Crop Evapotranspiration Calculation by Soil Water Balance Method for OAP Study
Tony Rho, PhD, Texas A&M AgriLife Research at Amarillo
Published on May 10, 2019
Updated on May 10, 2019
A work by Tony Rho
This document is written to describe the calculation procedure of crop evapotranspiration using the soil water balance approach. The data used in this article is from the Ogallala Aquifer Program study performed by the author and the others1 in 2018. There is source code containing global parameters and functions to execute some of the codes below. These resources will be released as a seperate R-script file in the future when the package development for this research project is accomplished. The script file contains many useful calculators, constants, unit converters, and user created functions. Most of the FAO-56 equations (Allen et al. 1998) needed for the dual crop coefficient method are incorporated into this file. To learn more about basic concepts and principles on crop evapotranspiration, consult the FAO-56.
Introduction
There are a number of ways to calculate or estimate crop evapotranspiration (ETc) (Colaizzi et al. 2017; S. R. Evett et al. 2012; Shaughnessy et al. 2015). Among these the one considered most accurate is using a mass balance or a soil water balance method. Although both methods incorporate relatively heavy deployment of instruements compared with other commercially competitive methods, the accuracy excels since the loss of water by the plant and the soil surfaces is basically measured, not estimated like the methods based on meteorological measurement of weather variables ( FAO-56)(Allen et al. 1998).
The soil water balance method requires measurement of soil water content (SWC) in any forms at given time intervals. The SWC measurement can be done with either manual data collection by a neutron probe or automatic data collection by an intelligent sensor. The measurement should be made at different layers of the soil by varying the depth of the measurement. With the collected soil water profile, one can estimate how much of water is consumed by crops and at which layer(s) the water is taken. The data collection process is often laborious and technically difficult. So, many researchers rely on automated measurement by field sensors. Typically, field sensors can be deployed directly to the soil at layering depths where crop(s) of interest stands. When combined with measurement of water fluxes to the designated soil volume (a.k.a. the control volume), water loss by the crop stand – ETc – can be calculated using the following equation that is used to calculate ETc.
\(ET_c = I + P + F + R + \Delta S\)
where I is irrigation, P is precipitation, F is net subsurface flux into the control volume, R is net runoff or runon to the control volume surface, and \(\Delta S\) is the net change in volumetric SWC in the control volume. All of the measures are in ‘mm’ units. In many cases of agricultural lands with flat soil surfaces, R is assumed to be 0.
Concurrently, the crop coefficient – Kc – can be estimated by solving the equation below.
\(K_c = \frac{ET_c}{ET_0}\)
where Kc is crop coefficient, ETc and ET0 stand for crop evapotranspiration and reference crop evapotranspiration each.
Procedures
- Import packages & source code
- Import & tidy data sets – weather data (
met), irrigation data (irg), soil temperature & water data (tempswc), & yield data (yd) - Calculate ET0 using
met - Calculate ETc using the SWB equation
- Calculate Kc from ETc
- Calculate WUE using
yd& the available data sets created
Steps 1-3 are a duplicate of those in Crop Evapotranspiration Calculations excluding that there is a tweak in importing SWC data. The calculations presented in Steps 4-6 are referred to Crop Evapotranspiration Calculation by Soil Water Balance Method except the methodology and the time intervals of SWC measurements are different: Intelligent sensors were used to collect SWC data at hourly time intervals in the previous study while a neutron gauge with weekly time intervals in the present study.
Step 1: Import packages & source codes
library(tidyverse) # includes many useful data manipulation & exploration pkgs
library(lubridate) # deals with timeseries data
library(DT) # creates interactive data tables
library(scales) # enables graphical modifications on ggplot2 objects
library(directlabels) # enables graphical modifications on ggplot2 objects
library(nlme) # builds & analyzes linear mixed effect model
library(lsmeans) # conducts a post hoc comparison
library(knitr) # compiles html objects & generates a report file
library(openxlsx) # exports tabulated dataframes or R-objects to xlsx files
library(ggradar) # creates a radar plot for quick-viewing of quality profile data
source("0_oap_src.R") # provides useful unit conversion & calculation tools## Error in .f(.x[[i]], ...): object 'value' not foundThe source code also contains package loading functions that are outlined above.
Step 2: Import & tidy data sets
The meteorological data were collected by a weather station ( RX3000, Onset Computer Co., Bourne, MA). Due to a large size of the data, the raw data is not presented here, but rather the processed, summarized data will be presented later in Step 3.
The phenology & physiology data were collected by various instruments and tools. Only height of the crops will be used in the further steps. I extract hgt after summarizing the raw data, time.
The irrigation data were corrected manually by Jimmy Gray. The irrigation records will be used in the calcuation of daily soil water balance for Ke cal.
The yield data is also required to further calculate water use efficiency of the crops with each treatment.
Volumetric SWC were measured on a weekly basis starting from 32/33 days after transplanting for tomato/pepper and 22 days after seeding for corn using a hydroprobe gauge ( 503TDR, CPN Inc., Concord, CA). The neutron probe gauged the water contents at varying depths (12 points; from 0.1 m to 2.3 m, 20 cm apart) to map the soil moisture profile for making irrigation decisions. The collected information about the soil water content was used to estimate the amount of irrigation on the same week to fully replenish the soil moisture upto the field capacity (FC) for growing the vegetable crops without any deficit. Deficit irrigation was applied to meet the different demands of water use for the plants. Irrigation and the measurements were continued until the plants reached the maturing stage. \(\Delta S\) is calculated by subtracting the SWC on the previous week from the SWC on a given week.
Soil temperature sensors ( U23ProV2-003, Onset Computer Co.) were buried at a 5-cm depth in each plot where the plant stands were established. The soil temperature was recorded every 5 min from 44/45/34 days after transplanting/seeding for tomato/pepper/corn to the end of the study.
Step 3: Calculate ET0
The FAO-56 is implemented into the CalET0 function. Details can be found in the source code.
et0 is set aside to a seperate data frame for future convenience.
Step 4. Calculate ETc using the SWC equation
Step 4.1. Calculate \(\Delta S\)
Let’s combine et0 and dswcabb to compile the weather data and the soil water data, wtrbal.
The compiled dataframe contains et0, etc, swc, and kc to plot over time.
See the below table and find more details about the properties of the soil type. PAW/WP/FC stands for plant available water/wilting point/field capacity of the soil. The raw data measured by the TDR probes are presented without any modifications. Note that there are some values more than the field capacity (FC) of the soils. FC and WP of the Pullman Soils at ~ 1 m depth is 357 and 187 mm, respectively. These are indicated in select plots down below.
Irrigation was applied to FC of the soil during the growing season (DOY158-255, . The amount of water applied to each plot was determined based on SWC calculated (swc) a day before each irrigation event. The SWC of individual plot was calculated by VWC readings (vwc) with the neutron probe. Time course responses of VWC can be summarized by plotting seasonal variation of VWC.
The seasonal variations of VWC in the soils show irrigation control was well managed over time.
SWC on a weekly basis can be plotted along with wetting events – irrigation and precipitation.
To better compare the differences in SWC responses between the irrigation treatments, the SWC are plotted on the days after transplanting (DAT) scale.
Step 4.2. Calculate ETc & Cumulatives
ETc can be calculated using week-to-week \(\Delta S\) of this graph. Following is the soil water balanced ETc and cumulative ETc over the season. Plots are on the DAT scale.
Compared to the Dual Crop Coefficient method, the calculations yielded some errorneous (e.g. negative values) data points on a few days.
Cumulative ETc and water input from irrigation plus precipitation can be plotted separately.
Least water was input from precipitation and irrigation to the Mch plots compared with the Ctrl and Pvt plots. The least amount of water was evapotranspirated in total in Pvt plots. Marginal differences in water use was found between Ctrl and Mch, the latter being a little less in cumulative ETc.
Cumulative stats can be summarized in a table.
About 7.7, 7.5, and 7.5% decreases in water input were found under Mch compared to Ctrl for Corn, Pep, and Tom, respectively. In contrast, the water input under Pvt was increased by 4.6, 4.4, and 4.4% for Corn, Pep, and Tom, respectively.
ETc of Mch and Pvt both were reduced to a different degree, compared with Ctrl. By Mch, ETc was decreased by 11.5, 14.9, and 8.6% for Corn, Pep, and Tom while it was 34.4, 42.9, and 24.8% by Pvt. The considerable reductions in ETc under Pvt are likely from less use of water due to staggered growth of the crops under Pvt.
Step 5. Calculate Kc from ETc
Kc is calculated by dividing ETc from the soil water balance method by ET0 from the meteorological method.
However, the time-course of Kcs seems incorrect for some reason. There are too many outliers to make a conclusion on the results. Kcs should fall into a 0-1.5 range. Further investigation should be followed to step forward to break the Kc values down to Ke and Kcb.
Step 6. Calculate WUE using yd & the available data sets created
This is an extra step to make calculations of water use efficiency of the crops in each treatment group. Water use efficiency can be defined by the following equation.
\(WUE = \frac{YD}{\sum ET_c}\)
The yield data is also required to further calculate water use efficiency of the crops with each treatment.
Statistical analysis is conducted on the raw data to test the effects of irrigation method (noted irg) on calculated WUE. A linear mixed-effect model was used to run two-way ANOVA for testing irg within spp, and the interaction effects. irg was set to a fixed variable and zn (Zone) was set to a random variable in the model. The Tukey’s method was used in post hoc comparisons between treatments.
cwue <- wue %>%
filter(spp == "corn")
pwue <- wue %>%
filter(spp == "pep")
twue <- wue %>%
filter(spp == "tom")
md.c1 <- lme(data = cwue, wue ~ irg, random = ~1 | zn)
anova(md.c1) # ANOVA table, n.s.## numDF denDF F-value p-value
## (Intercept) 1 6 279.84674 <.0001
## irg 2 6 0.14108 0.8712summary(md.c1) # regression model summary## Linear mixed-effects model fit by REML
## Data: cwue
## AIC BIC logLik
## 52.57585 51.53465 -21.28792
##
## Random effects:
## Formula: ~1 | zn
## (Intercept) Residual
## StdDev: 5.981119 2.24292
##
## Fixed effects: wue ~ irg
## Value Std.Error DF t-value p-value
## (Intercept) 34.21312 3.688020 6 9.276826 0.0001
## irgmch 2.76943 5.215648 6 0.530986 0.6145
## irgpvt 1.45093 5.215648 6 0.278187 0.7902
## Correlation:
## (Intr) irgmch
## irgmch -0.707
## irgpvt -0.707 0.500
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -0.51287013 -0.10279058 -0.01325674 0.19273233 0.52612687
##
## Number of Observations: 9
## Number of Groups: 9lsmeans(md.c1, pairwise ~ irg, adjust = "tukey") # ctrl:mch:pvt = a, a, a## $lsmeans
## irg lsmean SE df lower.CL upper.CL
## ctrl 34.2 3.69 8 25.7 42.7
## mch 37.0 3.69 6 28.0 46.0
## pvt 35.7 3.69 6 26.6 44.7
##
## d.f. method: containment
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## ctrl - mch -2.77 5.22 6 -0.531 0.8595
## ctrl - pvt -1.45 5.22 6 -0.278 0.9585
## mch - pvt 1.32 5.22 6 0.253 0.9656
##
## P value adjustment: tukey method for comparing a family of 3 estimatesmd.p1 <- lme(data = pwue, wue ~ irg, random = ~1 | zn)
anova(md.p1) # ANOVA table, p = .002 for irg**## numDF denDF F-value p-value
## (Intercept) 1 6 328.2178 <.0001
## irg 2 6 19.8173 0.0023summary(md.p1) # regression model summary## Linear mixed-effects model fit by REML
## Data: pwue
## AIC BIC logLik
## 63.55683 62.51563 -26.77841
##
## Random effects:
## Formula: ~1 | zn
## (Intercept) Residual
## StdDev: 14.93473 5.600523
##
## Fixed effects: wue ~ irg
## Value Std.Error DF t-value p-value
## (Intercept) 84.06434 9.208908 6 9.128590 0.0001
## irgmch 57.98411 13.023363 6 4.452314 0.0043
## irgpvt -21.20907 13.023363 6 -1.628540 0.1545
## Correlation:
## (Intr) irgmch
## irgmch -0.707
## irgpvt -0.707 0.500
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -0.535095805 -0.090985122 -0.009060496 0.100045618 0.501618335
##
## Number of Observations: 9
## Number of Groups: 9lsmeans(md.p1, pairwise ~ irg, adjust = "tukey") # ctrl:mch:pvt = b, a, b## $lsmeans
## irg lsmean SE df lower.CL upper.CL
## ctrl 84.1 9.21 8 62.8 105.3
## mch 142.0 9.21 6 119.5 164.6
## pvt 62.9 9.21 6 40.3 85.4
##
## d.f. method: containment
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## ctrl - mch -58.0 13 6 -4.452 0.0103
## ctrl - pvt 21.2 13 6 1.629 0.3053
## mch - pvt 79.2 13 6 6.081 0.0022
##
## P value adjustment: tukey method for comparing a family of 3 estimatesmd.t1 <- lme(data = twue, wue ~ irg, random = ~1 | zn)
anova(md.t1) # ANOVA table, ns, ctrl:mch:pvt = a, a, a## numDF denDF F-value p-value
## (Intercept) 1 6 34.39095 0.0011
## irg 2 6 0.92519 0.4465summary(md.t1) # regression model summary## Linear mixed-effects model fit by REML
## Data: twue
## AIC BIC logLik
## 78.7329 77.6917 -34.36645
##
## Random effects:
## Formula: ~1 | zn
## (Intercept) Residual
## StdDev: 52.89781 19.83668
##
## Fixed effects: wue ~ irg
## Value Std.Error DF t-value p-value
## (Intercept) 100.78382 32.61734 6 3.0898848 0.0214
## irgmch 44.71750 46.12788 6 0.9694246 0.3698
## irgpvt -15.76149 46.12788 6 -0.3416911 0.7442
## Correlation:
## (Intr) irgmch
## irgmch -0.707
## irgpvt -0.707 0.500
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -0.59870767 -0.01821037 0.01123619 0.08579933 0.55320260
##
## Number of Observations: 9
## Number of Groups: 9To conclude the data analysis, let’s take a look at WUE of the crops under different irrigation management practices. The two-way ANOVA results and following post hoc analysis results are marked on the graphs. Statistical significance codes are provided at P < .10, .05, .01, .001 with o, *, **, and ***, respectively. Different alphabet letters indicate significant differences at P < .05 level.
A significant Mch effects was found only for Pep (P = 0.002). Ctrl being the baseline, there was a 68.9% increase in WUE by the Mch treatment for Pep. No differences were found in WUE of the other treatment groups.
Conclusions
Mch reduced the loss of water from ETc in select vegetables, but a significance was only found in Pep. The reduction of ETc led to the increases in WUE for Pep. # References
Allen, Richard G., Luis S. Pereira, Dirk Raes, and Martin Smith. 1998. “Crop Evapotranspiration (guidelines for computing crop water requirements).” Rome: FAO. doi:10.1016/j.eja.2010.12.001.
Colaizzi, Paul D., Susan A. O’Shaughnessy, Steve R. Evett, and Ryan B. Mounce. 2017. “Crop evapotranspiration calculation using infrared thermometers aboard center pivots.” Agricultural Water Management 187. Elsevier B.V.: 173–89. doi:10.1016/j.agwat.2017.03.016.
Evett, Steven R., Robert C. Schwartz, Terry A. Howell, R. Louis Baumhardt, and Karen S. Copeland. 2012. “Can weighing lysimeter ET represent surrounding field ET well enough to test flux station measurements of daily and sub-daily ET?” Advances in Water Resources 50. Elsevier Ltd: 79–90. doi:10.1016/j.advwatres.2012.07.023.
Shaughnessy, Susan A O, Steven R. Evett, Paul D. Colaizzi, Susan A. O’Shaughnessy, Steven R. Evett, and Paul D. Colaizzi. 2015. “Dynamic prescription maps for site-specific variable rate irrigation of cotton.” Agricultural Water Management 159. Elsevier B.V.: 123–38. doi:10.1016/j.agwat.2015.06.001.
Dr. Paul Colaizzi and Melanie Baxter from USDA-CPRL at Bushland, Drs. Charles Rush, Qingwu Xue from Texas A&M AgriLife Research at Amarillo, James Gray, Jewel Arthur, Jared Bull, student workers from Texas A&M AgriLife Research at Bushland.↩