviation among the 18 years.

Conclusions

Crop water consumption use for irrigation scheduling in North Dakota is calculated from ETref by the Jensen-Haise method and the Kc curves developed in the 1970’s and 1980’s. The standardized ETref methods by the American Society of Civil Engineers, Environmental and Water Research Institute (ASCE-EWRI) reference evapotranspiration task force [1] has been widely accepted and applied across the world. However, application of the ASCE-EWRI method requires sequential changes to the Kc curves associated with the Jensen-Haise method. This paper compared ETref estimates for 11 methods, including the ASCEEWRI and the Jensen-Haise methods using 18 years of data collected in southeast North Dakota. The results showed that the annual ETo by the Jensen-Haise method was nearly the same (0.39% underestimation) as the ASCE-EWRI grass ETo, but with a higher RMSD, 0.903 mm d-1, and a lower R2 0.8659, comparing to the ASCE-EWRI ETo. Since the Jensen-Haise method was initially developed using growing season data collected from 15 crops, ETo comparison for the growing season showed an RMSD of 1.007 mm d-1, R2 of 0.7996 and 8.13% overestimation. The ETo by the Jensen-Haise method has a higher monthly ETo than that y the ASCE-EWRI in June, July, and August, and lower monthly ETo for all other months. The ETo using the two methods does not show a strong agreement, so direct replacement of the Jensen-Haise method by the ASCE-EWRI method is not recommended. New Kc curves should be developed prior to the application of the ASCE-EWRI ETref method in southeastern North Dakota. In addition, interest in irrigating alternative crops, development of new crop cultivars of current irrigated crops and climate change will require the development of new Kc curves if ASCE-EWRI ETref values are used for irrigation scheduling. The ETref comparison also showed that the HPRCC Penman method has the best accuracy and correlation with the ASCE-EWRI ETref method overall. Indeed, all alfalfa based ETref methods, including Penman models, showed a better performance than grass based ETref methods.

Acknowledgements

This project is supported by the North Dakota Agricultural Experiment Station, CRIS project ND01464, and USDA CSREES project 2008-35102-19253. Mention of trade names is for information purposes only and does not imply endorsement by the authors or NDSU.

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