Figure 2 presents the actual data for the two most extreme periods (November-January and May-July), as well as sine curves adjusted to pass through the minimum and maximum for the relevant periods, since sine curves are normally used for the period from minimum to maximum.
The sine curve used for the period from the minimum up to the maximum is sometimes only the first quadrant of the sine curve (Parton and Logan 1981; Goudriaan and van Laar 1994), so the rate of increase in temperature in the model is most rapid immediately after the minimum, rather than the fourth quadrant of the sine curve for the minimum halfway to the maximum, then the first quadrant for the following period to the maximum.
For the period from the maximum to the transition point, the sine curve used is sometimes treated as a the second quadrant of the same sine curve used for the period up to the maximum (Parton and Logan 1981; Goudriaan and van Laar 1994), although others have preferred a separate sine curve with a different phase length for this section (Cesaraccio et al.
A sine curve centred halfway between the minimum and maximum temperatures (Watson and Beattie 1996; Roltsch et al.
The first sine curve was from [H.sub.min] to [H.sub.x] and the second from [H.sub.x] to [H.sub.max]; [D.sub.x] is the actual temperature at time [H.sub.x], while time H and temperature D define the points to be fitted.
However, in this case the period from the transition point may not be a sine curve so exponential and square-root decay functions were considered.
The difference of sensor output under different temperature could be approximate sine functions to roll angle, and the amplitude of the sine curve is also an approximate sine function to inclination.
Since we have simplified the model, it is easy to determine the whole sine curve by using only 4 data points.