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Field validation of empirical functions used to estimate crop water use

Hamish E. Brown, Derrick J. Moot1 and Bruce A. McKenzie

Agriculture and Life Sciences Division, P.O. Box 84, Lincoln University, Canterbury, New Zealand.


Water use (WU) of lucerne crops was measured over a two-year period at Lincoln University (4338'S, 17228’E, 11ma.m.s.l.) and used to validate empirical methods of estimating soil evaporation (ES) and crop transpiration demand (ET demand). The most realistic estimation of ES was given by a modified form of the Ritchie ES calculation. Modifications included calculating second stage ES as a function of accumulated Penman potential evapotranspiration (PE) and a crop cover (I/Io) factor that reduced ES to account for crop roots drying the soil. Unmodified Ritchie ES overestimated ES by >45mm over a 300d continuous drying cycle. The product of transpiration efficiency and vapour pressure deficit (ET_eff*VPD) was variable throughout the season, indicating estimates of ET demand based on a constant ET_eff*VPD may be erroneous. However, the seasonal variation of ET_eff*VPD could be explained by a linear increase (R2 = 0.81) from 7 to 22kgDMha-1mm-1kPa-1 as temperature increased from 7 to 14C. The ET_eff*VPD decreased below this relationship in autumn when increased partitioning of DM to roots reduced shoot DM production.

Media summary

Soil evaporation could be accurately estimated from the Ritchie calculation adjusted for potential evapotranspiration and root extraction. Transpiration efficiency*VPD increased with air temperature.

Key words

soil evaporation, transpiration demand, transpiration efficiency, vapour pressure deficit


An accurate estimation of crop water use (WU) is vital for simulation of crop growth and soil water dynamics. Crop WU consists of ES and ET. Ritchie (1972) presented functions for calculating ES that consisted of an initial energy limited phase (ES1) and a second diffusion limited phase (ES2). Additional improvements have been suggested including calculating ES2 as a function of PE (rather than time) to improve estimations in a cool climate (Boesten and Stroosnijder 1986). The Ritchie (1972) calculations also fail to account for soil drying by crop roots that decreases ES (Eastham and Gregory 2000). In spite of suggested improvements it is difficult to accurately measure ES from an area of crop in a field situation so there are few suitable comparisons of different methods.

Crop ET is the lessor of supply or demand and ET demand can be calculated from the product of ET_eff and VPD (Monteith 1986). This method assumes that an increase in VPD causes a linear increase in ET with no effect on photosynthesis so the product of ET_eff and VPD is constant and has been widely adopted because it requires fewer data inputs than alternatives (Meinke et al. 2002). However, recent studies have shown ET_eff*VPD is not constant (Zhang and Nobel 1996) and simulation models using ET_eff*VPD to predict ET demand may be erroneous.

The objectives of this study were to assess methods of calculating ES and ET demand by comparing calculations with WU of lucerne measured over two years in the field at Lincoln University, New Zealand.

Materials and Methods


Measurements were conducted in two experiments in adjacent fields (Iversen 8 and 9) at the Lincoln University Field Service Centre. Each lucerne field had three replicates of full and nil irrigation treatments and full details of establishment and design were given in Brown (2004). Lucerne crops were rotationally grazed throughout each year. Mean monthly temperature ranged from 6C in June/July to 17C in January/February with mean daily solar radiation of 5–23MJm-2 and VPD of 0.3-1.3kPa over the same period. The 00/01 season (I July 2000 – 30 June 2001) had an annual rainfall of 587mm, 1058mm PE with 281 and 325mm of irrigation applied to treatments in I8 and I9 respectively. The 01/02 season (1 July 2001 – 30 June 2002) had an annual rainfall of 785mm, 943mm PE with 65 and 220mm of irrigation applied to treatments in I8 and I9 respectively.

Measurements are reported for a two-year period (1 July 2000 – 30 June 2002). Soil water content was measured at 5–14d intervals in 22 layers of the soil profile to a depth of 2.3 m at each measurement date. The top layer (0-0.2m) was measured with a time domain reflectometer and the other 21 layers (0.1m layers from 0.2–2.3m) were measured at their mid depth with a neutron probe. Dry matter (DM) production was measured at 7–10d intervals from a single 0.2m quadrat. The radiation interception (I/Io) was recorded at 3–7d intervals using a LI-COR LAI-2000 canopy analyser.

Data analysis

Soil evaporation was calculated using three methods, full details were given in Brown (2004). Method 1 was Ritchie ES (Ritchie 1972), which calculated ES in two phases following rewetting of the soil (Equation 1).


a) ES1 = PE * I/Io

when ΣES ≤ U


b) ES2 = α * t1/2

when ΣES > U

Where t is time (d) since the wetting event, U = 9mm and α = 4.4mm d-1/2 (Jamieson et al. 1995). Soil evaporation was limited to ES1 when ES2 > ES1. Method 2 was the same as Ritchie ES, but ES2 was calculated in response to accumulated ES1 using Equation 2 (Boesten and Stroosnijder 1986):


ES2 = β * ΣES11/2

Where β = 2.4 mm1/2 and is analogous to α in Equation 1b (Brown 2004) and ΣES1 is summed from the end of the wetting event. Method 3 was similar to Method 2 but included a 1-I/Io factor, which reduces ES when water uptake by crop roots (ET) speeds the drying of the soil and reduces ES.


ES2 = (1-I/Io) * β * ΣES11/2

This is based on the assumption that the fraction of soil drying caused by ET will increase and ES decrease in opposing proportions to increasing I/Io. This reduction is additional to the shading effects of I/Io on ES1.

Comparisons of ES calculations were made in the dryland treatments in I901/02, where rainfall was excluded (using rain-shelters) for 300d giving an extended period where cumulative errors in ES calculations could be assessed. The ΣES calculated by the three ES methods was compared with the change in soil water content (ΔSWC), which displayed actual soil water depletion in the top 0.2m of soil. The lucerne crop was growing during this period so it was assumed that some of the ΔSWC was due to root extraction for ET and ΣES ≥ ΔSWC indicated an overestimation in ES.

The ET_eff was calculated for dryland and irrigated treatments in each regrowth cycle from all field/season combinations by regressing DM accumulation against accumulated ET (slope = ET_eff). The ET_eff values were multiplied by the mean VPD for each regrowth cycle.


Soil evaporation

The measured ΔSWC in the top 0.2m of soil showed three distinct phases (Figure 1) and these were arbitrarily defined as Periods 1-3. Period 1 was the first regrowth cycle (1 August 2001 – 29 September 2001) when the soil dried rapidly (ΔSWC increased from 0 to 30mm). All three ES calculations were less than ΔSWC indicating reasonable ES predictions during this period. Period 2 was from 30 September 2001 – 1 February 2002 when drying was slower (ΔSWC increased from 30-45mm). During this period Method 3 gave the most sensible prediction with an ES of 8mm. The other two methods predicted ES > 15mm. Period 3 was when SWC was stable at 45mm (1 February 2001 – 12 June 2001) and Method 3 predicted ES of 5mm, Method 2 predicted 10mm and Ritchie ES predicted 20mm.

Transpiration efficiency

The ET_eff*VPD showed a seasonal pattern increasing from ~14kgDMha-1mm-1kPa-1 in September to ~22kgDMha-1mm-1kPa-1 in January and then decreasing abruptly between February and May (Figure 2a). Data were examined as a function of the mean temperature, which showed (R2 = 0.81) an increase in ET_eff*VPD from ~7kgDMha-1mm-1kPa-1 at 7C, to 22kgDMha-1mm-1kPa-1 at ~15C (Figure 2b). Data from regrowth cycles occurring as temperatures decreased during February–May were omitted from the regression because they had a lower ET_eff*VPD compared with similar temperatures from earlier in the growth season.

Figure 1. Cumulative Ritchie (───), Method 2 (--) Method 3 (--) soil evaporation (ΣES) and actual change in soil water content (ΔSWC) from the top 0.2m of soil () for dryland lucerne crops grown under rain-shelters at Lincoln University, Canterbury, New Zealand.

Figure 2. The product of transpiration efficiency (ET_eff) and vapour pressure deficit (VPD) throughout the growth season (a) and in relation to temperature (b) for dryland (○●) and irrigated (□■) lucerne crops grown at Lincoln University, New Zealand from 1 July 2000 – 30 June 2002. Grey points are those that occurred between 1 February and 1 May which were omitted from the regression, y=-3.7(1.82)+1.5(0.15)x.


Soil evaporation

Method 3 ES was the most appropriate for estimating ES based on the assumption that realistic ES calculations would always give a ΣES less than ΔSWC in the top 0.2m of soil. Errors in ES calculations were most evident between 1 October and 30 January, when the Ritchie calculation overestimated ES by more that 25mm. These errors would have an important influence on WU calculations in sparse crops and perennial forages that are frequently defoliated.

Two reasons were identified for the overestimations by Ritchie ES. Firstly, ES2 was calculated in relation to time, assuming diffusion decreases as the soil dries and limits ES. However, diffusion from the soil is also dependent on temperature gradients in the soil, which may reduce diffusion in cool climates (Boesten and Stroosnijder 1986). This error was corrected by calculating ES2 as a function of PE (i.e. ES1) and Method 2 demonstrated the improvement this adjustment made (Figure 1). The second error in Ritchie ES was the failure to account for drying of the topsoil by crop root extraction (Eastham and Gregory 2000). Method 3 ES included a factor to reduce ES to account for ET drying the soil (Equation 3) and its influence on ES calculations can be seen by comparing with Method 2. The I/Io factor is an empirical adjustment that assumes soil drying by roots will increase in proportion to increased canopy cover.

Transpiration efficiency

The product of ET_eff and VPD was not stable throughout the season (Figure 2a) indicating a single ET_eff would not give reliable calculations of ET demand. Some of the seasonal variability in ET_eff*VPD could be attributed to changes in temperature (Figure 2b) and a temperature response may be used to improve predictions of ET demand using ET_eff*VPD. This temperature response may be caused by changes in the ratio of internal leaf to atmosphere CO2 concentration (Monteith 1988). The effects of temperature on Ci/Ca are recognised in the adjustment of RUE for temperature (Sands 1996) and the link between RUE and ET_eff has been recognised (Sadras et al. 1991). However, the influence of temperature on ET_eff has not previously been quantified. The temperature response of ET_eff*VPD may also be caused by a non-linear response of ET to increased VPD which generally increases with temperature.

The period in the autumn where ET_eff*VPD was lower than for similar temperatures at other times of the year (Figure 2b) was likely to have been caused by a change in the partitioning behaviour of the crop. This coincided with the period when the crop was allocating a higher proportion of its DM production to the roots and crowns (Brown 2004) but this was not accounted for in ET_eff calculations (above ground biomass only). The seasonal decline in ET_eff is well documented for lucerne (Smeal et al. 1991) and is an additional factor that needs to be considered in the study of perennial crops.


This study provided useful field scale validation of empirical functions used to predict ES and ET demand.

  • The Ritchie calculation overestimated ES but predictions could be improved by calculating ES2 as a function of ES1 and including a factor to account for soil drying by crop ET.
  • The product of lucerne ET_eff and VPD was not constant and increased from 7 to 22kgDMha-1mm-1kPa-1 as temperatue increased from 7 to 15C with variation from this relationship in autumn.


The New Zealand Foundation for Science, Research and Technology for financial support to Hamish Brown during this study.


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