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Estimating FAO56 Single and Dual Crop coefficients with a water balance model in R

Source: R/kc.R
kc.Rd

This function computes FAO56 crop coefficients and water balance. The output of the model includes crop evapotranspiration, water stress coefficient, irrigation requirements, soil available water, etc. In addition to point estimation, spatial modelling is integrated using Evaporation fractions from sebal, sebi, ETo, sseb, sebs. cal.kc can be used to calibrate the model.

Usage

kc(
  ETo,
  P,
  RHmin,
  soil = "Sandy Loam",
  crop,
  I = 0,
  CNII = 67,
  u2 = 2,
  FC = NULL,
  WP = NULL,
  h = NULL,
  Zr = NULL,
  Ze = 0.1,
  kc = NULL,
  p = NULL,
  lengths = NULL,
  fw = 0.8,
  fc = NULL,
  kctype = "dual",
  region = NULL,
  regexpr = "sweet",
  initgw = 50,
  LAI = 3,
  rc = NULL,
  Kb = 0,
  Rn = NULL,
  hmodel = "gaussian",
  Zrmodel = "linear",
  xydata = NULL,
  REW = NULL,
  a1 = 360,
  b1 = -0.17,
  a2 = 240,
  b2 = -0.27,
  a3 = -1.3,
  b3 = 6.6,
  a4 = 4.6,
  b4 = -0.65,
  report = "stages",
  time = "06:00",
  HWR = 1,
  latitude = NULL,
  density = "full",
  DOY = NULL,
  slope = NULL,
  y = NULL,
  r1 = 100,
  nongrowing = "weeds",
  theta = NULL,
  profile = "variable",
  Kcmin = 0.15,
  Ky = NULL
)

# Default S3 method
kc(
  ETo,
  P,
  RHmin,
  soil = "Sandy Loam",
  crop,
  I = 0,
  CNII = 67,
  u2 = 2,
  FC = NULL,
  WP = NULL,
  h = NULL,
  Zr = NULL,
  Ze = 0.1,
  kc = NULL,
  p = NULL,
  lengths = NULL,
  fw = 1,
  fc = NULL,
  kctype = "dual",
  region = NULL,
  regexpr = "sweet",
  initgw = 50,
  LAI = 3,
  rc = NULL,
  Kb = 0,
  Rn = NULL,
  hmodel = "gaussian",
  Zrmodel = "linear",
  xydata = NULL,
  REW = NULL,
  a1 = 360,
  b1 = -0.17,
  a2 = 240,
  b2 = -0.27,
  a3 = -1.3,
  b3 = 6.6,
  a4 = 4.6,
  b4 = -0.65,
  report = "stages",
  time = "06:00",
  HWR = 1,
  latitude = NULL,
  density = "full",
  DOY = NULL,
  slope = NULL,
  y = NULL,
  r1 = 100,
  nongrowing = "weeds",
  theta = NULL,
  profile = "variable",
  Kcmin = 0.15,
  Ky = NULL
)

# S3 method for class 'kc'
plot(
  x,
  output = "AW_measured",
  main = NULL,
  cex = 1,
  legend = TRUE,
  pos = "top",
  horiz = FALSE,
  ...
)

fit.kc(x, output = "AW_measured")

Arguments

ETo

Numeric. Reference evapotranspiration [mm]. This can be estimated with ETo

P

numeric. Precipitation [mm]

RHmin

numeric. Minimum Relative Humidity [per cent]

soil

character. Name of soil texture as written in FAO56 TABLE 19

crop

character. Name of the crop as written on FAO56 Table 11, TABLE 12 and TABLE 17

I

numeric. Irrigation [mm]

CNII

numeric. The initial Curve Number of the study site. This can be calibrated with cal.kc.

u2

numeric. Wind speed of the nearby weather station [m/s] measured at 2m

FC

numeric. soil water content at field capacity [-][m3 m-3]. This can be calibrated with cal.kc.

WP

numeric. soil water content at wilting point [-][m3 m-3]. This can be calibrated with cal.kc.

h

numeric. Maximum crop height [m]. See details below. This can be calibrated with cal.kc

Zr

numeric. Rooting depth. See details below. This can be calibrated with cal.kc

Ze

numeric. The depth of the surface soil layer that is subject to drying by way of evaporation [0.10-0.15 m]. This can be calibrated with cal.kc

kc

list. The tabulated Kc values for single crop c(kcini,kcmid,kcend) or dual crop model c(kcbini,kcbmid,kcbend). To use with sebal or any of the Surface Energy Balance models, it should be linked as list(model1,model2,model3) or c(model1$EF,model2$EF,model3$EF) but not a mixture of both. This can be calibrated with cal.kc

p

The depletion coefficient. This can be calibrated with cal.kc

lengths

list. The lengths of the crop growth stages. It can take dates in the form of c(start of planting ('YYYY-mm-dd), start of rapid growth, start of mid season, start of maturity, harvesting) or in the form number of days: c(initial days, dev days, mid days, late days). See FAO56 TABLE 11. If performing time series simulation, different dates or one season dates can be set; for instance two seasons simulation can be of the form c(initial days, dev days, mid days, late days, initial days, dev days, mid days, late days) or just c(initial days, dev days, mid days, late days)

fw

list or numeric or character. This can take different fw values throughout the growing season. It can also take one numeric value and this will be transform depending on the type of wetting. If the wetting event is only Precipitation, it is set to 1; if it is only Irrigation it is set to the provided fw value. If it is both Precipitation and Irrigation weights are assigned for calculation of fw. fw can also take a character such as "Drip", "Sprinkler", "Basin", "Border", "alternated furrows", "Trickle", "narrow bed" and "wide bed". In this case fw values from FAO56 are assigned.

fc

numeric. fraction of ground covered by tree canopy

kctype

character. The type of model either "single" or "double". In spatial modelling involving Evaporation Fraction, kctype can be set to "METRIC" or "SSEB" so that Actual Evapotranspiration will be estimated as ETo*EF else it will be estimated with Rn as ETa=(EF*Rn)/2.45. Note that Rn is in MJm-2 day-1.

region

character. The region of the crop as on FAO56 TABLE 11

regexpr

character. Extra term that can be used to search crop names on FAO56 Tables

initgw

numeric. Initial ground water level [m]

LAI

numeric. Leaf Area Index

rc

numeric Runoff coefficient [0-1]. This must be used if there is no information on Curve Number. This can be calibrated with cal.kc

Kb

ground water (base flow) recession parameter. The default is zero where no baseflow occurs

Rn

Net daily radiation [w/m2]. Estimated this with ETo

hmodel

character. The type of crop growth model during the simulation. It takes "gaussian","linear", "exponential"

Zrmodel

character. The type of root growth model during the simulation. It takes "gaussian","linear", "exponential"

xydata

list c(longitude, latitude). The observation points of the model. This should be set only if the model is spatial.

REW

numeric Readily Evaporable Water. It can be calibrated with cal.kc

a1

soil water storage to maximum root depth (Zr) at field capacity

b1

Liu et al. (2006) parameter for computing capillary rise [-0.17]. It can calibrated with cal.kc

a2

Liu et al. (2006) parameter for computing capillary rise [240]. It can be calibrated with cal.kc

b2

Liu et al. (2006) parameter for computing capillary rise [-0.27]. It can be calibrated with cal.kc

a3

Liu et al. (2006) parameter for computing capillary rise [-1.3]. It can be calibrated with cal.kc

b3

Liu et al. (2006) parameter for computing capillary rise [6.6]. It can be calibrated with cal.kc

a4

Liu et al. (2006) parameter for computing capillary rise [4.6]. It can be calibrated with cal.kc

b4

Liu et al. (2006) parameter for computing capillary rise [-0.65]. It can be calibrated with cal.kc

report

list. In case of spatial modelling, which days' map should be reported. The default is "stages" where the periods of stages maps are reported as values. In an ascending order it can take values such as 1:12 days or c(1,3,6:12) days.

time

character. Time of the occurrence Irrigation or Precipitation.

HWR

numeric. Default is 1. Height to width ratio of individual plants or groups of plants when viewed from the east or from the west [-].

latitude

geographical coordinates in decimal degrees. It should be negative for southern hemisphere

density

character. density factor for the trees, vines or shrubs on how they are arranged. It can take "full", "row" or "random" or "round".

DOY

Numeric or Date [YYYY-mm-dd]. Day of the Year. If you give data in the form of date [YYYY-mm-dd], it will be converted to DOY

slope

numeric. slope of saturation vapour pressure curve at air temperature T [kPa oC-1].

y

numeric. psychometric constant [kPa oC-1]

r1

leaf resistance FOR STOMATAL CONTROL [s/m]

nongrowing

character. The type of surface during non-growing season. It can take "weeds", "bare", or "mulch"

theta

numeric. The measured soil water content [m3/m3] in the profile. Leave those days without measured data blank.

profile

numeric or character. The profile depth to perform water balance. It takes "variable" when updating the depth with root growth (default). Or taking "fixed" when the maximum root zone is used. It can also take numeric value and this can be longer than maximum root length.

Kcmin

Minimum Kc value

Ky

list or array. yield response factor [-] in the form of c(initial Ky,crop dev't Ky, mid season Ky, late season Ky, total season Ky). For instance Maize Ky is c(0.4,0.4,1.3,0.5,1.25). Ky values for other crops are tabulated in FAO Irrigation and Drainage Paper 33 (Doorenbos and Kassam, 1979) and Paper 56 (Allen et al., 1998). If only one Ky value is supplied it will be repeated for all the seasons.

x

a return object of the function.

output

The kind of plot that should be displayed. It takes 'AW_measured' for plotting Available and modelled soil moisture; 'TS_measured' for Total Available and modelled soil moisture; 'Kc' for displaying Kcb and Kc 'Evaporation' for displaying of Evaporation and Transpiration 'balance' for displaying Irrigation, precipitation, ETa and critical water deficit

main

Title of the plot

cex

the relative font size of the texts. Vlaues: "horiz"; logical: if TRUE, set the legend horizontally rather than vertically

legend

logical. TRUE or FALSE. Whether a legend should be displayed or not.

pos

the position of legend. It takes one of the following 'top', 'topright', 'topleft', 'bottom', 'bottomright' 'bottomleft', 'center'. This must be set so that the legend should not obscure the main plot.

horiz

logical; if TRUE the legend is drawn horizontally rather than vertically.

...

further arguments passed to the plotting functions.

Value

The output of the function depends of the kctype and kc data type. For single and dual crop coefficient, an "output" dataframe contains variables such as TAW,RAW,Runoff,Ks,Kcb,h,Kc,ETc,DP,CR,Drend,Kr,De,AW,E,Ke,CN. In case kc is set to EF the function returns Kc,Kcxy,ETc,ETcxy,Drend,Drendxy,TAW,TAWxy,RAW,RAWxy,AW,Awcxy,Ineed,Ineedxy

output:

dataframe of the return values

ETc_adj:

The soil water stress adjusted ETc [mm]

Ya_by_Ym:

actual yield by potential yield

yield_decrease:

The relative yield decrease: 1-Ya/Ym

ETdecrease:

The relative evapotranspiration deficit :1- ETc_adj/ETc

yield_by_ET_decrease:

he relative yield decrease: 1-Ya/Ym and the relative evapotranspiration deficit in one dataframe

Awcxy:

Available Soil water for each location at each time step [mm]

CR:

capillary rise [mm/day]

GW:

Updated ground water depth

CN:

Curve Number

De:

cumulative depth of evaporation (depletion) from the soil surface layer [mm] at the end of the day [mm/day]

DP:

Deep Percolation [mm/day]

Drend:

cumulative depth of evapotranspiration (depletion) from the root zone at the end of the day [mm]. This is equal to the amount of water needed to bring soil water to field capacity

Drendxy:

cumulative depth of evapotranspiration (depletion) from the root zone at the end of the day [mm] for each xydata location at each time step. This is equal to the amount of water needed to bring soil water to field capacity

E:

evaporation [mm/day]

ETc:

crop evapotranspiration [mm/day]. If water stress coefficient (Ks) is less than 1, ETc is crop evapotranspiration under non-standard conditions else ETc is crop evapotranspiration under standard conditions

ETcxy:

crop evapotranspiration [mm/day] for each location at each time step. crop evapotranspiration under standard conditions

h:

crop height [m]

Ineed:

Amount of soil water that is below maximum allowed depletion [mm]

Ineedxy:

Amount of soil water that is below maximum allowed depletion for each xydata location at each time step [mm]

Kc:

standard crop coefficient [-]

Kc_adj:

adjusted crop coefficient [-]

EF:

Evaporation Fraction [-]

EFxy:

Evaporation Fraction for each monitored location [-]

kcb:

basal crop coefficient for the growing season [-]

Kcxy:

crop coefficient for each location at each time step [-]

Ke:

soil evaporation coefficient

Kr:

soil evaporation reduction coefficient [-]

Ks:

Water stress coefficient [-]

RAW:

Readily Available Water [mm]

RAwcxy:

Readily Available Soil water for each xydata location at each time step [mm]

Runoff:

Runoff [mm/day]

TAW:

Total Available Water [mm]

TAwcxy:

Total Available Soil water for each location at each time step [mm]

Details

Using Existing Tables

The function include backend database of FAO Tables. The user can use the parameter values such as Zr, h, p, FC, WP, etc from FAO56 tables. Most of the parameters with NULL values can take default values from FAO56 Tables. When a crop name results in 3 crops, the user can differentiate that with regexpr parameter. For example, a crop parameter with a name "maize" can match two crops on FAO Table 12. Including regexpr parameter with "sweet" with match only one.

Modelling crop height and Rooting Depth

At each time step a crop height or root depth is estimated. The crop or rooting depth growth model can take exponential model of the form hday=0+0.75*max(h)*(1-exp(-day/0.75*max(days))) or Zrday=0+0.75*Zr*(1-exp(-day/0.75*max(days))) The gaussian model is of the form hday=0+0.75*max(h)*(1-exp(-day^2/(0.75*max(days)^2))) or Zrday=0+0.75*(1-exp(-day^2/(0.75*max(day))^2)) The linear model is of the form hday=(day*max(h))/max(days), Zrday=(day*Zr)/max(days)

Point modeling with Single and dual crop coefficients

The function can estimate kc curve for the growing period by using the traditional kcini, kcmid and kcend and crop lengths growth stages, in case of single crop coefficients. Just like single crop coefficients, the dual crop coefficients kcbini, kcbmid, kcbend are embedded in kc parameter. The "kc" parameter must take 3 values as c(initial, mid, end). The values of "lengths" parameter must also be specified as c(initial, dev, mid, late). See example section for more details.

Spatial modeling With Evaporation Fraction

Instead of supplying kcs values as described above, Evaporation Fraction (EF) from can be used. The corresponding EF at initital, mid amd end seasons can be supplied. The EF curve will be developed for each location at each time step and ETa derived from (EF*Rn)/2.45.

Interpolation of Input data

Once EF is used instead of Kcs, one can provide longitudes and latitudes in xydata parameter data frame. A 2D column data of P, I,ETo,RHmin, u2, Rn for each time step for each location can be provided. At each time step an inverse distance interpolation will be perform to get continuous surface. In case of initial and static input column data such as CNII, FC, WP, initgw, Zr, h can also be interpolated.

Calibration

A calibration of unmeasured variables can be done with cal.kc

References

  • Allen, R. G., PEREIRA, L. S., RAES, D., & SMITH, M. (1998). Crop Evapotranspiration (guidelines for computing crop water requirements) FAO Irrigation and Drainage Paper No. 56: FAO.

  • Allen, R.G., Wright, J.L., Pruitt, W.O., Pereira, L.S., Jensen, M.E., 2007. Water requirements. In: Hoffman, G.J., Evans, R.G., Jensen, M.E., Martin, D.L., Elliot, R.L. (Eds.), Design and Operation of Farm Irrigation Systems. , 2nd edition. ASABE, St. Joseph, MI, pp. 208-288.

  • Liu, Y., Pereira, L.S., Fernando, R.M., 2006. Fluxes through the bottom boundary of the root zone in silty soils: parametric approaches to estimate groundwater contribution and percolation. Agric. Water Manage. 84, 27-40.

See also

cal.kc

Author

George Owusu

Examples

if (FALSE) { # \dontrun{
#FAO56 Example 32: Calculation of the crop coefficient (Kcb + Ke) under sprinkler irrigation
FAO56Example32=kc(ETo=7,P=0,RHmin=20,soil="sandy loam",crop="Broccoli",I=10,
kctype = "dual",u2=3,kc=c(0.9,0,0),h=1,Zr=0.1)
FAO56Example32$output$fc
FAO56Example32$output$Kc_adj
#FAO56 Example 33: Calculation of the crop coefficient (Kcb + Ke) under furrow irrigation
FAO56Example33=kc(ETo=7,P=0,RHmin=20,soil="sandy loam",crop="Broccoli",I=10,
         kctype = "dual",u2=3,kc=c(0.9,0,0),h=1,Zr=0.1,fw=0.3)
#FAO56 Example 34: Calculation of the crop coefficient (Kcb + Ke) under drip irrigation
FAO56Example34=kc(ETo=7,P=0,RHmin=20,soil="sandy loam",crop="Broccoli",I=10,
           kctype = "dual",u2=3,kc=c(0.9,0,0),h=1,Zr=0.1,fw="drip")
         
file=system.file("extdata","sys","irrigation.txt",package="sebkc")
data=read.table(file,header=TRUE)  
P=data$P
rc=0
I=data$I
ETo=data$ETo
Zr=data$Zr
p=0.6
FC=0.23
WP=0.10
u2=1.6  
RHmin=35
soil="sandy loam"
crop="Broccoli"
############Single crop coefficient model###########
modsingle=kc(ETo,P=P,RHmin,soil,crop,I)
#dataframe of the return values
modsingle$output 
modsingle$output$TAW #Total Avalaible water [mm]
#Single with runoff coefficient
############Dual crop coefficient model###########
moddual=kc(ETo,P=P,RHmin,soil,crop,I,kctype = "dual",FC=FC,p=p,WP=WP,u2=u2,kc=c(0.3,0,0),Zr=Zr)
#Reproducing FAO56 Example 36
fc=(0.00667*1:12)+0.07333
h=1:12/1:12*0.3
 moddual=kc(ETo,P=P,RHmin,soil,crop,I,kctype = "dual",FC=FC,p=p,WP=WP,u2=u2,rc=0,
 kc=data$Kcb,Zr=Zr,lengths = c(4,4,2,2),h=h,hmodel="linear",fc=fc,fw=0.8)
 plot(moddual$output$Day,moddual$output$Kc_adj,type="l",ylim=c(0,1.2))
 lines(moddual$output$Day,moddual$output$Kcb,type="l", lty=2)
###########Spatial model I: Evaporation Fraction (EF) Model###################
#landsat folder with original files but a subset
folder=system.file("extdata","stack",package="sebkc") 

sebiauto=sebi(folder=folder,welev=317,Tmax=31,Tmin=28) #sebi model
kc2=stack(sebiauto$EF/2,sebiauto$EF,sebiauto$EF/3) #assign EF to kc
modEF=kc(ETo,P=P,RHmin,soil,crop,I,kc=kc2,Rn=8,lengths = c(4,4,2,2))
spplot(modEF$EF)

#############Spatial model II: interpolating precipitation ######################
h=1:12
Zr=1:12/12
xydata=data.frame(cbind(longitude=data$longitude,latitude=data$latitude))
print(xydata) #take a look at xydata
P2=data.frame(matrix(rep(P,12),ncol=12))
print(P2) #take a look at the format of precipitation data
modEFh=kc(ETo,P=P2,RHmin,soil,crop,I,kc=kc2,Rn=8,lengths = c(4,4,2,2),h=h,Zr=Zr,xydata=xydata)
#Amount of irrigation water needed 
spplot(modEFh$Drend)
#Amount of water Irrigation that is critically needed to reach maximum allowed depletion level
modEFh$Ineedxy
ETcxy=modEFh$ETcxy ##get ETc for each location at each time step
TAW=modEFh$TAW ## 


############FAO56 Example 41: Estimation of mid-season crop coefficient for Trees or weeds ########
FAOExample41 =kc(fc=0.3,DOY=200,latitude=40,u2=1.5,h=2,density="row",lengths=c(0,0,1,0),
ETo=0,P=0,RHmin=55,soil="sand",crop="Broccoli",kctype="dual")
FAOExample41$output$Kcb

#FAO56 Example 43: Estimation of Kcb mid from ground cover with reduction for stomatal control
FAOExample43 =kc(fc=0.196,DOY=180,latitude=30,u2=2,h=5,density="round",y=0.0676,slope=0.189,
r1=420,RHmin=25,lengths=c(0,0,1,0),ETo=0,P=0,soil="sand",crop="Broccoli",kctype="dual")
FAOExample43$output$Kcb
} # }