# Accuracy and Transferability of Artificial Neural Networks in Predicting in Situ Root-Zone Soil Moisture for Various Regions across the Globe

^{*}

## Abstract

**:**

_{RAV}) of SSM over 10, 30, and 90 days was developed. The results show that applying a standard scaling (SSCA) to the ANN input features improves the correlation, Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE) for 52%, 91%, and 87%, respectively, of the tested stations, compared to MinMax scaling (MMSCA). Different training sets are suggested, namely, training on data from all networks, data from one network, or data of all networks excluding one. Based on these trainings, new transferability (TranI) and contribution (ContI) indices are defined. The results show that one network cannot provide the best prediction accuracy if used alone to train the ANN. They also show that the removal of the less contributing networks enhances performance. For example, elimination of the densest network (SCAN) from the training enhances the mean correlation by 20.5% and the mean NSE by 42.5%. This motivates the implementation of a data filtering technique based on the ANN’s performance. A median, max, and min correlation of 0.77, 0.96, and 0.65, respectively, are obtained by the model after data filtering. The performances are also analyzed with respect to the covered climatic regions and soil texture, providing insights into the robustness and limitations of the approach, namely, the need for complementary information in highly evaporative regions. In fact, the ANN using only SSM to predict RZSM has low performance when decoupling between the surface and root zones is observed. The application of ANN to obtain spatialized RZSM will require integrating remote sensing-based surface soil moisture in the future.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. In Situ Soil Moisture Datasets from ISMN

- -
- Soil moisture data lie within the temporal range (January 2013–December 2019) to maximize common temporal coverage. Some stations do not have data that cover the whole temporal interval (absence of measurements, gaps generated after quality control) but are still selected as long as they fall into that period. The total number of considered records is 10,054,406 hourly values. The representativeness and size of the training dataset is an important criterion since ANNs are data-driven methods [27].
- -
- A station is selected when soil moisture data are available at a depth of 5 cm for SSM and depths ranging between 30 and 60 cm for RZSM. Stations do not always have the same sensor installation and layout. Some stations have horizontal sensors (depth
_{from}= depth_{to}), whereas, for other stations, soil moisture sensors are disposed vertically (depth_{from}<> depth_{to}). In the latter case, stations that fall into the interval [30, 60 cm] were chosen. - -
- A station is selected if it has at least 3000 hourly soil moisture values (cf. Section 2.2.2 and Section 3.2).

#### 2.2. Methods

#### 2.2.1. Configuration of the Artificial Neural Network

_{1}and f

_{2}are the activation functions of the hidden layer and the output layer, respectively. w

_{ij}and w

_{j}are the weights given to the neurons in the input layer and hidden layer, respectively. b

_{1}and b

_{2}are the biases of the input layer and hidden layer, respectively. L and N are the number of hidden neurons and inputs, respectively. Figure 4 includes a simplified diagram of a fully connected ANN with one hidden layer.

#### 2.2.2. Features and Scaling

- -
- ANN
_{H}: A one-feature ANN such as the feature is the hourly values of SSM. - -
- ANN
_{D}: A one-feature ANN such as the feature is the daily mean values of SSM. - -
- ANN
_{RAV}: A three-feature ANN such as the three features is the SSM backward rolling average values over 10, 30, and 90 days.

- -
- SSCA (Standard scaling): Standard scaling or Z-score normalization transforms the distribution of a dataset such that the mean and standard deviation of the observations are 0 and 1, respectively, using Equation (2):

_{norm}is the normalized data, x is the input, $\overline{\mathrm{x}}$ is the mean, and σ

_{x}is the standard deviation of the input data [32].

- -
- MMSCA (MinMax scaling): This scaling scheme constrains the range of each input feature or each output of a neural network. This is usually performed by rescaling the features or outputs from one range of values to a new range of values. Generally, the features are rescaled to lie within a range of 0 to 1 or from −1 to 1. The rescaling is often accomplished by using a linear interpolation formula such as [34]:

_{target}and min

_{target}are the new maximum and minimum values, respectively, and max

_{value}and min

_{value}are the original maximum and minimum values of the input data, respectively.

#### 2.2.3. Training and Test Configuration

- -
- ANN-TOT refers to a training/test approach where 70% of the whole global dataset (70% of the stations of all networks) forms the training set, the remaining 30% of the global dataset consists of a validation set, and the test set is made up of the whole dataset.
- -
- ANN-Net
_{i}refers to a training/test approach where 70% of the values belonging to the stations of a given network (Net_{i}) form the training set, the remaining 30% of values remaining in Net_{i}serve as a validation set, and the test set is made up of the whole dataset. - -
- ANN-(TOT-Net
_{i}) refers to a training/test approach where 70% of the whole global dataset minus the values of a given network (Net_{i}) form the training set, the remaining 30% of the global dataset minus measurements of Net_{i}serve as a validation set, and the test set is made up of the whole dataset.

#### 2.2.4. Performance Indicators

#### Individual Station Performance Metrics

#### Skill Indices

_{i}are assessed through a coefficient termed TranI

_{Neti}(Transferability Index)

**,**which is based on the correlation values yielded by each test network (Net

_{j}) (Equation (5)).

_{i}) are compared with those yielded by ANN-TOT. Consequently, we computed the coefficient ContI

_{Neti}(Contribution Index) (Equation (6)).

#### 2.2.5. Data Filtering

_{th}quantiles of the correlation values yielded by each test station using the ANN-TOT approach. Once the training/test process is over and the performance metrics for each station are retrieved, a loop runs through the stations one by one and selects those whose correlation is less than the q

_{th}quantile of correlation. The training/test process is then reconducted such as the training set is made up of 70% of the non-eliminated stations, the validation set is made up of the remaining 30% of the non-eliminated stations, and the test set is formed by both eliminated and non-eliminated stations. This operation is repeated q times. This new training/test approach is hereafter referred to as ANN-TOT-Qual-Stat (“Qual” represents quality since this method aims to improve the quality of results).

## 3. Results and Discussion

#### 3.1. Impact of Scaling

^{3}/m

^{3}). This confirms the statement that the application of preprocessing transformations to the input data is always profitable in practice before presenting data to the neural network [37] and that scaling techniques enhance the reliability of the trained network [38]. The outputs are likewise post-processed to obtain the required output values. It is, then, more relevant to only compare MMSCA with SSCA.

- -
- Bias is considerably reduced with the application of SSCA. This is expected, as the SSCA method by construction tends to eliminate bias. These values ranged between −0.002 and 0.002 m
^{3}/m^{3}for SSCA, whereas MMSCA yielded bias values between −0.105 and 0.196 m^{3}/m^{3}. - -
- Correlation values are quite similar for the two scaling methods. An insignificant difference of less than 0.001 for correlation values is obtained by MMSCA and SSCA for approximately 60% of the stations (206 stations). Approximately 52% of the stations (181 stations) have higher correlation values with SSCA, approximately 6% of the stations (23 stations) have the same correlation values for both scaling methods, and the remaining stations (142 stations) have higher correlation values with MMSCA.
- -
- RMSE values are also improved with SSCA in comparison with MMSCA mainly due to the enhancement of bias correction. Approximately 87% of the stations (302 stations) show lower RMSE values with SSCA, approximately 7% of the stations (25 stations) have invariable RMSE values, and the remaining stations (19 stations) have better RMSE values with MMSCA. The maximum decrease (and thus, improvement) in RMSE is recorded for the “Reynolds Homestead” station (“SCAN” network) with SSCA such that the decrease is equal to 0.145 m
^{3}/m^{3}. RMSE values yielded by SSCA and no scaling are consistent with previous results advanced in [27] for RZSM estimates at a depth of 50 cm in the case of the “SCAN” network. Actually, the authors in [27] used linear rescaling to compare ANN-simulated soil moisture (generated by SMOS data) to the reference datasets (GLDAS-1/Noah output). The ANN-simulated RZSM values were bias-corrected to match the mean and standard deviation of the reference set. The authors in [27] obtained a mean RMSE of 0.054 m^{3}/m^{3}following bias correction against a mean RMSE of 0.082 m^{3}/m^{3}without bias correction. In our case, for the network “SCAN”, SSCA gives a mean RMSE equal to 0.042 m^{3}/m^{3}against a mean RMSE of 0.090 m^{3}/m^{3}without scaling. For SSCA, RMSE is equal to the unbiased root mean square error (ubRMSE) since bias is eliminated by construction. In fact, the relation between these two metrics is as follows:

- -
- NSE values are drastically improved when the SSCA is applied. Approximately 91% of the stations (315 stations) have better NSE values. The best improvements are recorded for stations “PrairieView#1” and “GuilarteForest”, which belong to the network “SCAN”, such as NSE differences (SSCA-MMSCA), which are equal to 86.827 and 85.483, respectively. The difference in behavior between correlation and NSE can be explained by the fact that NSE is a function of RMSE (Equation (8)). Given that RMSE is considerably reduced for most stations with SSCA, NSE is improved.

#### 3.2. Impact of the Temporal Information

_{RAV}) (Figure 7). The mean correlation is equal to 0.509, 0.511, and 0.561 with the hourly, daily mean, and rolling average SSM values, respectively. Similarly, the mean NSE is equal to 0.260, 0.263, and 0.325, and the mean RMSE is equal to 0.0392, 0.0391, and 0.0359 m

^{3}/m

^{3}with the hourly, daily mean, and rolling average SSM values, respectively. In light of the results above, the backward rolling average approach (ANN

_{RAV}) is adopted for the rest of the paper.

#### 3.3. Impact of the Training Approach

_{i}, which corresponds to training over one network. Table 2 presents the TranI

_{Neti}values as introduced in Section 2.2.4. Columns indicate the training approach, and rows specify the network on which the test was done. A positive cell value means that ANN-Net

_{i}outperforms ANN-TOT and vice versa for negative values.

_{i}is that the latter gives slightly better results when the test network is Net

_{i}, i.e., the model works better for a given network when the training is solely processed on that network. The positive TranI

_{Neti}coefficients displayed in the diagonal element of Table 2 demonstrate that.

_{i}performs worse than ANN-TOT for the Net

_{j}test network and vice versa (ANN-Net

_{j}performs worse than ANN-TOT for test network Net

_{i}). If we separately consider the “OZNET” and “FR-Aqui” test networks, we see that ANN-TOT gives better correlation values than ANN-FR-Aqui and ANN-OZNET. Actually, the FR-Aqui network is situated in southwestern France (Figure 1), and its sites cover “the Les Landes“ forest of the Bordeaux-Aquitaine region with one additional site (Parcmeteo) in Bordeaux city. The soil texture in the “Les Landes” forest is mainly sandy and characterized by the presence of dark organic matter to a depth of 30 cm. The “OZNET” network lies within the Murrumbidgee River Catchment in Australia. The soil texture in the top layer is predominantly silty loam, loamy sand, and sandy loam. The study area of network “OZNET” covers farms of flood irrigation and dryland cropping (Coleambally Irrigation Area (CIA)) and pastures of grazing.

_{i}) setups are presented. The aim of ContI is to help assess the potential influence of a given network Net

_{i}. Table 3 presents the ContI values as introduced in Section 2.2.4. Columns indicate the training approach, and rows specify the network on which the test was performed. A positive cell value indicates that ANN-(TOT-Net

_{i}) outperforms ANN-TOT and vice versa for negative values. The first observation that can be drawn from Table 3 is the positive impact the extraction of the “SCAN” network from the training process would have on all of the test networks except for “OZNET” (loss of −0.13% against ANN-TOT) and “SCAN” (loss of −0.53% against ANN-TOT). This is an interesting case study since “SCAN” is the densest network (Table 1). The negative impact induced by the elimination of the “SCAN” network from the training process on the “OZNET” network can be explained by the climate classification of the stations of both networks. Actually, 7 stations of the “OZNET” network have a common climate class (“cfa”) with approximately 30% of the stations of the “SCAN” network (66 stations). The remaining 12 stations of the “OZNET” network share the climate class (“Bsk”) with approximately 20% of the stations of the “SCAN” network (41 stations).

#### 3.4. Data Filtering

_{th}quantiles of the correlation vector given by the test stations when ANN-TOT is adopted. Table 4 presents the number of eliminated stations (ES) and non-eliminated stations (NES) in accordance with the value of q.

_{th}quantile. Figure 12 shows that the poorest performances (negative NSE and negative correlation values) are recorded for the stations that were eliminated from the training process (regardless of q). Such a result is expected. More importantly, for the non-eliminated stations, q value 0.1 yields better performance metrics than the rest of q values until the level where the correlation is equal to 0.5 and NSE is equal to 0. Beyond that level, q values yield quite similar performance metrics with a slight enhancement for q = 0.9 (a maximum correlation of 0.963 against 0.955 with q = 0.9 and q = 0.1, respectively, and a maximum NSE of 0.922 against 0.809 for q = 0.9 and q = 0.1, respectively). The maximum correlation value is recorded for the station “Nalohou-Mid” (“AMMA-CATCH” network) with both q = 0.9 and q = 0.1. The correlation value yielded for the same station before the application of this data filtering technique is equal to 0.856. Similarly, the maximum NSE value is obtained by the station “Nalohou-Mid” with both q values, whereas it is equal to 0.593 before the application of the data filtering method. This station has a tropical savanna climate and is characterized by strong seasonal dynamics that the ANN model manages to capture.

_{th}quantile. Of the non-eliminated stations, 60.98% (q = 0.4) to 73.68% (q = 0.9) show better correlation values. A total of 67.85% (q = 0.1) to 100% (q = 0.9) of the non-eliminated stations give better NSE values, and 39.94% (q = 0.1) to 100% (q = 0.9) yield better RMSE.

#### 3.5. Impact of Climate and Soil Texture

_{m}) from the in situ SSM of the SMOSREX network in France and the SIM model outputs. The seasonal and interannual variability of SWI

_{m}were also captured after the optimization of the characteristic time length of the filter (T

_{opt}). Reference [6] found that over the tested sites, no link could be established between soil texture and the characteristic time length T and highlighted that there is a potential climatic effect that may exist but requires further investigation. The exponential model can be assimilated in fluid mechanics to apply mass conservation equations to an emptying bucket with a transfer function. Alternatively, the ANN does not require assumptions on the model structure (non-linearity is addressed by increasing the complexity of the Neural Network), and because of this, it can be considered more suitable to study its transferability. On the other hand, CDF matching [45] and ANN [27,42] are two statistical methods that have been used to derive RZSM from SSM. While CDF matching determines the RZSM from SSM by correcting the SSM probability density function to match the observed RZSM, ANNs do not require a priori knowledge of probabilities. As such, they provide a more general framework and the trained ANN model can be applied outside of the training dataset. However, they have some drawbacks as they require a larger dataset than CDF matching to determine the network weighting coefficients. If not available, a risk of overfitting can exist. In the current study, this risk is not present considering the large number of available SSM and RZSM datasets. Nonetheless, as shown in this paper, the results cannot be completely generalized in areas of high evaporation, for instance. Figure 13a also presents the performance for the “Dfa” class, which covers northern areas characterized by harsh cold winters. The presence of frost events may explain a weaker link between SSM and RZSM and thus, weaker correlations. Reference [35] obtained low average correlation values between the different LSM products in high northern latitudes and explained that by the differences in the parameterization of snow and frozen soil for each product. Overall, the performances across climate conditions obtained in our paper are coherent with the results over the continental United States in [27]. In fact, the authors in [27] developed several ANN models to retrieve RZSM at depths of 20 and 50 cm using data from sites located in the continental United States. Each ANN model used a combination of soil texture, SSM, and cumulative values of air temperature, surface soil temperature, rainfall, and snowfall for the input features. Reference [27] confirmed that the retained soil moisture sites could not be considered representative of all soil and climate conditions at a global scale and showed that the ANNs were effective at retrieving RZSM at a depth of 20 cm with a correlation coefficient above 0.7 in most cases, whereas they were less effective at predicting RZSM at 50 cm. This can be explained by surface–subsurface decoupling. Reference [41,46] showed that for a given surface zone depth, the deeper the profile is, the less the correlation between surface and profile soil moisture. Reference [47,48] also confirmed that this surface–subsurface decoupling, controlled by the soil’s hydraulic properties, may occur in coarse-textured and stratified soils as well as dry conditions. Reference [6] also showed that soil depth or thickness is the main factor impacting RZSM retrieval. This exposes a second limitation in addition to the impact of evapotranspiration mentioned above. Figure 13b shows that the low clay fractions present a larger dispersion of correlation in comparison with percentages greater than 30%. In our case, the result can be explained by the small number of stations having such clay percentages. In general, no direct relation between soil texture and model performances can be concluded, which is in agreement with [6].

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Brocca, L.; Ciabatta, L.; Massari, C.; Camici, S.; Tarpanelli, A. Soil Moisture for Hydrological Applications: Open questions and New Opportunities. Water
**2017**, 9, 140. [Google Scholar] [CrossRef] - Dorigo, W.A.; Wagner, W.; Hohensinn, R.; Hahn, S.; Paulik, C.; Xaver, A.; Gruber, A.; Drusch, M.; Mecklenburg, S.; van Oevelen, P.; et al. The International Soil Moisture Network: A data hosting facility for global in situ soil moisture measurements. Hydrol. Earth Syst. Sci.
**2011**, 15, 1675–1698. [Google Scholar] [CrossRef] [Green Version] - Haubrock, S.-N.; Chabrillat, S.; Lemmnitz, C.; Kaufmann, H. Surface soil moisture quantification models from reflectance data under field conditions. Int. J. Remote Sens.
**2008**, 29, 3–29. [Google Scholar] [CrossRef] - Mladenova, I.E.; Bolten, J.D.; Crow, W.; Sazib, N.; Reynolds, C. Agricultural Drought Monitoring via the Assimilation of SMAP Soil Moisture Retrievals Into a Global Soil Water Balance Model. Front. Big Data
**2020**, 3, 10. [Google Scholar] [CrossRef] [Green Version] - Manfreda, S.; Brocca, L.; Moramarco, T.; Melone, F.; Sheffield, J. A physically based approach for the estimation of root-zone soil moisture from surface measurements. Hydrol. Earth Syst. Sci.
**2014**, 18, 1199–1212. [Google Scholar] [CrossRef] [Green Version] - Albergel, C.; Rüdiger, C.; Pellarin, T.; Calvet, J.-C.; Fritz, N.; Froissard, F.; Suquia, D.; Petitpa, A.; Piguet, B.; Martin, E. From near-surface to root-zone soil moisture using an exponential filter: An assessment of the method based on in-situ observations and model simulations. Hydrol. Earth Syst. Sci.
**2008**, 12, 1323–1337. [Google Scholar] [CrossRef] [Green Version] - Gao, X.; Wu, P.; Zhao, X.; Zhang, B.; Wang, J.; Shi, Y. Estimating the spatial means and variability of root-zone soil moisture in gullies using measurements from nearby uplands. J. Hydrol.
**2013**, 476, 28–41. [Google Scholar] [CrossRef] - Han, E.; Merwade, V.; Heathman, G.C. Application of data assimilation with the Root Zone Water Quality Model for soil moisture profile estimation in the upper Cedar Creek, Indiana. Hydrol. Process.
**2012**, 26, 1707–1719. [Google Scholar] [CrossRef] - Lekshmi, S.U.S.; Singh, D.N.; Baghini, M.S. A critical review of soil moisture measurement. Measurement
**2014**, 54, 92–105. [Google Scholar] - Kerr, Y.H.; Waldteufel, P.; Wigneron, J.-P.; Delwart, S.; Cabot, F.; Boutin, J.; Escorihuela, M.-J.; Font, J.; Reul, N.; Gruhier, C.; et al. The SMOS Mission: New Tool for Monitoring Key Elements of the Global Water Cycle. Proc. IEEE
**2010**, 98, 666–687. [Google Scholar] [CrossRef] [Green Version] - Entekhabi, D.; Njoku, E.G.; O’Neill, P.E.; Kellogg, K.H.; Crow, W.T.; Edelstein, W.N.; Entin, J.K.; Goodman, S.D.; Jackson, T.J.; Johnson, J.; et al. The Soil Moisture Active Passive (SMAP) Mission. Proc. IEEE
**2010**, 98, 704–716. [Google Scholar] [CrossRef] - Owe, M.; de Jeu, R.; Holmes, T. Multisensor historical climatology of satellite-derived global land surface moisture. J. Geophys. Res. Earth Surf.
**2008**, 113. [Google Scholar] [CrossRef] - Wagner, W.; Hahn, S.; Kidd, R.; Melzer, T.; Bartalis, Z.; Hasenauer, S.; Figa-Saldaña, J.; de Rosnay, P.; Jann, A.; Schneider, S.; et al. The ASCAT Soil Moisture Product: A Review of its Specifications, Validation Results, and Emerging Applications. Metz
**2013**, 22, 5–33. [Google Scholar] [CrossRef] [Green Version] - Ceballos, A.; Scipal, K.; Wagner, W.; Martínez-Fernández, J. Validation of ERS scatterometer-derived soil moisture data in the central part of the Duero Basin, Spain. Hydrol. Process.
**2005**, 19, 1549–1566. [Google Scholar] [CrossRef] - Wagner, W.; Naeimi, V.; Scipal, K.; de Jeu, R.; Martínez-Fernández, J. Soil moisture from operational meteorological satellites. Hydrogeol. J.
**2007**, 15, 121–131. [Google Scholar] [CrossRef] - Wagner, W.; Blöschl, G.; Pampaloni, P.; Calvet, J.-C.; Bizzarri, B.; Wigneron, J.-P.; Kerr, Y. Operational readiness of microwave remote sensing of soil moisture for hydrologic applications. Hydrol. Res.
**2007**, 38, 1–20. [Google Scholar] [CrossRef] - Sabater, J.M.; Jarlan, L.; Calvet, J.-C.; Bouyssel, F.; De Rosnay, P. From Near-Surface to Root-Zone Soil Moisture Using Different Assimilation Techniques. J. Hydrometeor.
**2007**, 8, 194–206. [Google Scholar] [CrossRef] - Masson, V.; Le Moigne, P.; Martin, E.; Faroux, S.; Alias, A.; Alkama, R.; Belamari, S.; Barbu, A.; Boone, A.; Bouyssel, F.; et al. The SURFEXv7.2 land and ocean surface platform for coupled or offline simulation of earth surface variables and fluxes. Geosci. Model Dev.
**2013**, 6, 929–960. [Google Scholar] [CrossRef] [Green Version] - Noilhan, J.; Mahfouf, J.-F. The ISBA land surface parameterisation scheme. Glob. Planet. Chang.
**1996**, 13, 145–159. [Google Scholar] [CrossRef] - Oleson, W.; Lawrence, M.; Bonan, B.; Flanner, G.; Kluzek, E.; Lawrence, J.; Levis, S.; Swenson, C.; Thornton, E.; Dai, A.; et al. Technical Description of version 4.0 of the Community Land Model (CLM); NCAR: Boulder, CO, USA, 2010. [Google Scholar] [CrossRef]
- Raes, D.; Steduto, P.; Hsiao, T.C.; Fereres, E. AquaCrop—The FAO Crop Model to Simulate Yield Response to Water: II. Main Algorithms and Software Description. Agron. J.
**2009**, 101, 438–447. [Google Scholar] [CrossRef] [Green Version] - Battude, M.; Al Bitar, A.; Brut, A.; Tallec, T.; Huc, M.; Cros, J.; Weber, J.-J.; Lhuissier, L.; Simonneaux, V.; Demarez, V. Modeling water needs and total irrigation depths of maize crop in the south west of France using high spatial and temporal resolution satellite imagery. Agric. Water Manag.
**2017**, 189, 123–136. [Google Scholar] [CrossRef] - Pleim, J.E.; Xiu, A. Development of a Land Surface Model. Part II: Data Assimilation. J. Appl. Meteor.
**2003**, 42, 1811–1822. [Google Scholar] [CrossRef] [Green Version] - Tanty, R.; Desmukh, T.S. MANIT BHOPAL Application of Artificial Neural Network in Hydrology—A Review. IJERT
**2015**, V4, IJERTV4IS060247. [Google Scholar] [CrossRef] - Elshorbagy, A.; Parasuraman, K. On the relevance of using artificial neural networks for estimating soil moisture content. J. Hydrol.
**2008**, 362, 1–18. [Google Scholar] [CrossRef] - Kolassa, J.; Reichle, R.H.; Liu, Q.; Alemohammad, S.H.; Gentine, P.; Aida, K.; Asanuma, J.; Bircher, S.; Caldwell, T.; Colliander, A.; et al. Estimating surface soil moisture from SMAP observations using a Neural Network technique. Remote Sens. Environ.
**2018**, 204, 43–59. [Google Scholar] [CrossRef] [PubMed] - Pan, X.; Kornelsen, K.C.; Coulibaly, P. Estimating Root Zone Soil Moisture at Continental Scale Using Neural Networks. J. Am. Water Resour. Assoc.
**2017**, 53, 220–237. [Google Scholar] [CrossRef] - Peel, M.C.; Finlayson, B.L.; McMahon, T.A. Updated world map of the Köppen-Geiger climate classification. Hydrol. Earth Syst. Sci.
**2007**, 11, 1633–1644. [Google Scholar] [CrossRef] [Green Version] - Ramchoun, H.; Amine, M.; Idrissi, J.; Ghanou, Y.; Ettaouil, M. Multilayer Perceptron: Architecture Optimization and Training. IJIMAI
**2016**, 4, 26. [Google Scholar] [CrossRef] - Oyebode, O.; Stretch, D. Neural network modeling of hydrological systems: A review of implementation techniques. Nat. Resour. Modeling
**2019**, 32, e12189. [Google Scholar] [CrossRef] [Green Version] - Heaton, J. Introduction to Neural Networks with Java; Heaton Research, Inc.: St. Louis, MO, USA, 2008; ISBN 9781604390087. [Google Scholar]
- Chai, S.-S.; Walker, J.; Makarynskyy, O.; Kuhn, M.; Veenendaal, B.; West, G. Use of Soil Moisture Variability in Artificial Neural Network Retrieval of Soil Moisture. Remote Sens.
**2009**, 2, 166–190. [Google Scholar] [CrossRef] [Green Version] - Yonaba, H.; Anctil, F.; Fortin, V. Comparing Sigmoid Transfer Functions for Neural Network Multistep Ahead Streamflow Forecasting. J. Hydrol. Eng.
**2010**, 15, 275–283. [Google Scholar] [CrossRef] - Bishop, C.M.; Bishop, P. Neural Networks for Pattern Recognition; Clarendon Press: Oxford, UK, 1995; ISBN 9780198538646. [Google Scholar]
- Koster, R.D.; Guo, Z.; Yang, R.; Dirmeyer, P.A.; Mitchell, K.; Puma, M.J. On the Nature of Soil Moisture in Land Surface Models. J. Clim.
**2009**, 22, 4322–4335. [Google Scholar] [CrossRef] [Green Version] - Crow, W.T.; Miralles, D.G.; Cosh, M.H. A Quasi-Global Evaluation System for Satellite-Based Surface Soil Moisture Retrievals. IEEE Trans. Geosci. Remote Sens.
**2010**, 48, 2516–2527. [Google Scholar] [CrossRef] - Priddy, K.L.; Keller, P.E. Artificial Neural Networks: An Introduction; SPIE Press: Bellingham, WA, USA, 2005; ISBN 9780819459879. [Google Scholar]
- Jayalakshmi, T.; Santhakumaran, A. Statistical Normalization and Back Propagation for Classification. IJCTE
**2011**, 89–93. [Google Scholar] [CrossRef] - Dabrowska-Zielinska, K.; Musial, J.; Malinska, A.; Budzynska, M.; Gurdak, R.; Kiryla, W.; Bartold, M.; Grzybowski, P. Soil Moisture in the Biebrza Wetlands Retrieved from Sentinel-1 Imagery. Remote Sens.
**2018**, 10, 1979. [Google Scholar] [CrossRef] [Green Version] - Dorigo, W.A.; Xaver, A.; Vreugdenhil, M.; Gruber, A.; Hegyiová, A.; Sanchis-Dufau, A.D.; Zamojski, D.; Cordes, C.; Wagner, W.; Drusch, M. Global Automated Quality Control of In Situ Soil Moisture Data from the International Soil Moisture Network. Vadose Zone J.
**2013**, 12, vzj2012.0097. [Google Scholar] [CrossRef] - Jackson, T.J.; Hawley, M.E.; O’Neill, P.E. Preplanting Soil Moisture Using Passive Microwave Sensors1. Jawra J. Am. Water Resour. Assoc.
**1987**, 23, 11–19. [Google Scholar] [CrossRef] - Kornelsen, K.C.; Coulibaly, P. Root-zone soil moisture estimation using data-driven methods. Water Resour. Res.
**2014**, 50, 2946–2962. [Google Scholar] [CrossRef] - Wagner, W.; Lemoine, G.; Rott, H. A Method for Estimating Soil Moisture from ERS Scatterometer and Soil Data. Remote Sens. Environ.
**1999**, 70, 191–207. [Google Scholar] [CrossRef] - Stroud, P.D. A Recursive Exponential Filter For Time-Sensitive Data; Los Alamos National Laboratory: Los Alamos, Mexico, 1999.
- Gao, X.; Zhao, X.; Brocca, L.; Pan, D.; Wu, P. Testing of observation operators designed to estimate profile soil moisture from surface measurements. Hydrol. Process.
**2019**, 33, 575–584. [Google Scholar] [CrossRef] - Arya, L.M.; Richter, J.C.; Paris, J.F. Estimating profile water storage from surface zone soil moisture measurements under bare field conditions. Water Resour. Res.
**1983**, 19, 403–412. [Google Scholar] [CrossRef] - Walker, J.P.; Willgoose, G.R.; Kalma, J.D. Three-dimensional soil moisture profile retrieval by assimilation of near-surface measurements: Simplified Kalman filter covariance forecasting and field application. Water Resour. Res.
**2002**, 38, 37-1–37-13. [Google Scholar] [CrossRef] [Green Version] - Hirschi, M.; Mueller, B.; Dorigo, W.; Seneviratne, S.I. Using remotely sensed soil moisture for land–atmosphere coupling diagnostics: The role of surface vs. root-zone soil moisture variability. Remote Sens. Environ.
**2014**, 154, 246–252. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**The International Soil Moisture Network (ISMN) network distribution (adapted from the ISMN web data portal, scale 1 cm:1000 km).

**Figure 2.**Clay/sand percentages for all of the stations. (

**a**) Clay/sand percentages for the depth interval [0, 30 cm]. (

**b**) Clay/sand percentages for the depth interval [30, 100 cm].

**Figure 3.**Climate class repartition for the SM stations (the color code is the same as that used in the updated world map of the Köppen–Geiger climate classification [28]).

**Figure 5.**In situ SSM, in situ RZSM, and predicted RZSM times series. (

**a**) Station “Hillan2” (“FR-Aqui”). (

**b**) Station “Lezignan-Corbieres” (“SMOSMANIA”).

**Figure 6.**Performance metrics for all of the stations with the different scaling schemes; blue—MMSCA; red—SSCA; green—no scaling (training approach: ANN-TOT). (

**a**) Bias. (

**b**) Correlation. (

**c**) NSE (Nash–Sutcliffe efficiency; NSE values less than 10 were replaced by −10 for better readability). (

**d**) RMSE.

**Figure 7.**Correlation and NSE scatter plots (training approach: ANN-TOT); blue cross—ANN

_{H}; red star—ANN

_{D}; green circle—ANN

_{RAV.}

**Figure 8.**Performance metrics for the stations of the “OZNET” network with the different training approaches. (

**a**) Correlation. (

**b**) NSE.

**Figure 9.**Performance metrics for the “SCAN” test network with ANN-TOT, ANN-SCAN, and ANN-(TOT-SCAN). (

**a**) Correlation. (

**b**) NSE.

**Figure 11.**Correlation and NSE scatter plots. Blue circle—before the elimination of the “SCAN” network; red star—after eliminating the “SCAN” network.

**Figure 13.**Correlation boxplots after the application of the data filtering technique (q = 0.65) with respect to climate classes (

**a**) and subsurface soil clay percentage (

**b**).

Network | Country | Number of Selected Stations | Selected RZSM Depth (cm) | SM Sensors | Length of Record (Hourly) |
---|---|---|---|---|---|

AMMA-CATCH | Benin, Niger | 5 (3 in Benin +2 in Niger) | 40 | CS616 | 191,997 |

BIEBRZA-S-1 | Poland | 3 | 50 | GS-3 | 11,401 |

CTP-SMTMN | China | 54 | 40 | EC-TM/5TM | 716,139 |

HOBE | Denmark | 29 | 55 | Decagon-5TE | 819,591 |

FR-Aqui | France | 5 | 30, 34, 50 | ThetaProbe ML2X | 200,087 |

OZNET | Australia | 19 | 30 | Hydra Probe-CS616 | 519,938 |

SCAN | USA | 209 | 50 | Hydraprobe-Sdi-12/Ana | 6,777,222 |

SMOSMANIA | France | 22 | 30 | ThetaProbe ML2X | 818,031 |

Training Test | ANN-AMMA-CATCH | ANN-BIEBRZA-S-1 | ANN-CTP-SMTMN | ANN-FR-Aqui | ANN-HOBE | ANN-OZNET | ANN-SCAN | ANN-SMOSMANIA |
---|---|---|---|---|---|---|---|---|

AMMA-CATCH | +1.12% | +0.10% | +0.61% | +0.61% | 0% | 0% | −1.02% | +0.51% |

BIEBRZA-S-1 | −0.66% | +3.53% | −2.21% | −0.55% | −0.55% | −3.31% | −1.88% | +0.99% |

CTP-SMTMN | −0.88% | −3.62% | +0.77% | −0.33% | +0.33% | +0.11% | −0.99% | −0.21% |

FR-Aqui | +0.46% | −3.56% | −1.26% | +2.53% | −1.49% | −3.1% | −2.76% | −2.07% |

HOBE | −2.40% | −1.49% | −1.03% | −1.83% | +0.34% | −0.92% | −1.26% | −0.34% |

OZNET | −5.03% | −6.42% | −1.51% | −5.28% | −0.50% | +1.26% | −1.89% | −3.02% |

SCAN | −1.5% | −1.39% | −1.07% | −1.07% | −0.43% | −0.64% | +0.11% | −1.28% |

SMOSMANIA | +0.57% | −1.82% | +0.11% | −0.57% | +1.82% | −1.25% | −3.65% | +3.53% |

Training Test | ANN-(TOT- AMMA-CATCH) | ANN-(TOT-BIEBRZA-S-1) | ANN-(TOT-CTP-SMTMN) | ANN-(TOT- FR-Aqui) | ANN-(TOT- HOBE) | ANN-(TOT- OZNET) | ANN-(TOT- SCAN) | ANN-(TOT- SMOSMANIA) |
---|---|---|---|---|---|---|---|---|

AMMA-CATCH | −0.20% | −0.10% | −0.31% | −0.20% | 0% | 0% | 0.92% | 0% |

BIEBRZA-S-1 | −0.44% | −0.44% | −0.66% | −0.22% | −0.44% | −0.33% | −0.33% | −0.11% |

CTP-SMTMN | 0% | 0% | −0.33% | 0.11% | 0% | 0% | 0.66% | 0.22% |

FR-Aqui | −0.46% | −0.35% | −0.46% | −0.58% | −0.12% | −0.12% | 1.61% | −0.12% |

HOBE | −0.11% | −0.11% | −0.23% | −0.11% | −0.23% | −0.11% | 0.34% | 0.11% |

OZNET | 0% | −0.13% | −0.38% | 0% | −0.13% | −0.38% | −0.13% | 0.25% |

SCAN | 0% | 0% | 0.11% | 0% | 0% | 0% | −0.53% | 0% |

SMOSMANIA | −0.12% | −0.23% | −0.81% | 0% | 0% | 0.12% | 2.77% | 0.69% |

**Table 4.**Number of eliminated stations (ES) and non-eliminated stations (NES) based on q

_{th}quantiles.

q | Number of ES | Number of NES |
---|---|---|

0.9 | 308 | 38 |

0.8 | 275 | 71 |

0.75 | 254 | 92 |

0.65 | 224 | 122 |

0.5 | 170 | 176 |

0.4 | 141 | 205 |

0.3 | 105 | 241 |

0.2 | 71 | 275 |

0.1 | 38 | 308 |

**Table 5.**Improvement rates in the individual performance metrics for the eliminated stations (ES) and non-eliminated stations (NES) based on the q

_{th}quantiles.

Q | Number of ES | Number of NES | Correlation | NSE | RMSE |
---|---|---|---|---|---|

0.9 | 308 | 38 | 48.7% of ES 73.68% of NES | 28.57% of ES 100% of NES | 34.41% of ES 100% of NES |

0.8 | 275 | 71 | 44.72% of ES 63.38% of NES | 26.18% of ES 97.18% of NES | 36.72% of ES 97.18% of NES |

0.75 | 254 | 92 | 47,24% of ES 70.65% of NES | 24.8% of ES 95.65% of NES | 17.71% of ES 88.04% of NES |

0.65 | 224 | 122 | 41.07% of ES 63.93% of NES | 19.19% of ES 88.53% of NES | 11.16% of ES 78.69% of NES |

0.5 | 170 | 176 | 47.06% of ES 66.48% of NES | 14.71% of ES 88.07% of NES | 10.59% of ES 73.86% of NES |

0.4 | 141 | 205 | 41.13% of ES 60.98% of NES | 14.18% of ES 78.05% NES | 7.09% of ES 63.41% of NES |

0.3 | 105 | 241 | 39.05% of ES 66.39% of NES | 13.33% of ES 78% of NES | 7.62% of ES 60.17% of NES |

0.2 | 71 | 275 | 25.35% of ES 60% of NES | 11.26% of ES 73.45% of NES | 0% of ES 50.18% of NES |

0.1 | 38 | 308 | 23.68% of ES 63.31% of NES | 13.16% of ES 67.85% of NES | 0% of ES 39.94% of NES |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Souissi, R.; Al Bitar, A.; Zribi, M.
Accuracy and Transferability of Artificial Neural Networks in Predicting in Situ Root-Zone Soil Moisture for Various Regions across the Globe. *Water* **2020**, *12*, 3109.
https://doi.org/10.3390/w12113109

**AMA Style**

Souissi R, Al Bitar A, Zribi M.
Accuracy and Transferability of Artificial Neural Networks in Predicting in Situ Root-Zone Soil Moisture for Various Regions across the Globe. *Water*. 2020; 12(11):3109.
https://doi.org/10.3390/w12113109

**Chicago/Turabian Style**

Souissi, Roïya, Ahmad Al Bitar, and Mehrez Zribi.
2020. "Accuracy and Transferability of Artificial Neural Networks in Predicting in Situ Root-Zone Soil Moisture for Various Regions across the Globe" *Water* 12, no. 11: 3109.
https://doi.org/10.3390/w12113109