International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
Where: 
TR, = actual transpiration rate /kg ms! 1 
LATHEAT = latent heat of vaporisation [2.46 * | 05 Jkg'] 
Isolating TR,,, as a function of AT yields: 
  
by AERODR 
eet LATHEAT 
/ * / . 
INTER — [arr H ud 
TR (Eq.8) 
  
Introducing Equation 8 in crop growth simulation is only possible 
if parameter values are commensurate with the minimum 
temporal resolution of the simulation. The actual transpiration 
rate, TRacn Must be presented as a daily value, which implies that 
AT cannot be the instantaneous value measured at the time of the 
satellite pass but must be converted to an equivalent daily value. 
The following procedure was adopted to obtain equivalent canopy 
temperature values for whole days (from instantaneous satellite 
observations): 
e Calculate the equivalent satellite-derived instantaneous 
canopy temperature for days in-between measurements 
as a function of the daily rate of change over the interval 
between two successive cloud-free satellite observations 
in a linear interpolation procedure. 
e Convert obtained instantaneous canopy temperatures to 
equivalent daily values by accounting for actual 
conditions during the day. To this end, the instantaneous 
canopy temperature values are multiplied by the 
fraction of sunshine hours for the day of year plus 2076 
of the clouded fraction. (It is assumed that there is still 
209^ radiation under an overcast sky.) 
In the crop growth model, the equivalent daily canopy 
temperature for each day in the crop cycle is approximated with: 
INTERTcan(adj.) = INTERTcan * CONVFAC (Eq.9) 
Where: 
INTERTcan = interpolated Satellite-derived temperature value [°C] 
CONVFAC = conversion factor for actual daytime conditions. 
With: 
CONVFAC = (SUNH + 0.2 * (DL — SUNH)) / DL (Eq.10) 
Equation 10 is applied to days with measurements as well as to 
days between measurements. 
The maximum transpiration rate (TRmax) is a reference value 
conditioned by the evaporative demand of the atmosphere 
(represented by the potential water use from a Penman-type 
reference canopy) and the properties of the actual crop canopy, 
notably its exposure to the atmosphere: 
TR. = TR) *CFLEAF * FC (Eq.11) 
Where: 
TR, = maximum transpiration rate [kg m^ s! ] 
TR, = potential transpiration rate from Penman-type canopy [kg m^ s!] 
CFLEAF = ground cover fraction of the actual canopy [0-1] 
TC = “actual turbulence coefficient’ /-/ 
With: 
CFLEAF = 1- EXP(-ke * LAI) (Eq.12) 
Where: 
ke = extinction coefficient for visible light /0-17 
LAI 7 Leaf Area Index /m' m] 
The potential transpiration rate from a Penman-type canopy 
equals the potential evapotranspiration rate (ET,) minus the 
evaporation component (Ep). The Penman-type reference 
canopy is defined as a short, green, closed, well-watered canopy 
with standard properties. The leaf area index (LA7) of this canopy 
will be close to LAI = 6 and the extinction coefficient is of the 
order of 0.5. It follows that the maximum rate of evaporation from 
underneath this reference canopy is approximated by E, — E, * 
exp (-ke * LAI) ^ Es * exp (- 3) = 0.05 * E, Consequently, 
potential transpiration from the reference canopy amounts to: 
TR, 7 ET, — 0.05 * E, (Eq.13a) 
Where: 
ET, = potential evapotranspiration rate from reference canopy [kg 
m?s'] ; 
E, = is potential evaporation rate /kg ms’) 
If it is assumed that the difference between ET, and E, is small, 
ie. within the error margin of satellite-derived ETy-estimates, TR, 
can be approximated by: 
TR, = 0.95 * ET, (Eq13b) 
The ground cover fraction of the actual crop canopy was 
described by equation 12. The effects of turbulence on the 
theoretical maximum transpiration rate are variable and complex; 
they depend on such diverse factors as wind speed, ET), canopy 
height, canopy roughness and parcel size. Driessen and Konijn 
(1992) propose a turbulence coefficient with values between 1.0 
and a maximum coefficient value TCM. The value of TCM is set 
equal to the maximum value of the crop coefficient, kc, as defined 
by Doorenbos et al (1979). Driessen and Konijn (1992) suggest 
the following relationship: 
TC 21 * (TCM-1) * CFLEAF (Eq.14) 
With the sufficiency coefficient c/H20 equal to TR, / TR yas the 
parameter can thus be described as a function of the difference in 
temperature between the canopy and the surrounding air: 
* VHF Y 
INTER (ST HEAT 
\ 
AERODR 
: (Eq.15) 
LATHEAT * TRO * CFLEAF * TC 
  
cfH20 = 
On this basis, it becomes possible to adjust assimilation and 
calculated actual crop growth from instantaneous measurements 
or derivations of canopy and ambient temperatures. Note that the 
so obtained value of c/H20 takes the analysis beyond the water- 
limited production potential (PS-2 level) to the level of an actual- 
farmer (PS-n) without the necessity of accounting for all yield- 
limiting and yield-reducing factors (stress due to water scarcity, 
water logging, nutrient shortage or excesses, pests, diseases, 
pollutants etc). Stomatal closure due to water shortage is a well- 
documented and understood phenomenon. However, also pest and 
disease attacks on crops, depending on severity of the damage 
inflicted, reduce the numbers and/or the efficient functioning of 
stomata leading to reduced transpiration hence assimilation. The 
so-defined ‘Production Situation n° (PS-n) calculates an “actual- 
farmer's' production level of the crop as a function of available 
light, temperature, photosynthetic mechanism and compounded 
constraints (or crop stress) as reflected by the heating of the 
canopy: 
PS-n: P,Y = flight, temperature, C3/C4, canopy heating) (Eq.16) 
214 
  
  
  
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