Neural network models for soil moisture forecasting from remote sensed measurements


ACTA IMEKO 
ISSN: 2221-870X 
June 2020, Volume 9, Number 2, 59 - 65 

 

ACTA IMEKO | www.imeko.org June 2020 | Volume 9 | Number 2 | 59 

Neural network models for soil moisture forecasting from 
remotely sensed measurements 

Andrea Marini1, Loris Francesco Termite2,3, Alberto Garinei1,4, Marcello Marconi1,4, Lorenzo Biondi1,4 

1 Idea-re S.r.l., Via Cornelia, 498, 00166, Rome, Italy  
2 Radarmeteo S.r.l., via IV Novembre 119, 35020, Due Carrare (PD), Italy 
3 Agrosit S.r.l., Via Briganti 75, 06127, Perugia, Italy 
4 Department of Sustainability Engineering, Guglielmo Marconi University, via Plinio 44, 00193, Rome, Italy 

 

 

Section: RESEARCH PAPER  

Keywords: Soil Water Index modelling; Machine Learning; Artificial Neural Network; LSTM; ANFIS.   

Citation: Andrea Marini, Loris Francesco Termite, Alberto Garinei, Marcello Marconi, Lorenzo Biondi, Neural network models for soil moisture forecasting 
from remote sensed measurements, Acta IMEKO, vol. 9, no. 2, article 10, June 2020, identifier: IMEKO-ACTA-09 (2020)-02-10 

Editor: Oscar Tamburis, University of Naples Federico II, Italy 

Received March 5, 2020; In final form June 22, 2020; Published June 2020 

Copyright: This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, 
distribution, and reproduction in any medium, provided the original author and source are credited. 

Funding: The study presented in this paper is part of the WATCH-Decision support system for sustainable water management in agriculture under climate 
change project financed by Regione del Veneto POR FESR 2014-2020, Italy. 

Corresponding author: Andrea Marini, e-mail: amarini@idea-re.eu  

 

1. INTRODUCTION 

Knowledge of Soil Moisture (SM) is fundamental in several 
scientific fields, such as rainfall-runoff modelling, landslide 
forecasting, soil nutrient cycling processes, drought monitoring, 
and agriculture [1]. In particular, the importance of having clear 
control over SM in agriculture is obvious. This has become even 
greater in recent years due to the climate changes that are 
increasingly affecting our world. In mid-latitude zones, the 
effects are visible as both long drought periods (and consequent 
yield reduction) or extremely intense and localised rainfall events, 
which could not only ruin a harvest but also lead to crisis when 
flooding risk occurs. In such a context, it is imperative to 
properly schedule irrigation practices, which rely on SM as a key 
variable determining the actual need for water of the crops. 
Nevertheless, managing irrigation systems could be complicated, 
especially if irrigation is managed through the help of channels 
deriving from bigger water bodies, like the Po Valley in Italy. 
Generally, land reclamation authorities are responsible for the 

management of wide networks of interconnected channels, 
whose flow is regulated by the movement of inline or lateral 
gates. Generally, a gate is open in order to move irrigation water 
towards a specific area, and it is closed in order to direct the flow 
elsewhere. Traditionally, gates are open or closed manually, but 
in recent years, an automation process has started, using the 
introduction of remotely controlled actuators for moving the 
gates [2][3]. However, planning the manoeuvres still remains a 
complex task. Decision-makers often receive water requests 
from different stakeholders and must deal with conflicting 
objectives [4][5]. Sometimes, the schedule of gate-opening and 
irrigation planning is inconsistent with the actual crop need or 
with the forthcoming weather conditions. In this context, a 
Decision Support System (DSS) could be helpful. DSSs are 
information systems supporting decision-making processes, 
usually including a software component, and are emerging as 
powerful tools in several water management contexts [6][7]. 
According to Power’s classification [8], it is proper to consider 

ABSTRACT 
Machine learning techniques are employed to describe the temporal behavior of soil moisture using meteorological data as inputs. 
Three different Artificial Neural Network models, a feedforward Multi-Layer Perceptron, a Long-Short Term Memory and the Adaptive 
Network-based Fuzzy Inference System, are trained and their results are compared. The soil moisture is expressed in terms of Soil Water 
Index, derived from satellite retrievals, with the last known value also being used as input. The results are promising as the proposed 
methodology relies on free-access data with a worldwide coverage, allowing to easily estimate the forthcoming soil moisture. The 
knowledge of the expected value of this variable could be extremely useful for irrigation scheduling and it is the basis of Decision Support 
Systems to efficiently manage water resources in agriculture. 

mailto:amarini@idea-re.eu


 

ACTA IMEKO | www.imeko.org June 2020 | Volume 9 | Number 2 | 60 

data-driven, knowledge-driven, and model-driven DSSs (or a mix 
of the three) for use in irrigation management and scheduling. 

The common feature of DSSs in the hydrological context is 
the collection of in-situ and remotely sensed variables describing 
the past and current status of the physical processes, and their 
elaboration aims to forecast their evolution so that decision-
makers can act promptly. In this way, real innovative irrigation 
‘smart grids’ can be realised. In a cultivated area, knowledge of 
SM may give an indication of crop status and help decision-
makers decide whether to schedule irrigation or not. Thus, 
monitoring the values of SM and forecasting its evolution are 
among the primary features that should be implemented in a DSS 
aimed at optimally managing irrigation. 

SM can be monitored in several ways. The most efficient one 
is by direct in-situ measurements through specific sensor devices, 
such as Time Domain Reflectometry (TDR) [9] or Frequency 
Domain Reflectometry (FDR) probes [10]. However, at the time 
of writing, the actual diffusion of these sensors is quite limited, 
and this does not allow a reasonably uniform cover of the 
variable in extended areas [11]. Paying the price of the lower 
accuracy and spatial resolution of the measurements, an 
alternative way of deriving water content information is by 
means of satellite data, thanks to recently developed Earth 
observation programmes [12]. The great advantage in using 
satellite data is that they are easily accessible and also provide 
worldwide coverage. 

Moreover, the knowledge of the forthcoming SM evolution 
could improve irrigation scheduling, e.g. avoiding water supply if 
the SM is estimated to increase because of weather variables. The 
temporal dynamic of SM can be estimated through physical, 
conceptual, or data-driven models [13]. The latter type is used in 
this study to carry out an exploratory quantitative analysis on the 
temporal behaviour of SM in agricultural fields. 

The use of machine learning has become widespread in many 
different contexts, ranging from medical [14] to industrial [15] 

applications. In the hydrological and environmental fields, 
machine learning is widely used to predict the future behaviour 
of several relevant variables [16]. 

In this study, using machine learning techniques, three 
Artificial Neural Network (ANN) models are trained to predict 
SM; subsequently, they are tested, and their results are compared. 
Among the models’ inputs, remotely sensed data are used as a 
measure of the water content in soil. 

The main objective of this article is to develop a model that 
describes SM evolution in terms of meteorological data, which 
are clearly among the key factors affecting it. This will allow the 
forecasting of the future behaviour of the water content in the 
fields; thus, it will possibly represent the basis of a DSS for water 
management in irrigation. 

2. MATERIALS AND METHODS 

A specific case study is considered by selecting a limited 
geographic area in the Italian region of Veneto. In particular, the 
area taken into account is located between the cities of Venice 
and Padua, next to the Venetian Lagoon (Figure 1). This can be 
considered as a strategic location for the analysis, since it has 
traditionally been devoted to agriculture and is furnished with a 
wide and diffused water grid used for irrigation and land 
reclamation. 

The proposed approach makes use of remotely sensed SM 
data retrieved from Copernicus, the Earth observation program 
developed by the European Union and European Space Agency. 
In particular, the SM, which is the target variable to be modelled, 
is described through the Soil Water Index (SWI), which provides 
an estimate of water content at various depths in the soil and is 
computed based on satellite measurements of the Surface Soil 
Moisture (SSM) [17]. SSM and, consequently, SWI are expressed 
as relative soil moisture, i.e. percentage of saturation. SWI data 
can be accessed freely at the Copernicus Global Land Service 
[18], which is part of the Copernicus programme. The 
Copernicus SWI data for Europe have a 1 km resolution and are 
based on SSM data from Sentinel-1/C-band Synthetic-Aperture 
Radar (SAR) and MetOp/ASCAT sensors [19], [20]. 

SWI allows for the control of SM at different depths through 
parameter T: characteristic time length. This parameter describes 
the temporal dynamics of the water flux below the surface: 
increasing values of T correspond to deeper soil layers. The great 
advantage in using SWI is that it requires fixing only one 
parameter, namely T, which is usually calibrated by means of 
comparison with probe measurements at the soil depth of 
interest [21]. Copernicus Global Land Service provides SWI 
values for eight different characteristic time lengths, varying from 
1 to 100. The value of the characteristic time length that was 
taken into account in this study is T = 15. Of course, the same 
approach presented here can be equally repeated for other 
choices of T. 

The meteorological data taken into account in the analysis are 
the daily measurements of rainfall; minimum and maximum 
temperatures; average relative humidity; and wind speed. These 
data are measured by both ground-based and remote meters 
(weather radars) and are provided by Radarmeteo. The 
meteorological data are available for the years 2015-2018, so the 
analysis is focused on this time period. 

The selected methodology involves using machine learning 
techniques, specifically ANN models, to estimate the future 
evolution of SWI given the available meteorological information. 
The last observed SWI value, which, due to processing time, is 

 

Figure 1. Study area. 



 

ACTA IMEKO | www.imeko.org June 2020 | Volume 9 | Number 2 | 61 

assumed to be available four days after the observation, is also 
used as input. Thus, at time t the last available SWI value is 
assumed to be 𝑆𝑊𝐼𝑡−4. The target is the expected difference, 
ΔSWI, between the present-day SWI and the last observed SWI 
value. Table 1 summarises the symbolism used for the models’ 
variables. 

Three ANN models have been taken into account in this 
study: a Multi-Layer Perceptron (MLP), a Long Short-Term 
Memory (LSTM) network [22], and an Adaptive Network-Based 
Fuzzy Inference System (ANFIS) model [23]. 

A single hidden layer structure is selected to implement the 
MLP (Figure 2). The number of units in the hidden layer is 40. 
The MLP inputs are 

𝑅𝑡, 𝑅𝑡−1, 𝑅𝑡−2, 𝑅𝑡−3, 𝑅𝑡−4, 

𝑇𝑡, 𝑇𝑡−4,𝑡−1, 

𝑅𝐻𝑡, 𝑅𝐻𝑡−4,𝑡−1, 
𝑤𝑠𝑡 , 𝑤𝑠𝑡−4,𝑡−1, 

𝑆𝑊𝐼𝑡−4. 

Note that the meteorological variables on day t are also used 
as inputs of the model. In real predictive applications, forecasted 
values have to be used for such inputs. 

The LSTM network belongs to the wider class of Recurrent 
Neural Networks (RNNs), i.e. those with feedback connections 
that allow information to persist over the data sequence. This 
characteristic makes them naturally suited for modelling time 
series datasets. The second model taken into account in this 

study is an ANN with one hidden layer formed by 20 LSTM cells 
(Figure 3). The inputs used in this setup are 

𝑅𝑡, 𝑇𝑡
𝑚𝑖𝑛 , 𝑇𝑡

𝑚𝑎𝑥 , 𝑅𝐻𝑡, 𝑤𝑠𝑡 , 𝑆𝑊𝐼𝑡−4. 

In this case, it is sufficient to pass the current values of the 
variables as inputs, since the model is already capable – by itself 
– of keeping the relevant past information for the predictions. 

ANFIS is a particular type of ANN used to implement Fuzzy 
Inference Systems (FISs), i.e. inference rules based on the fuzzy 
logic concept [24][25]. ANFIS has a fixed structure of five layers 
corresponding to the five FIS steps (input variables fuzzification, 
antecedent values combination, implication, aggregation of the 
consequents, and defuzzification of the output variable). Since 
the number of ANFIS parameters requiring optimization grows 
exponentially with the number of inputs, the available 
meteorological data have been aggregated differently with 
respect to the two previous considered models in order to keep 
the number of inputs small. Thus, the inputs used in the ANFIS 
model are 

𝑅𝑡−4,𝑡 
Σ , 𝑇𝑡−4,𝑡−1, 𝑅𝐻𝑡−4,𝑡−1, 𝑤𝑠𝑡−4,𝑡−1, 𝑆𝑊𝐼𝑡−4. 

A schematic of the ANFIS network is depicted in Figure 4. 
For each ANFIS input, three membership functions defined in 
Equation (1) are used: 

Table 1. Input symbols. 

Symbol Description 

𝑅𝑡   Rainfall on day t 

𝑇𝑡
min, 𝑇𝑡

max Minimum and maximum temperatures on day t 

𝑇𝑡   Mean temperature on day t (a) 

𝑅𝐻𝑡  Mean relative humidity on day t 

𝑤𝑠𝑡   Mean wind speed on day t 

𝑆𝑊𝐼𝑡  Soil Water Index on day t 

𝑋𝑡1,𝑡2   
Mean of variable X over days t1 ÷ t2 

𝑋𝑡1,𝑡2
Σ   Cumulative value of variable X over days t1 ÷ t2 

(a) The mean temperature 𝑇𝑡  has been computed as the arithmetic mean of 
the minimum and the maximum daily temperatures. 

 

Figure 2. Scheme of the MLP network. 

 

Figure 3. Scheme of the LSTM network. 

 

Figure 4. Scheme of the ANFIS network. 



 

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𝑓memb(𝑥; 𝜇, 𝜎, 𝜈, 𝛼) = exp [ −
|𝑥 − 𝜇|𝜈

𝜎 2
 

1

1 +  𝑒−𝛼 𝑥
] (1) 

Each membership function has four free parameters, μ, σ, ν, 
and α, and can be seen as a deformation of the gaussian. Indeed, 
setting ν = 2 and α = 0 yields the usual gaussian function, with 
mean μ and variance σ2. The parameter ν allows for different 
peak shapes, while the sigmoid factor (1 +  𝑒−𝛼 𝑥)−1 allows for 
skewness. 

It is customary in machine learning applications to split the 
available dataset into three subsets: the training, the validation, 
and the test sets. The training set, which usually comprises the 
most data, is used to feed the learning algorithm. The validation 
set is used for the selection of the model’s hyperparameters or 
for comparing models. The test set is only used at the end to 
evaluate the performance of the selected model (observing how 
well the model works when applied to unseen data). In this 
analysis, in order to exploit as much data as possible for training, 
the data has been split only into training and validation sets, 
disregarding the test set. In practice, the validation set has been 
used both for the model selection and for the final assessment of 
the selected model. Though this is not optimal from a statistical 
point of view, this strategy is quite commonly used when the 
amount of available data is quite limited. 

For all the three models, data from January 2015 to December 
2017 are used for training, and data from January to December 
2018 are used for validation. 

As is usual in such modelling, the dataset has been normalised 
in order to facilitate the training procedure. The normalisation 
has been performed in such a way that all the variables have zero 
mean and unitary standard deviation, i.e. by computing the 
standard scores. 

The mean squared error of the output variable has been used 
as loss function Regularisation strategies have been exploited in 
order to keep possible overfitting issues under control. For the 
MLP and LSTMnetworks the dropout technique has been used 
[26]. Instead, in the ANFIS model, an L2 regularisation penalty 
for the weights of the consequent part of the if-then rules has been 
added to the loss function. 

The training has been performed by minimising this loss 
function by means of ADAM optimisation [27]. The training 
procedure has been carried out 100 times for all the considered 
models, and the values of the parameters have been set to the 
ones giving the least value of the mean squared error for the 
validation set. The models have been evaluated by means of Root 
Mean Square Error (RMSE) and the Nash-Sutcliffe Efficiency 
(NSE) index computed for the validation data. 

3. RESULTS 

At the end of the training phase, the best MLP, LSTM, and 
ANFIS models have been selected according to the 
abovementioned criteria, and a deeper analysis of the results has 
been carried out. 

Figure 5 shows the scatter plots of the predicted vs. observed 
ΔSWI for the three selected models. The blue dots refer to the 
training set, and the orange ones to the validation set. From these 
plots, a good agreement of the predictions can be observed when 
the actual ΔSWI is in the intermediate region (approximately 
between −7 and 7). Conversely, the predictions seem to be less 
accurate in the correspondence of the remaining external regions 
of the observed ΔSWI, where the points deviate more markedly 

 
 

 
 

 

Figure 5. Scatter plots of the predicted vs. observed ΔSWI for the three 
models. 



 

ACTA IMEKO | www.imeko.org June 2020 | Volume 9 | Number 2 | 63 

from the perfect forecast line: in these regions, the models tend 
to underestimate the amplitude of the real ΔSWI. It can be clearly 
observed that this effect is sharper for the MLP and the ANFIS 
models than for the LSTM. A possible explanation of this issue 
may be related to the small number of occurrences of such events 
in the available dataset. Note, however, that the difficulty of 

correctly reproducing extreme observations is also a known 
problem in machine learning modelling [28]. 

The plots in Figure 6 show the temporal behaviour of the 
ΔSWI predicted by the MLP, LSTM, and ANFIS models on the 
validation set, along with the corresponding observed values. 

 

 

 

Figure 6. Predicted and observed ΔSWI  for the validation set. 



 

ACTA IMEKO | www.imeko.org June 2020 | Volume 9 | Number 2 | 64 

The evaluation metrics, NSE and RMSE, are shown in Table 
2 for both the training and validation data. In particular, the 
metrics for the validation set are the most interesting ones for an 
assessment of the models. 

The results in Table 2 shows that among the three models 
taken into account, the one that has the best performance, both 
in terms of the least RMSE and higher NSE, is the LSTM one. 
The ANFIS model slightly outperforms the MLP. 

It is interesting to note that the RMSE on the validation set 
and the RMSE on the training set are quite similar. This is quite 
surprising, since one usually expects a worsening of the 
performance metrics on the validation set compared to that of 
the training set. Indeed, for the ANFIS model, the validation 
RMSE is even better than the training RMSE. This ‘strange’ 
behaviour is probably due to the presence of a higher number of 
outliers in the training set with respect to the validation set. 

4. CONCLUSIONS 

This article presented an approach for modelling SM using 
machine learning techniques. SM is expressed in terms of SWI 
retrieved from satellite measurements. These products are 
released on the Copernicus website with a time delay of two days 
after observation. To be cautious, it has been assumed that the 
last available SWI value dates back to four days earlier. Thus, the 
variation of SWI in a four-day period has been modelled through 
three different network-based models: a single hidden layer 
feedforward MLP, an LSTM network, and an ANFIS. 
Meteorological data, comprising rainfall, temperature, relative 
humidity, and wind speed records, have been used as inputs in 
both models along with the last known SWI value. 

In the qualitative analysis, the temporal behaviours of the 
predicted and the observed ΔSWI appear to correlate well. Yet, 
at the quantitative level, the agreement is not always satisfying, 

especially when the observed value lies in the tail of the ΔSWI 
distribution. However, when modelling a complex phenomenon 
using only a limited fraction of the actual set of variables 
influencing it, it is essential for the measured data to be extremely 
accurate and numerous. On the contrary, in this research, the 
available dataset spans over just four years (only three were used 
for training), and it could be that it has been insufficiently 
extended so as to guarantee an adequate generalisation capability 
to the models. Moreover, while they have been extremely useful 
thanks to their worldwide coverage and daily frequency, the SWI 
data obviously do not have the same accuracy as in-situ 
measurements. Finally, due to lack of historical records, all the 
variables influencing the system status related to human 
interventions, e.g. irrigation supplies, have been neglected. 

The comparison of the results of the models that have been 
taken into account indicates that the LSTM model outperforms 
the other two selected ANNs. 

The output of the models, i.e. ΔSWI, may be added to the last 
known SWI value, 𝑆𝑊𝐼𝑡−4, in order to obtain the predicted SWI, 
SWIpred, which is what the decision-makers are eventually 
interested in. The time series of the observed SWI and the LSTM 
SWIpred are shown in Figure 7. 

The results of the research are encouraging, as they show that 
in the absence of networks of in-situ sensors, satellite-derived 
measurements of SM can be forecasted by machine learning 
models, using simple meteorological data as inputs. This could 
be extremely useful in managing water resources, since SM is a 
fundamental variable to be considered when supplying irrigation. 

In principle, the proposed approach can be applied in all those 
settings where measurements from different sources over large 
areas (whether ground-based or remote sensing), meteorological 
data, and any quantitative information need to be processed to 
provide synthetic outputs for the final user. The exploitation of 
artificial intelligence techniques allows for modelling complex 
and highly nonlinear processes. Furthermore, this factor makes 
it possible to avoid the use of those parameters that would be 
necessary in physical modelling and would require extensive field 
campaigns to characterise the study area or should be estimated 
during model calibration. For example, no information about the 
hydraulic and pedologic characteristics of the soil is provided to 
the ANN models presented in this study. 

One limitation of the proposed approach is that it allows for 
the modelling of SM on a scale that is larger than the typical plot 

Table 2. Model results. 

 Training Validation 

 NSE RMSE NSE RMSE 

MLP 0.590 2.579 0.397 2.599 

LSTM 0.746 2.027 0.606 2.113 

ANFIS 0.558 2.677 0.468 2.440 

 

Figure 7. SWI time series reconstructed from the LSTM model. 



 

ACTA IMEKO | www.imeko.org June 2020 | Volume 9 | Number 2 | 65 

dimension. The resolution of this approach is indeed set by that 
of the satellite data, namely 1 km. However, this resolution is 
sufficiently high so as to provide a decision support tool for the 
authorities that are responsible for irrigation scheduling over 
large areas. 

Moreover, even if the spatial resolution of this kind of model 
is coarse compared to the typical field dimensions, valuable 
information can be applied also on a smaller scale. Indeed, it has 
been proven that SM follows a similar behaviour at global and 
local scales, and this allows for the downscaling of satellite 
measurements of this variable [29]. 

ACKNOWLEDGEMENT 

The authors are grateful to Acque Risorgive Consorzio di 
Bonifica (www.acquerisorgive.it) for providing the information 
and the data of the water channels system it manages. We also 
thank L. Brocca (Research Institute for Geo-Hydrological 
Protection IRPI, Italian National Research Council) for the 
useful discussion and the advice on the use of remotely sensed 
data. 

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