Comparison of Methods for Computing a Crop Coefficient for Grapes

Deficit irrigation can improve grape quality. See Evans et al. 1993 for cutoff temperatures for grapes and Crop coefficient based on growing degree days 

The crop coefficient (K_c) is a parameter used by various irrigation scheduling methods to scale potential evaporation and transpiration (evapotranspiration) to the actual levels for the particular crop. The crop coefficient (K_c) is usually computed as a function of total accumulated growing degree days. The value of K_c for grapes was obtained by fitting a function to theoretical data obtained from:

• Crop Water Requirements
  FAO Irrigation and Drainage Paper 24
  
  Pg 50, Table 27: Kc Values for Grapes (Clean Cultivated, Infrequent Irrigation, Soil Surface Dry Most of the Time)
  
  Using the data for areas of only light frosts, ground cover of 30-35 percent, with dry and light to moderate wind conditions.

The Growing Degree Days data was computed using 1995 Data in Las Cruces, NM, using both the averaging and the single sine methods of computation. The Growing Degree Days were calculated using the following parameters:

• Upper Threshold:	30°C
  Lower Threshold:	10°C
  Lower Cutoff:	10°C

Charts and Fit Data for Grapes Crop Coefficient

Average Method GDD Curves Curve Type Constant Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 R2 SSZA 0 0.811436 -0.08699 0.112481 -0.10204 -0.01225 -0.08359 0.98 SSNZA -0.01536 0.830959 -0.08689 0.119135 -0.10183 -0.00721 -0.08306 0.98 6th Order 0.029296 -0.00116 6.48E-06 -7.8E-09 4.07E-12 -9.7E-16 8.57E-20 0.98 3rd Order -0.09053 0.000881 -1.5E-07 -3E-11 0.90 Double 3rd Order 1 -0.08323 0.000587 6.3E-07 -4.4E-10 0.94 Double 3rd Order 2 1.102266 -0.00176 2.42E-06 -1.1E-09 0.99	Single Sine Method GDD Curves Curve Type Constant Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 R2 SSZA 0 0.833604 -0.05884 0.147892 -0.06764 0.037183 -0.12312 0.97 SSNZA -0.024 0.864526 -0.05885 0.158585 -0.06692 0.045289 -0.12274 0.97 6th Order -0.035 -9E-07 4.45E-06 -6.6E-09 3.78E-12 -9.5E-16 8.65E-20 0.97 3rd Order -0.054 0.001027 -2.7E-07 -1.7E-11 0.86 Double 3rd Order 1 -0.099 0.001236 -1.8E-07 -2.1E-10 0.94 Double 3rd Order 2 1.932366 -0.00479 5.82E-06 -2.3E-09 0.99
key SSZA Sine Series, Zero Average SSNZA Sine Series, Non-Zero Average 6th Order 6th Order polynomial 3rd Order 3rd Order polynomial Double 3rd Order 1 First 3rd Order polynomial for 2-part fit series Double 3rd Order 2 Second 3rd Order polynomial for 2-part fit series

Description of Curve Fit Equations

Sine Series

• The sine series curve fits have the following form:
  
  • K_c= A₀ + B₁ * sin( T ) + B₂ * sin( 2T ) + B₃ * sin( 3T ) + B₄ * sin( 4T ) + B₅ * sin( 5T ) + B₆ * sin( 6T )

  where:

  • T is (GDD * pi/MaxGDD),
    A₀ is the constant coefficient in the function parameters, and
    B_i is the i^th Term coefficient.

6^th Order Polynomial

• The 6^th order polynomial function is:
  
  • K_c= A₀ + B₁ * GDD¹ + B₂ * GDD² + B₃ * GDD³ + B₄ * GDD⁴ + B₅ * GDD⁵ + B₆ * GDD⁶

  where:

  • A₀ is the constant coefficient in the function parameters, and
    B_i is the i^th Term coefficient.

3^rd Order Polynomial

• The 3^rd order polynomial function is:
  
  • K_c= A₀ + B₁ * GDD¹ + B₂ * GDD² + B₃ * GDD³

  where:

  • A₀ is the constant coefficient in the function parameters, and
    B_i is the i^th Term coefficient.

Double 3^rd Order Polynomial

• The Double 3^rd order polynomial function is a special case. This function uses two separate 3^rd order polynomials to fit the rising and falling portions of the crop coefficient curve. A switch point was chosen at approximately the mid-point of the period of the function and the first polynomial was fit the the data up to that point, while the second polynomial was fit the the remainder of the data, with the GDD accumulation reset to zero at the switch point. Both equations have the same form as the regular 3^rd order equation:
  
  • K_c= A₀ + B₁ * GDD¹ + B₂ * GDD² + B₃ * GDD³

  where:

  • A₀ is the constant coefficient in the function parameters, and
    B_i is the i^th Term coefficient.

Another method of calculating the maximum crop coefficient is to measure the percent cover a midday and use a formula developed by Williams where k_c = 0.002 + 0.017x, where x is percent shaded area. See an extension publication on this method. A photograph from above the grapvins can also be used to measure the percent cover using Adobe Photoshop software.