e-ISSN: 2548-6861
JAIC Vol. 7, No. 2, December 2023: 150 – 155
152
Table 1 shows that although using
different types of soil
and sensors, in general gravimetric tests are carried out by
calculating soil volume (cm
3
), container weight, mass of the
dry soil (g), bulk density (g/cm
3
), mass of the wet soil (g) and
raw sensor data (v). The difference in the gravimetric test is
whether the gravimetric soil moisture content (θ
g
) is done
iteratively [10], [12] or without iteration [11], [13], [14] . If
it’s done iteratively, the bulk density (𝜌
𝑠𝑜𝑖𝑙
) will be
recalculated for each increase in the
volume of water in the
soil. Conversely, without iteration, bulk density (
𝜌
𝑠𝑜𝑖𝑙
) is only
calculated once using a soil sample and then used for each
increase in the volume of water in the soil. In this research,
we use gravimetric test without iterations because it provides
efficiency in the measurement process without
sacrificing the
quality of the test results.
B. Regression Model
Data from the gravimetric test results were then analysed
using a soil moisture sensor as the independent variable and
volumetric soil moisture content as the dependent variable.
The model to be used is based
on following a linear or
quadratic pattern.
Lot of time and cost required make it impossible to
calibrate the soil moisture sensor
at all levels of increasing
water volume. The output value of the soil moisture sensor,
for all levels of increasing water volume, is obtained based on
the predicted value of the linear or non-linear models. The
linear model (linear regression) will provide a prediction of
the maximum voltage generated by the soil
moisture sensor
so that soil moisture can be calibrated using a percentage
ratio. Linear regression models are very often used for
modelling soil moisture as has been done by [15]. The linear
model to be used is as follows:
𝑦
̂
= 𝛽
0
+ 𝛽
1
𝑥
1
+ 𝜀
(3)
The non-linear model will
provide predictions of soil
moisture by assuming the soil moisture sensor voltage varies
during time the sensor is used. The non-linear model that will
be used in this study is a polynomial model with order 2 and
3. The polynomial model is as follows
𝑦
̂
= 𝛽
0
+ 𝛽
1
𝑥
1
+ 𝛽
2
𝑥
1
2
+ 𝛽
3
𝑥
1
3
+ 𝜀
(4)
The model results will then be evaluated using R squared
(
𝑅
2
). Considering that the number of observed samples in the
gravimetric test is small, the adjusted R squared is used. The
adjusted R squared equation is as follows [16].
𝑅
2
= 1 −
∑
(
𝑦
𝑖
−𝑦
̂
𝑖
)
2
𝑛
𝑖=1
∑
(
𝑦
𝑖
−𝑦
̅)
2
𝑛
𝑖=1
(5)
𝑅
𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑
2
= 𝑅
2
−
(1−𝑅
2
)𝑘
𝑛−(𝑘+1)
(6)
