Use of Stable Isotopes Deuterium and Oxygen-18 to Derive Evaporation from Flood Irrigation on the Basis of Pan Evaporation Techniques

van den Akker, J.; Simmons, C. T.; Hutson, J. L.

doi:10.1061/(ASCE)IR.1943-4774.0000361

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TECHNICAL PAPERS

Mar 4, 2011

Use of Stable Isotopes Deuterium and Oxygen-18 to Derive Evaporation from Flood Irrigation on the Basis of Pan Evaporation Techniques

Authors: J. van den Akker [email protected], C. T. Simmons [email protected], and J. L. Hutson [email protected]Author Affiliations

Publication: Journal of Irrigation and Drainage Engineering

Volume 137, Issue 12

https://doi.org/10.1061/(ASCE)IR.1943-4774.0000361

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Abstract

The loss of water to the atmosphere during flood irrigation occurs through evaporation and transpiration. Whereas transpiration can be estimated through the FAO56 methodology, actual evaporation is difficult to quantify in water balance studies. In this study, two analytical models, previously developed to quantify evaporation from lakes on the basis of stable isotopes, were applied to determine evaporation losses from four flood irrigation sites of varied characteristics. Evaporation losses were determined by empirical relationships derived between heavy isotope enrichment and percentage of water loss in evaporation pan experiments. Validation of the two isotopic models in this setting was achieved by comparison with conventional nonisotopic methods, carried out in parallel. Results showed that heavy isotope enrichment of applied irrigation waters varied among each of the study sites. Isotope enrichment was notably different among irrigation bays that drained rapidly [

+ 0.05

to

+ 0.18

per mil (‰) for

δ {}^{18}O

and

+ 1.7

to

+ 2 ‰

for

δ {}^{2}H

] from those in which ponding occurred for up to 18 h after application (

+ 1

to

+ 2 ‰

for

δ {}^{18}O

and

+ 2

to 7.5‰ for

δ {}^{2}H

). When compared with local pan enrichment, these isotope enrichments corresponded to evaporation losses of 0.2–2.7% (0.5–4 mm) and 2–5% (4.5–7 mm), respectively. This study demonstrated that the use of stable isotope data for irrigation waters provided valuable new insights into evaporation losses across different flood irrigation systems. The use of these techniques may be useful in suggesting which management strategies are most effective in improving water use efficiency and water quality.

Introduction

The monitoring of stable isotopes

δ {}^{2}H

and

δ {}^{18}O

in water can provide a sensitive indicator of water loss by evaporation, exclusive of transpiration. Isotopic techniques for measuring evaporation from lakes is theoretically sound (Dincer 1968; Gonfiantini 1986; Gat and Bowser 1991; Gat and Matsui 1991; Simpson et al. 1987; Froechlich et al. 2005) but few applications to irrigation waters are reported. The aim of this study was to apply a new approach through the use of stable isotopes

δ {}^{2}H

and

δ {}^{18}O

to quantify evaporation losses from flood irrigation water, across four irrigation sites, which differ in soil type, irrigation application rate, crop type, and bay architecture.

In this study, evaporation losses were estimated by using the analytical models developed by Gonfiantini (1986) and Simpson et al. (1987), in which relationships were derived between heavy isotope enrichment and fractional water loss from evaporation pan experiments. Previously, these analytical techniques were applied to estimate evaporation losses from lakes and river systems. However, because the principles (water balance and isotopic processes) are much the same, this study examines the validity of the analytical models to estimate evaporation rates from a flood irrigation setting, by comparison with (nonisotopic) conventional weather station (Penmen-Monteith) methods described by Debarro (2006).

In the irrigation districts of Padthaway and the Hundred of Stirling in the southeast of South Australia, pasture and lucerne is generally flood irrigated. The greatest loss of water to the atmosphere occurs through two pathways: (1) transpiration through crop plants and (2) evaporation from delivery channels, surface distribution systems, and moist soil. Transpiration and evaporation are often integrated and called evapotranspiration (ET). Both processes concentrate salts in irrigation water and soil; however evaporation can be managed and is the undesirable component of water loss from any irrigation practice. In principle, the greater the proportion of water loss by transpiration through crop plants relative to evaporation, the greater the efficiency of water use.

The importance of quantifying evaporation from flood irrigation is essential to determine the salinity effects and overall efficiency of the irrigation network. Although the total ET by a crop can be estimated by using the standard Food and Agriculture Organization of the United Nations (FAO) Irrigation and Drainage Paper No. 56 (FAO56) pan evaporation methodology [Eq. (1)], the evaporation of surface water and shallow soil water at different points in a flood irrigation network is much more difficult to quantify and is often neglected

ET = K_{c} \cdot K_{p} \cdot E_{pan}

(1)

where ET = crop evapotranspration (

mm {day}^{- 1}

);

K_{c}

= crop coefficient;

K_{p}

= pan coefficient; and

E_{pan}

is pan evaporation (

mm {day}^{- 1}

).

Traditionally, evaporation from flood irrigation has been measured and described in several ways. Actual ET is the actual water lost through transpiration, soil evaporation, and evaporation of surface water. It can measured by sophisticated and expensive climate stations or flux towers through the eddy covariance technique (Mauder et al. 2007), lysimeters (Lewis 2009), and water balance and soil water depletion methods (Jensen et al. 1990). Potential evaporation (

E_{p}

) is the theoretical upper limit to evaporation. Potential evaporation can be defined in many ways. The general definition is that

E_{p}

is the maximum evaporation rate that can be sustained from a moist surface and is given by the FAO Penman equation (Penman 1948; Allen et al. 1998):

E_{p} = \frac{[Δ (R_{n} - G)] / (λ + γ E_{a})}{(Δ + γ)}

(2)

where

E_{p}

= potential evaporation of open water (

kg / m^{2} s

);

R_{n}

= net radiation (

MJ m^{- 2} {day}^{- 1}

);

G

= soil heat flux (

MJ m^{- 2} {day}^{- 1}

);

Δ

= slope of saturation vapor pressure curve (

kPa ° C^{- 1}

);

γ

= psychrometric constant (

kPa ° C^{- 1}

);

E_{p}

= potential evaporation (

mm {day}^{- 1}

);

λ

= latent heat of vaporization (

MJ {kg}^{- 1}

); and

E_{a}

= isothermal evaporation rate (

kg / m^{2} s

).

Pan evaporation is the daily evaporation rate as measured by a Class-A evaporation pan. The pan evaporation rate (

E_{pan}

) is related to potential evaporation (

E_{p}

) by a pan coefficient (

K_{p}

):

E_{p} = K_{p} \cdot E_{pan}

(3)

which in turn can be related to evapotranspiration by a crop coefficient through Eq. (1)

Debarro (2006) quantified actual evaporation from flood irrigation waters at two common research sites. In his study, he used a weather station to compute

E_{p}

and calculated volume of actual evaporation (

E

) as follows:

E = A \cdot E_{p} \cdot t

(4)

where

A

= surface area (

m^{2}

) of the inundated bay or saturated soil surface;

E_{p}

= potential evaporation (

mm h^{- 1}

) measured on-site through an automatic weather station; and

t

= period (h) the bay was inundated/irrigated or soil was at saturation after standing water had drained from the surface. Debarro (2006) assumed that dense lucerne cover was a strong inhibitor of evaporation, and hence, calculations for bay evaporation were made only for the irrigations without crop canopy. According to the FAO, for evaporation measurements made in pans surrounded by tall crops, the

C_{p}

will need to be increased by 30% for dry wind climates (Allen et al. 1998).

Better quantification of the surface water evaporation (

E

) component of the water balance during different stages of irrigation is needed to improve understanding of the salinity effects of flood irrigation. In particular, identifying when and how much surface water evaporation occurs may assist in developing benchmark irrigation practices for flood irrigation.

Measurement of changes in stable isotopic composition of water is one technique that has been used successfully in the quantification of evaporation from lakes and rivers (Gat 1981; Simpson et al. 1992; Gonfiantini 1986). The principal is that when water evaporates, the ratio of the concentrations of

{}^{1}H {}^{16}O

and

{}^{2}H {}^{18}O

to that of

{}^{2}H {}^{16}O

changes because of small differences in the physical properties of the isotopes (Zimmermann et al. 1967). During evaporation, molecules containing lighter isotopes (

δ {}^{16}O

and

δ {}^{1}H

) leave the liquid surface more easily than heavier ones (

δ {}^{18}O

and

δ {}^{2}H

), with the result that isotopic fractionation occurs and the remaining liquid is enriched in heavy isotopes (Zimmermann et al. 1967; White and Gedzelman 1984). Because transpiration and evaporation affect residual water isotopic compositions differently, the relative contribution of these two water loss fluxes may theoretically be resolved from observed changes in residual irrigation water isotopic compositions (Dincer et al. 1978).

The theory behind the two analytical models trialled by this study is described as follows.

Analytical Model 1

To allow a comparison of each flood irrigation site, this study expanded the approach of Simpson et al. (1987) and adopted an approach that uses pan evaporation experiments to calculate the percentage of evaporation loss from ponded irrigation water. Because local humidity, temperature, and wind shear effects are similar to both, the results obtained from drying pan experiments should be comparable to local irrigation waters through the following relationship:

E = \frac{δ_{s} - δ_{i}}{E_{f}}

(5)

where

E

= percentage of water loss by evaporation;

δ_{i}

= average isotopic composition of the irrigation source (per mil, ‰),

δ_{s}

= isotopic composition of surface water (‰) at any stage during irrigation (i.e., during irrigation or ponding periods); and

E_{f}

= amount of isotopic enrichment (‰) per 1% of water loss from an evaporation pan at the study site.

Analytical Model 2

Water loss by evaporation from flood irrigation was evaluated by using the equation given by Gonfiantini (1986), who estimated the water loss from a lake through the following expression:

E = \frac{(δ_{s} - δ_{i}) (1 - h + Δ ε)}{(δ_{s} + 1) (Δ ε + ε / ε^{*}) + h (δ_{A} - δ_{s})}

(6)

where

E

= calculated percentage of water loss by evaporation (actual evaporation);

δ_{s}

= mean isotopic values of the lake (‰) (in this case

δ_{s}

= ponded irrigation water);

δ_{i}

= mean isotopic value of the input to the lake (‰) (flood bay);

δ_{A}

= mean isotopic composition of atmospheric water vapor (‰);

h

= mean relative humidity (%);

ε^{*}

= equilibrium fractionation factor and is well-known for both oxygen and hydrogen as a function of temperature (see Gonfiantini 1986); and

Δ ε

= kinetic enrichment factor and

ε = ε^{*} - 1

.

Of these parameters, several can be measured or calculated routinely; however, the isotopic composition of atmospheric moisture

δ_{A}

has proven more difficult to assess in natural situations. This is because of the logistical complications associated with the collection of vapor in suitable volumes for mass spectrometric analysis, and spatial and temporal weighting of data for mass balance calculations, given the transient nature of atmospheric processes (Gibson et al. 1999). An alternate method for estimating

δ_{A}

was proposed by Gibson et al. (1999). If lakes are large enough in volume and have sufficient isotopic inertia to minimize shorter fluctuations in atmospheric parameters, it may be sufficient to assume

δ_{A}

is in isotopic equilibrium with local precipitation (i.e.,

δ_{A} = δ_{p} - ε^{*}

), where

δ_{p}

= weighted mean isotopic composition of precipitation; and

ε^{*}

is approximated by using mean air temperature records. This technique has been applied to study lakes using isotopic models (e.g., Zuber 1983; Gibson et al. 1993). In general, precipitation equilibrium is not a valid assumption for isotopic balance studies on times scales of the order of weeks to months (Gibson et al. 1999). Hence, this approach is not applicable for the estimation of

δ_{A}

over short-duration irrigation events.

Isotopic mass balance of evaporation pans has been used in several studies to derive

δ_{A}

at time scales ranging from days to months (e.g., Gibson et al. 1999). Various methodologies are summarized by Gibson et al. (1999) according to various derivations (Gat 1970; Welhan and Fritz 1977; Allison et al. 1979; Allison and Leaney 1982; Barnes and Allison 1982; Simpson and Herczeg 1992) and showed that isotopic mass balance of a constant volume pan can be a reliable method for characterizing temporal changes in

δ_{A}

. Results of the preceding study suggest that standard Class-A pans are also appropriate for this purpose, and also that Class-A pans, if allowed to partially dry, can be used in a similar fashion, providing that drying is limited to less than approximately 50% of the original volume (Gibson et al. 1999). For the simple case of a drying pan with no inflow or outflow, the volume

V

and isotopic changes in the pan water are controlled only by evaporation

E

.

This study used drying pan experiments conducted during irrigation to first estimate

δ_{A}

(with known

E

,

h

,

δ_{i}

,

δ_{s}

,

ε^{*}

, and

Δ ε

values) from Class-A pan waters, which will then allow the subsequent determination of

E

from irrigation waters (with known

δ_{A}

,

h

,

δ_{i}

,

δ_{s}

,

ε^{*}

, and

Δ ε

values). Both

δ_{A}

and

E

were calculated by using Eq. (6).

Irrigation Efficiency

Stable isotope abundance changes in irrigation water was used to provide a direct indication of evaporation, and can thus provide a new tool to monitor key parameters (such as soil type, irrigation application rate, and bay architecture) relevant to water use efficiency.

The overall efficiency (

I_{E}

) of the irrigation network in actual evaporation losses with respect to potential evaporation [Eq. (7)] and total irrigation volume can be assessed via the following equation:

I_{E} = 100 \cdot (E / E_{p})

(7)

where

E_{p}

= potential evaporation measured from Class-A evaporation pan (mm); and

E

= actual evaporation calculated from irrigation waters (mm) by isotopic methods.

By monitoring the changes in isotopic composition and chloride (salinity) concentration of irrigation water at different stages during the irrigation delivery (at several locations across the bay during irrigation application and ponding), the amount of irrigation water lost through evaporation at various stages was quantified, which was then used to evaluate the efficiency of the irrigation network. It is intended that the findings will also improve understanding of factors that contribute to excessive surface water evaporation from flood irrigation and will therefore be used to develop efficient flood irrigation practices.

Methods

Site Description

The four irrigation study sites selected for this study lay within the interdunal flats of Padthaway and Tatiara prescribed wells areas (PWAs) in the upper southeast of South Australia (Fig. 1). Pasture, clover, and lucerne crops are flood irrigated at these sites. The climate within the study areas can be characterized by warm to hot dry summers and cool wet winters. The average annual maximum temperature is 22°C, with February the hottest month at 29.8°C and July the coldest month at 5.5°C. A rainfall gradient exists across the study area, with average annual rainfall slightly higher in Padthaway (

509 mm / year

) than in Keith (

490 mm / year

). 40% of the annual rainfall occurs during the months of June to August. Annual potential evaporation is 1,600 and

1, 700 mm / year

for Padthaway and Keith, respectively.

The soil texture under each field site varies from loam in the northern portion of the Padthaway PWA to sand in the Hundred of Stirling Management Area. The partial size distribution of top soil (0–0.50 m) at each flood irrigation site was determined previously (Harrington et al. 2004; Wohling 2007). At Padthaway, the top soil is 70% sand, 7% silt, and 21% clay (sandy loam), whereas the soil at the Hundred of Stirling is 87% sand, 2.4% silt, and 9.8% clay (sand). The topsoil is primarily shallow (

< 0.50 m

) and overlies a shallow calcrete topped limestone known as the Padthaway Formation. The overlying calcrete is a hard 2–5 cm thick layer and in some cases has been ripped to allow drainage. The Padthaway Formation is one of the main unconfined aquifer systems in the region. Because of the secondary porosity of the limestone, bore yields are highly variable and can range from 0.2–

300 L / s

(Harrington et al. 2004). Depths to water in bores below the interdunal flats range from 3–7 m, and groundwater salinity ranges from 1,000–

3, 000 mg / L

in Padthaway and from 2,000–

8, 000 mg / L

within the Hundred of Stirling irrigation district.

Study Site Selection

Field measurements outlined subsequently were made at four flood irrigation sites (Fig. 1). Each field site differs in soil type, thickness of top soil, irrigation delivery (i.e., pumping rate, length, and head of delivery channel), area of irrigation bay, and crop type. The characteristics of the four flood irrigation sites are summarized in Table 1.

Table 1. Characteristics of the Four Flood Study Sites

Site	Soil and crop type			Irrigation application			Dimensions of irrigation bay				Irrigation channel
Site	Top soil	Soil thickness (m)	Crop type	Application duration (h)	Volume ( $ML / ha$ )	Ponding duration (h)	Width (m)	Length (m)	Area (ha)	Laser leveled	Length (m from bore)	Head at sluice gate (m), start and end of irrigation
NAP4	Loam	0.35-0.5	Pasture	10	1.10	24–28	125	200	2.50	N	180	0.244	0.22
NAP5	Loam	0.1	Clover	8	1.47	18–22	50	500	2.50	Y	620	0.175	0.175
MTM	Sand	$< 0.30$	Lucerne	2.5	2.00	6–15	20	300	0.60	Y	500	0.27	0.23
PG	Sand	$< 0.30$	Lucerne	6	1.55	8	50	425	2.13	Y	105	0.8	0.2

A schematic diagram of the sampling locations and instrumentation set up for a typical irrigation bay is shown in Fig. 2.

Fig. 2. Schematic diagram of a typical flood irrigation site showing instrumentation and sampled water balance components of a flood irrigation system

Sampling and Surface Water Monitoring

Water samples for

δ {}^{2}H

,

δ {}^{18}O

,

{Cl}^{-}

, and EC were collected during two irrigation events from each irrigation bay during the 2005–2006 irrigation season. Water samples were collected in 50-mL glass McCartney bottles from (1) the irrigation bore, (2) along the irrigation channel, and (3) at five evenly distributed locations (labeled A to E) across the flood irrigation bay (Fig. 2). Water samples were collected at 2–4 h intervals during the irrigation and ponding periods.

Approximately 24 h after irrigation, soil water samples were extracted by vacuum pump from suction lysimeters buried within the vadose zone at nominal depths (0.30, 0.5, 1.0, 2.0, and 3.0 m). Because drainage can continue to occur at depth a number of days after irrigation, the changes in the isotopic signature of the wetting front as it moves through the vadose zone was monitored over time during the second round of sampling. By using the capacitance response as a guide, the suction lysimeters at NAP4 and NAP5 were subsequently sampled every 2–3 days after irrigation

Groundwater abstraction from irrigation bores was measured by flow meters, which recorded flow rate (

L / s

) pumped from the irrigation well. Inflow to the bay was measured by using either Dataflow Systems 392 or shaft encoders that record the depth of water flowing through the irrigation gate to the irrigation bay and the timing of an irrigation event. The depth of ponded water was measured manually along the bay at various time intervals during and after irrigation application to assess application uniformity, flow, distribution, and infiltration dynamics.

Evaporation Pan Experiments (Class-A Drying Pans)

A series of evaporation pan experiments were conducted at the time of irrigation. Class-A pans (272 L) having a diameter of 125.7 cm were used at each site. The pans were positioned close to the irrigation bay and filled with source water (from the irrigation bore) at the commencement of each irrigation event. No water was added after the initial filling of the pan. Water loss and evolution of chloride, EC,

δ {}^{2}H

, and

δ {}^{18}O

composition were measured in residual pan water at time intervals ranging from 2–4 h (in parallel with field sampling above), throughout irrigation application and ponding periods.

From this data, calculations for an enrichment factor were made, which represents the enrichment of

δ {}^{2}H

or

δ {}^{18}O

in residual pan water per 1% of water loss from the pan. From this relationship, the percentage of ponded irrigation water lost by evaporation was estimated through Eq. (5).

Pan evaporation (

E_{pan}

) measured from the Class-A pan was converted to potential evaporation (

E_{p}

) through a pan coefficient (

K_{p}

) by using Eq. (3).

K_{p}

was sourced from local Bureau of Meteorology (BoM) stations and typically ranged from 0.7–0.9. Calculations for

E

from flood irrigation waters were made according to the methodology of Debarro (2006) [Eq. (4)].

Where possible,

E_{p}

was compared with daily ET (FAO56) measurements obtained from the BoM stations located at Padthaway (Station 26089) and Keith (Station. 25507). In addition, local air temperature (

T

) and relative humidity (

h

) readings were also obtained from local BoM weather stations.

Determination of $δ_{A}$ and $E$ from Class-A Evaporation Pan Experiments

The value of

δ_{A}

was determined from drying pan experiments by rearranging Eq. (6) to solve for

δ_{A}

, where

E_{pan}

= measured percentage water loss by evaporation from the pan at end of the experiment (at time

t_{1}

);

δ_{s}

becomes the isotopic values of pan water (

t_{1}

);

δ_{i}

becomes the isotopic value of the input to the pan at time

t_{0}

;

h

= mean relative vapor pressure, obtained from local BoM weather stations;

ε^{*}

= equilibrium fractionation factor at 25°C (1.0093 and 1.08 for

δ {}^{18}O

and

δ {}^{2}H

, respectively);

Δ ε

= kinetic enrichment factor, evaluated here as

Δ ε^{*}

δ {}^{18}O = 14.2

(1-h) and

Δ ε

δ {}^{2}H = 12.5

(1-h) as most frequently encountered conditions in nature (Gonfiantini 1986); and

ε = ε^{*} - 1

.

Once

δ_{A}

was determined, Eq. (6) was subsequently used to calculate the percentage of water loss by actual evaporation

E

, where values for

δ_{s}

and

δ_{i}

were substituted with isotopic values for irrigation water (at different time intervals) and the mean isotopic value of the input to the flood bay, respectively.

Isotope Analysis

Groundwater samples for

δ {}^{2}H

and

δ {}^{18}O

were analyzed by the CSIRO isotopic laboratory in Adelaide, Australia, by using a Europa Scientific Ltd. GEO 20-20 dual inlet gas ratio mass spectrometer. Water samples for the

δ {}^{18}O

analysis were first equilibrated with

{CO}_{2}

of a known isotopic composition, and

δ {}^{18}O

was determined by mass spectrometry of the equilibrated

{CO}_{2}

gas with a precision of

\pm 0.1 ‰

. Results are expressed as

δ {}^{18}O

(

{}^{18}O / {}^{16}O

) in per mil (‰) as a deviation from the Vienna standard mean ocean water (V-SMOW):

δ_{sample} = 1, 000 [(R_{sample} / R_{V - SMOW}) - 1]

and therefore

δ {}^{18}O = \frac{({}^{18}O / {}^{16}O)_{sample} - ({}^{18}O / {}^{16}O) V - SMOW \times 1000}{({}^{18}O / {}^{16}O) V - SMOW}

(8)

For analysis of

δ {}^{2}H

, 20 µL of sample was reduced to hydrogen by circulating it as vapor across hot uranium at 810°C. This was then introduced into the mass spectrometer. Results are expressed as

δ {}^{2}H

(

{}^{2}H / {}^{1}H

) in per mil (‰) relative to V-SMOW, where

δ {}^{2}H ‰ = \frac{({}^{2}H / H)_{sample} - ({}^{2}H / H) V - SMOW \times 1, 000}{({}^{2}H / H) V - SMOW}

(9)

Including errors induced by the azeotropic distillation, the overall precision of the

δ {}^{18}O

and

δ {}^{2}H

analysis are

\pm 0.1

and

\pm 1 ‰

, respectively.

Results

Pan Evaporation Experiments

Pan evaporation measured on-site was corrected to potential evaporation by using the pan coefficient, which ranged from 0.67–0.92.

K_{p}

was calculated from weather data obtained from nearby BoM stations and averaged over a daily time step. Potential evaporation measured on-site during the sampling (irrigation) periods ranged from 3–7 mm, resulting in a 1.–3.5% reduction of the pan water volume (Fig. 3). Evaporation of flood waters, measured during the period the bays were inundated, as per the method of Debarro (2006) [Eq. (4)] revealed decreased evaporation rates (0.5–6 mm).

Fig. 3. Potential ( $E_{p}$ ) evaporation corrected from Class-A evaporation pan experiments conducted during each irrigation: (a) NAP5; (b) NAP4; (c) MTM; (d) PG

Potential evaporation measurements recorded here were similar to those measured at local BoM stations. Comparisons with the BoM stations could only be made for sites at which evaporation was measured over a full 24 h, i.e., measurements made at 9 a.m. each morning.

The potential daily evaporation was similar for all sampled irrigations and ranged from 4.7–6.2 mm per day. However, at NAP4 the potential evaporation was less during the first sampling event, when irrigation took place during the night (Fig. 3). At NAP5 the daily potential evaporation was 2.2 mm greater during the ponding period during the second (later) sampling period.

Determination of the Enrichment Factor

The enrichment trends for

δ {}^{18}O

and

δ {}^{2}H

as a function of the percentage of evaporation (water loss from the pan) for each pan experiment is illustrated in Fig. 4. A linear relationship between the stable isotopes and the percentage of initial volume is shown (

r^{2} = 0.92

–0.99).

Fig. 4. Relationship between isotopic composition and percentage of water loss from Class-A evaporation pans: (a) $δ {}^{18}O$ ; (b) $δ {}^{2}H$ ; (c) relationship of $δ {}^{2}H$ and $δ {}^{18}O$ of evaporating pan waters for each site

From all pan experiments conducted during the irrigation season, it was determined that every 1% of water evaporated from the pan leads to an enrichment of 0.19–0.38‰ for

δ {}^{18}O

(0.7–0.9‰ for

δ {}^{2}H

) (see Fig. 4). These values are consistent with pan experiments conducted in previous studies by Simpson et al. (1987), Aly et al. (1993), and El-Bakri et al. (1996) (0.19 for

δ {}^{18}O

and 0.7 for

δ {}^{2}H

), in which up to 70% of the pan water had evaporated. The slight variations calculated for each site may be attributed to differences in pan water salinity, which ranged from 1,400–

6, 500 mg / L

for irrigation sites at Padthaway and Hundred of Stirling, respectively. This is supported by Gonfiantini (1965) and Lloyd (1966), who showed that the isotopic enrichment of pan water was reduced at greater salinities.

Pan water enrichment trends are also shown in

δ {}^{18}O

versus

δ {}^{2}H

plots in relation to the Local Meteoric Water Line (LMWL) developed for the region (Fig. 4). Evaporation lines for each pan experiment are characterized by slightly decreased slopes (3–4), which fits within the range given by Gat (1980), Payne (1983), and Gibson et al. (1999) in comparison to the LMWL (7.65).

Determination of $δ_{A}$ from Class-A Evaporation Pan Experiments

From Eq. (3), it is evident that

δ_{A}

of atmospheric vapor can be derived from isotopic changes in pan water (

δ_{s}

), provided that

E_{pan}

,

h

,

δ_{i}

,

ε^{*}

, and

Δ ε

values are known. Calculations for

E

of pan water were made in Microsoft Excel allowing

δ {}^{18}O_{A}

values of atmospheric vapor to be adjusted until a close calibration between the measured

E_{pan}

(measured from Class-A pan) and calculated

E

was obtained. Fig. 5 shows good correlation (

r^{2} = 0.92

–0.99) between the calculated

E

and measured

E_{pan}

across all sites on the basis of pan data (

δ {}^{18}O_{s}

) alone. Isotopic values adjusted to achieve this strong correlation ranged from 19–25‰ for

δ {}^{18}O_{A}

, and 120–170‰ for

δ {}^{2}H

, and have been plotted in relation to

δ_{p}

and Local Meteoric Water Line (LMWL), developed for the area (Fig. 6).

δ_{A}

values are less enriched than

δ_{p}

and plot along the LMWL. Pan-derived estimates of

δ_{A}

under less humid conditions were less enriched than

δ_{A}

estimates under more humid conditions.

Fig. 5. Measured pan evaporation loss versus calculated evaporation loss: (a) NAP5; (b) NAP4; (c) MTM; (d) PG

Fig. 6. Plots of $δ {}^{18}O$ versus $δ {}^{2}H$ for calculated atmospheric vapor; also shown are $δ {}^{18}O$ and $δ {}^{2}H$ relationships of local precipitation collected, with the LMWL for Adelaide for reference

Irrigation Observations

The volume of irrigation applied to each irrigation bay ranged from 105–260 mm (Table 2). At PG, the initial head in the irrigation channel before irrigation was 0.8 m, which was significantly higher than the measured heads at the other irrigation sites, most notably NAP4, where the elevation of the channel floor is slightly lower than the elevation of the bay. The higher head at PG and slightly greater pump capacity resulted in faster irrigation application (covering an area of

0.35 ha / h

) compared with the other irrigation sites (

0.25 ha / h

). Irrigations at NAP4 and MTM were sampled under different conditions. At NAP4, the first sampling event was carried out when irrigation was applied between the hours of 12:00 to 22:00 and left to pond during the night. During the second sampling event in March, irrigation was applied between the hours of 22:00 to 8:00 and left to pond during the day. At MTM, the first sampled irrigation was conducted just after the lucerne was cut for hay. The second sampled irrigation was carried out a time when lucerne cover had reached approximately

90 %

. The second irrigation application was 1 h longer as a result of the denser crop. The two irrigations sampled at PG and NAP5 were carried out under similar conditions (i.e., time, crop cover, and meteorological conditions).

Table 2. Irrigation Observations

Study site	Start time	Finish time	Duration (h)	Pump rate ( $ML / day$ )	Application rate ( $ha / h$ )	$ML / ha$	Total (ML)	Start	End	Ponding duration (h)	Number of irrigations per season	Salinity( $mg / L$ )	Observations
Study site	Irrigation application					Volume applied		Head at sluice gate (m)					Observations
NAP5	9:30	17:30	8	11.13	0.31	1.48	3.71	0.175	0.175	24–28	9	1,889	Day irrigation, mature clover
NAP5	9:30	17:30	8	9.73	0.31	1.30	3.24	0.175	0.175	24–28	9	2,144	Day irrigation, mature clover
NAP4	12:00	22:00	10	12.59^a	0.25	1.05	2.62	0.244	0.22	18–22	16	1,434	Day irrigation, mature pasture
NAP4	22:00	8:00	10	12.6^a	0.25	1.05	2.63	0.244	0.22	18–22	16	1,384	Night irrigation, mature pasture
MTM	10:30	12:50	2.3	12.28	0.24	1.84	1.1	0.27	0.23	6–15	5	4,874	Day irrigation, min lucerne cover
MTM	12:15	15:30	3.25	12.28	0.24	2.60	1.56	0.27	0.23	6–15	5	4,565	Day irrigation, mature lucerne
PG	11:00	17:00	6	13.2	0.35	1.55	3.3	0.8	0.2	$> 8$	5	6,498	Day irrigation, mature lucerne
PG	9:30	15:30	6	13.2	0.35	1.55	3.3	0.8	0.2	$> 8$	5	6,458	Day irrigation, mature lucerne

^a

Two bays irrigated simultaneously.

Field Measurements of Surface Water Flow across the Irrigation Bay

Fig. 7 shows depth measurements of the irrigation water as it flows across the bay for each site during irrigation and for various time intervals during and after irrigation, which is referred to as the ponding period.

Fig. 7. Depth of irrigation water with distance along the irrigation bay at various times during irrigation: (a) NAP5; (b) NAP4; (c) MTM; (d) PG

During irrigation, the head of water was higher at the sluice gate and lower at the end of the wetting front. As soon as the irrigation application had ceased, the water at sites NAP4, MTM, and PG continued to flow down gradient toward the end of each bay, where the heads reversed, becoming higher at the end of the bay (down gradient) and lower at the start of the bay (up gradient). This was attributed to the laser-leveling of the bays at these sites. Because of the shallow nature of top soil (loam) at NAP5, the irrigation bays were not laser-leveled, causing the irrigation water to pond within the two low-lying areas located at each end of the bay. Although most of the irrigation water drained through the soil profile over night (within approximately 14 h after irrigation), 2–4 cm of ponded water was still evident 22 h after irrigation at each end of the bay (Fig. 7). At NAP4, where the soil consists of loam, ponding water covered a larger percentage of the bay (70–80%) for up to 17 h after irrigation. In contrast, sites MTM and PG exhibited higher drainage rates because most of the surface water had drained within 5 h and 8 h, respectively, after irrigation application. This was attributed to a higher sand composition of the topsoil at these sites (Table 1).

Estimation of Irrigation Water Loss by Evaporation

The enrichment of

δ {}^{18}O

and salt concentration of irrigation water along the flow path at each irrigation bay is shown in Fig. 8. Water samples collected at five places are arranged to be consistent with water movement in the irrigation bay (denoted by locations A to E) and collection time (denoted by A1, A2, and A3). The isotopic and salt concentration of drainage water taken from suction lysimeters at different depths following irrigation is also shown for comparison (denoted as SL).

Fig. 8. Evolution of $δ {}^{18}O$ enrichment and salinity of irrigation water along the flow path: (a) NAP5; (b) NAP4; (c) MTM; (d) PG; A1, A2, and A3, represent measurements taken from Location A at three different time intervals (see Fig. 2 for locations); and SL = suction lysimeter water

The isotopic enrichment of irrigation water measured at the sampled locations ranged from 0.05–2‰ for

δ {}^{18}O

(1.7–7.5‰ for

δ {}^{2}H

), and was accompanied by an increase in chloride concentration (30–

130 mg / L

). The isotopic and chloride signatures of drainage waters show low fractionating water loss (minor fractionation) and large increases in salinity in comparison to the irrigation waters during the application period. This suggests that water loss from transpiration is more dominant than evaporation.

The corresponding evaporation rates, calculated for each flood irrigation site on the basis of Simpson et al. (1987) and Gonfiantini (1986), are shown in Fig. 9 for each sample locations (A to E). The volume of water applied and the ponding time, recorded at the time each sample was collected, are also shown for reference.

Fig. 9. Percentage evaporation losses from flood irrigation calculated by using the equations of Simpson (1987) and Gonfiantini (1986) at sampled location (denoted A to E) for flood irrigation sites: (a) NAP5; (b) NAP4; (c) MTM; (d) PG; A1, A2 and A3, represent measurements taken from Location A at three different time intervals

The actual evaporation rates derived from both isotopic models are in close agreement. These have been compared with conventional pan techniques in Table 3. Evaporation calculated through the two methods ranged from 0.5–5.6 mm, which was slightly less than potential evaporation (1.5–8 mm) measured from Class-A evaporation pans, over the same time period (Fig. 9; Table 3).

Table 3. Evaporation and Efficiency Estimates from Flood Irrigation

Irrigation site		Irrigation duration	Volume applied	Potential evaporation from Class-A pan ( $mm / irrigation$ )			Average actual evaporation from flood irrigation				Efficiency indicator	Variable at time of irrigation
		Irrigation duration	Volume applied				Isotopic (Gonfiantini 1986; Simpson et al. 1987)		Conventional (Debarro 2006)		Efficiency indicator
		(h)^a	(mm)	Pan (mm)^b	$Pan \cdot K_{p}$ (mm)	(%)	(%)	(mm)	(%)	(mm)	$E / E_{p}$ (%)
NAP5	Earlier irrigation	30	148	8.8	7	4	3.1	4.6	3.09	4.57	34	Day irrigation, mature clover
NAP5	Later irrigation	32	130	12	8.04	5.45	4.8	6	4.35	5.65	25	Day irrigation, mature clover
NAP4	Earlier irrigation	18	105	5	3.55	2.27	1.1	1.2	2.82	2.96	66	Day irrigation, mature pasture
NAP4	Later irrigation	24	105	8	7.36	3.64	3.2	4.7	3.4	3.2	50	Night irrigation, mature pasture
PG	Earlier irrigation	9.5	155	4	3.36	1.82	0.18	0.4	0.46	0.70 (0.30)^c	88	100% lucerne crop cover
PG	Later irrigation	7.75	155	4	3.6	1.82	0.35	0.51	1.35	2.10 (0.62)^c	86	100% lucerne crop cover
MTM	Earlier irrigation	4	184	2	1.52	0.91	2.35	4.4	0.93	1.71	0	0% lucerne crop cover
MTM	Later irrigation	9	260	6	4.56	2.73	1.5	1.23	0.49	1.27 (0.37)^c	73	100% lucerne crop cover

Note: Average percentage evaporation loss calculated on the basis of Gonfiantini (1986) and Simpson et al. (1987).

^a

Irrigation duration represents the period from the start of irrigation to the time when the last sample was collected.

^b

Total evaporation measured at the time when the last irrigation sample was collected.

^c

K_{p}

adjusted by 0.30 to compensate for crop cover.

Similar evaporation rates were obtained from isotopic and traditional methods from irrigation bays characterized by open bodies of water (NAP4, NAP5, MTM-earlier irrigation). However, during irrigations at PG and MTM-later irrigation (carried out under dense crop cover), isotopic methods revealed lesser evaporation rates (up to 0.5 mm) than traditional methods (up to 2 mm), and thus confirm that dense crop cover is a strong inhibitor of evaporation. Under these conditions, a 30% adjustment was made to the

K_{p}

to account for dense crop cover, as recommended by the FAO56 for the correction of pan evaporation measurements near dense vegetation.

Potential evaporation during each irrigation event varied from 1.5 to 8.0 mm. To further explore this variable and allow a comparison of efficiency between each irrigation, the percentage of actual evaporation (calculated from ponded waters) relative to the total potential evaporation (measured from respective Class-A evaporation pans) was determined (

E_{a} / E_{p} \cdot 100

; Table 3). Here,

E

represents the average evaporation losses obtained from measurements made from all sampled locations, during the irrigation and ponding periods. The percentage of actual evaporation losses from flood irrigation relative to potential evaporation generally ranged from 10% in the Hundred of Stirling to 60% in Padthaway, with differences attributed to controlling factors such as duration of irrigation application/ponding, crop cover, and timing of irrigation.

The percentage of water loss by evaporation relative to the total volume of irrigation water applied is also shown in Table 3. Flood irrigation sites NAP5 and NAP4 revealed the greatest percentage of water lost (3–4.5%) compared with PG and NAP (0.2–0.8%). MTM reported a greater percentage loss (2.8%) when irrigation water was applied to a young crop.

Across all sites, there was no change in

δ {}^{2}H

and

δ {}^{18}O

composition of irrigation water as it flowed from the bore to the irrigation bay, suggesting minimal evaporation losses from the irrigation channels (Fig. 8). This was expected because the residence time of irrigation water within the channel was estimated to be

< 1 h

, making changes in isotopic composition very hard to detect within this small time frame.

During both sampled irrigation events at sites NAP5, MTM, and PG, minimal effects of evaporation were detected within the

δ {}^{18}O

,

δ {}^{2}H

signatures, and salinity concentration of the irrigation water as it flowed across the bay. This minor depletion observed (

< 0.2 ‰

for

δ {}^{18}O

and

< 0.8 ‰

for

δ {}^{2}H

) equated to an average evaporation loss of

< 0.3 %

. Data obtained from NAP4 during March 2006 showed some effects of evaporation during irrigation application, in which

δ {}^{2}H

increased by 5‰, which can be attributed to the longer duration of application during the day (Fig. 8).

Isotopic and salinity signatures of the ponded water collected from three locations along the bay at PG remained relatively unchanged during the day, in which only minor evaporation losses (

< 1 mm

) during these sampling intervals were calculated. In contrast to PG, isotopic enrichment and hence evaporation was noted at MTM, NAP5, and NAP4 during the ponding period, which varied across each site.

The December 2005 irrigation and sampling event at MTM was conducted at a time when there was no lucerne crop cover, shortly after the lucerne was cut for hay. Following the commencement of irrigation, the

δ {}^{2}H

concentration of the ponded water increased significantly from

- 26 ‰

to a maximum of

- 21 ‰

(Fig. 8). When compared with the local pan experiments, this enrichment corresponded to an average evaporation loss of 4 mm (Fig. 9). A slight increase in salinity of

248 mg / L

(from

2, 722

to

2, 970 mg / L

) was also observed at the sampling sites during this period. During the March 2006 irrigation and sampling event, which was conducted at a time when the crop cover had increased to 95%, the isotopic signatures and salinity concentration of the irrigation water remained steady during the application and ponding period, signifying a significantly decreased evaporation loss of

< 1.5 mm

. These data confirmed that crop cover was a strong regulator of evaporation loss and hence concentration of salt because evaporation was superior (up to 3 mm more) with a young crop, as determined by using isotopes and EC.

E_{p}

calculated from the pan experiments between the two sample events of (1) earlier irrigation/young crop and (2) later irrigation/mature crop, indicating greater evaporation potential during the later irrigation (dense crop cover), thereby indicating that crop cover was the primary factor for the differences observed (Fig. 8; Table 3).

Water samples collected from the ponded water at NAP5, which ponded at the southern and northern ends of the bay the following morning (Day 2) indicated only minor enrichment (0.4‰ for

δ {}^{18}O

; 2.7‰ for

δ {}^{2}H

), signifying that only a small amount of evaporation loss (corresponding to 1 mm) had occurred overnight. The greater effects of evaporation were most evident toward the evening (Day 2) when the compositions of

δ {}^{18}O

increased by 1–1.9‰ (5–7‰ for

δ {}^{2}H

) at sample times of 0 and 22.5 h, respectively (Figs. 8 and 9). An increase in salinity from 160 to

300 mg / L

coupled the preceding observed enrichment in isotopes. When compared with local pan experiments, the enrichment of both

δ {}^{18}O

and

δ {}^{2}H

represents an average evaporation loss of 6–9 mm from these pools. The greater evaporation losses calculated at NAP5 are attributed to the greater duration of ponding and less crop cover (pasture versus lucerne), which occurred here in contrast to the rapid draining sites at MTM and PG.

The January 2006 irrigation at NAP4 occurred during the day and was left to pond during the night. The isotopic and salinity signatures of water samples collected from ponded water the following morning (11 h after irrigation application) was only slightly more enriched in comparison to that of the source water at time 0, equating to minor evaporation losses (1 mm) during the night, when most ponding had taken place (Fig. 9). During the later irrigation, isotopic signatures remained stable when water was applied to the bay during the night, but had later increased (by 0.9 to 1.84‰ for

δ {}^{18}O

and 2.3 to 5.9‰ for

δ {}^{2}H

) once the water was left to pond for 11 consecutive hours the following day. As predicted, evaporation losses at this time were shown to be much greater (2–12 mm, average of 4 mm) in comparison to the earlier irrigation event. These results confirmed the benefit of irrigating at night (Fig. 8).

A qualitative comparison of evaporation rates from each irrigation bay is shown in Fig. 10, which plots

δ {}^{2}H

versus

δ {}^{18}O

values relative to the LMWL. The slope of the regression lines (3.6 to 4) deviated from the value (7.65) given by the LMWL. The slopes varied according to the intensity of evaporation and are consistent with slopes given by Gat (1980) for evaporation from open water bodies, and more importantly, slopes derived from the drying pan experiments (3 to 4).

Fig. 10. $δ {}^{2}H$ and $δ {}^{18}O$ plots of irrigation water potted against the LMWL: (a) NAP4; (b) NAP5; (c) PG; (d) MTM

Discussion

Pan Experiments

This study has shown that the enrichment of heavy isotopes

δ {}^{2}H

and

δ {}^{18}O

in residual waters as a result of evaporation can provide a sensitive indicator of water loss from flood irrigation systems. These losses were estimated by relationships between heavy isotope enrichment and percentage of water loss in evaporation pan experiments, according to analytical models by Simpson et al. (1987) and Gonfiantini (1986), which until now were previously applied for the determination of evaporation from lakes. When applied to irrigation, a close agreement of percentage of water loss

E_{c}

was obtained when applying the two equations; however, the method of Gonfiantini (1986) requires the

δ_{A}

of atmosphere to be known. It should be emphasis that the estimates of the percentage of water lost to evaporation are sensitive to the choices

δ_{A}

. As

E_{pan}

,

h

,

δ_{i}

,

ε^{*}

, and

Δ ε

values are known, values of

δ_{A}

were calculated on the basis of drying pan experiments, which yielded a value of 18‰ for

δ {}^{18}O_{A}

(

- 140 ‰

for

δ {}^{2}H_{A}

). Although these values lie within a realistic range for this climate, the calculation of evaporation from flood irrigation by the Gonfiantini (1986) equation relies on accurate characterization of

δ_{A}

. Such accuracies can only be verified by independent methods (e.g., vapor sampling traps).

Comparison of Evaporation Estimates to Nonisotopic Techniques

The average evaporation losses calculated from isotopic techniques compared well to traditional methods conducted in parallel at sites in which open water bodies were allowed to evaporate. However, during irrigations of dense crop cover, evaporation rates derived from isotopic techniques revealed lesser evaporation rates compared with traditional methods, suggesting that crop cover is a strong regulator of evaporation (by 23–28%). The close agreement in evaporation rates from open water bodies gives high confidence in the validity of applying the two isotopic methods to this irrigation setting.

Comparison of Water Loss by Evaporation (Efficiency) across Each Site

The mean evaporation loss calculated for all sites ranged from 0.2–5.0% (0.4–6 mm). Although the overall percentage of water loss by evaporation appears small, when multiplied by the total volume of water applied to an irrigation bay over an irrigation season (i.e., 5–16 irrigations multiplied by

1.1 - 2.6 ML / ha

per irrigation), the total evaporation loss can amount to

0.1 - 0.5 ML / ha / year

.

The differences in evaporation losses calculated here are believed to be attributed to variable factors, such as (1) soil type (ponding duration), (2) crop canopy cover, (3) time of irrigation, and (4) rate at which the water was applied. Hence, a new comparative measure of irrigation efficiency across each site was achieved by comparing the ratio of water evaporated from the flood bay to the potential evaporation measured (through Class-A evaporation pans) on-site. Flood bays characterized by rapid draining soils and dense crop canopy cover showed lesser evaporation ratios (higher efficiency, 73–88%) than sites that were characterized by poorer draining soils and minimal crop canopy cover (25–49%).

The duration of irrigation application varied across each site, ranging from 3–10 h; however, with the exception of NAP4, undetectable (or minor) changes in isotopic composition of irrigation water measured at all sites was noted, highlighting minimal evaporation during irrigation delivery (from the channel and as water flows across the bay). Evaporation was only detected during the ponding period, which varied from 6 to 28 h across each site and is considered to be the primary factor resulting in excess evaporation losses.

During conditions when irrigation is applied to bare soils (such as the MTM-earlier irrigation), evaporation from wet soil surfaces can be as high as from ponded water. However, because most of drainage was rapid and occurred during the night, no evaporation from the soil was detected.

In general, sites PG and MTM located in the Hundred of Stirling irrigation district both reflect less average evaporation losses of 0–5 mm (higher efficiency, 73–88%) when compared with Padthaway sites NAP4 and NAP5, which recorded average evaporation losses of 4.5–12 mm (lower efficiency, 25–49%). The greater evaporation losses (and lesser efficiency) calculated at both sites in Padthaway are reflected by the duration of ponding, which was approximately 10–15 h longer than observed at the sandier sites in the Hundred of Stirling. Here, sandier soils facilitated quicker drainage rates and therefore resulted in a lesser evaporation potential.

The high percentage of evaporation calculated at NAP5 (6–10 mm), was only detected in pools, which ponded for extended periods of time (20–22 h) at each end of the bay and therefore does not reflect the average evaporation loss across the bay, which was much less (4 mm). The highest evaporation loss (up to 8%) of residual water was detected at site NAP4 (March 2006 sample event), in which water was applied overnight and to left to pond for 11 h the following day (efficiency of 49%). During the January sampling event, when water was left to pond during the night, the evaporation losses of residual water were much less (1–3 mm, efficiency = 66%).

This study confirmed that a greater density of lucerne cover at MTM and PG also contributed to a reduction in evaporation. This was demonstrated at MTM, where there was a maximum difference of 27% (3 mm) in evaporation between an open water body (efficiency = 0%) and approximately 95% crop cover (efficiency = 73%).

Conclusion

This study has shown that actual evaporation from flood irrigation can be determined by using the analytical isotopic methods described by Gonfiantini (1986) and Simpson et al. (1987) for evaporation from lakes. Evaporation rates determined by these techniques were calibrated against Class-A drying pan experiments, which were used to derive relationships between isotopic enrichment and water loss from the pan.

This study has shown that the isotopic techniques used here to determine

E

compared well with traditional techniques described by Penman (1948) and later adopted by Debarro (2006) in this setting—especially for open water bodies, which gave high confidence in the calculations of evaporation rates from flood irrigation and to the validity of these models to this setting.

Under dense crop cover, evaporation rates derived by isotopic methods were 23–28% less than traditional methods, indicating that crop canopy cover is a strong inhibitor of evaporation. This observation is confirmed by FAO56, which has shown that under these conditions, pan coefficients need some adjustment (by 30%).

The use of stable isotopes allowed the quantification of evaporation rates at different stages of irrigation for different irrigation sites of varied characteristics (i.e., soil type, bay architecture, application rate). Average evaporation during ponding from flood irrigation ranged from 0.5–6 mm per irrigation, with greatest evaporation losses occurring during the ponding period.

By comparing actual evaporation to potential evaporation measured by using Class-A evaporation pans, the efficiency of different flood irrigation configurations was examined. Evaporation was strongly reduced at sites where irrigation application and soil infiltration rates were greater (i.e., less ponding time).

Notation

The following symbols are used in this paper:

$E$: actual evaporation ( $mm {day}^{- 1}$ );
$E_{a}$: isothermal evaporation rate ( $kg / m^{2} s$ );)
$E_{f}$: enrichment factor
$E_{p}$: potential evaporation ( $mm {day}^{- 1}$ );
$E_{pan}$: pan evaporation ( $mm {day}^{- 1}$ );
ET: crop evapotranspiration ( $mm {day}^{- 1}$ );
$G$: soil heat flux ( $MJ m^{- 2} {day}^{- 1}$ );
$h$: mean relative humidity (%)
$K_{c}$: crop coefficient;
$K_{p}$: pan coefficient;
$R_{n}$: net radiation ( $MJ m^{- 2} {day}^{- 1}$ );
$γ$: psychrometric constant ( $kPa ° C^{- 1}$ );
$Δ$: slope of saturation vapor pressure curve ( $kPa ° C^{- 1}$ );
$Δ_{i}$: isotopic composition of input water or irrigation water [per mil (‰)];
$Δ_{s}$: isotopic composition of surface water or ponded irrigation water [per mil (‰)];
$δ_{A}$: isotopic composition of amospheric vapor [per mil (‰)];
$ε$: kinetic enrichment factor and $ε = ε^{*} - 1$ ;
$ε^{*}$: equilibrium fractionation factor; and
$λ$: latent heat of vaporization ( $MJ {kg}^{- 1}$ ).

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Information & Authors

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Published In

Journal of Irrigation and Drainage Engineering

Volume 137 • Issue 12 • December 2011

Pages: 765 - 778

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History

Received: Jul 5, 2010

Accepted: Feb 23, 2011

Published online: Mar 4, 2011

Published in print: Dec 1, 2011

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J. van den Akker [email protected]

Postgraduate (Research), School of the Environment (Earth Sciences), Flinders Univ., GPO Box 2100, Adelaide, South Australia, Australia 5001 (corresponding author). E-mail: [email protected]

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C. T. Simmons [email protected]

Director and Professor, National Centre for Groundwater Research and Training, Flinders Univ., GPO Box 2100, Adelaide, South Australia, Australia 5001. E-mail: [email protected]

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J. L. Hutson [email protected]

Senior Lecturer in Hydrology, School of the Environment (Earth Sciences), Flinders Univ., GPO Box 2100, Adelaide, South Australia, Australia 5001. E-mail: [email protected]

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Abstract

Introduction

Analytical Model 1

Analytical Model 2

Irrigation Efficiency

Methods

Site Description

Study Site Selection

Sampling and Surface Water Monitoring

Evaporation Pan Experiments (Class-A Drying Pans)

Determination of δA and E from Class-A Evaporation Pan Experiments

Isotope Analysis

Results

Pan Evaporation Experiments

Determination of the Enrichment Factor

Determination of δA from Class-A Evaporation Pan Experiments

Irrigation Observations

Field Measurements of Surface Water Flow across the Irrigation Bay

Estimation of Irrigation Water Loss by Evaporation

Discussion

Pan Experiments

Comparison of Evaporation Estimates to Nonisotopic Techniques

Comparison of Water Loss by Evaporation (Efficiency) across Each Site

Conclusion

Notation

References

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Determination of $δ_{A}$ and $E$ from Class-A Evaporation Pan Experiments

Determination of $δ_{A}$ from Class-A Evaporation Pan Experiments