Appendix 1: Watermark sensors' interpretation reference

The next table shows the resistance value of the sensor at different soil water tension conditions (at a 75 Fahrenheit degree, equivalent to 23.8 Celsius degree):

Soil Water Tension (cbar)	Sensor Resistance (Ohms)
0	550
9	1000
10	1100
15	2000
35	6000
55	9200
75	12200
100	15575
200	28075

This series may be approached by this equation:

$$Equation 1: Rs = 137.5 * TA + 550$$

Where TA is the soil water tension expressed in centibars.

From the real values and the approximation we obtain the next graph of the sensor resistance versus the soil water tension.

Figure: Resistance of the sensor in function of the soil water tension

In the next figure we can see the frequency of the output of the adaptation circuit for the sensor, for the real resistance values and for the linearly approximated resistance values.

Figure: Output frequency of the adaptation circuit in function of the soil water tension

The formula used to draw this graph, from the sensor resistance, is shown bellow:

$$Equation 2: F = (Rs + 150390)/(0.021 * Rs + 8.19)$$

Where F is the output frequency in Hz and Rs the sensor resistance in ohms.

If we substitute Equation 1 in Equation 2, we get the output frequency in function of the soil water tension:

$$Equation 3: F = (137.5∗TA+550+150390)/(0.021∗(137.5∗TA+550)+8.19)$$

Equation 4. $F = \frac{\left( 137.5 \times \text{TA} + 150940 \right)}{\left( 2.8875 \times \text{TA} + 19.74 \right)}$

$$Equation 4: F = (137.5∗TA+150940)/(2.8875∗TA+19.74)$$

We can see that the frequency output for the working range is between 300 Hz (corresponding to the 200 cbar of maximum soil water tension) and 7600 Hz approximately for 0 cbar measurement. It has been empirically checked that for very wet soils, bellow 10 cbar, the behavior of different sensors is very variable, so calibration is highly recommended if accuracy under these conditions is needed.

To obtain the response of the sensor beyond this range, over the 200 cbar, we must extrapolate those soil water tension values from the linear approximation obtained in equation 1. These sensors are not prepared for working under those conditions, so these graph must be only taken as a reference.

Figure: Soil water tension in function of the output frequency of the circuit

Figure: Soil water tension (in logarithmic scale) in function of the output frequency of the circuit