Estimation of Soil Moisture Profile Using Wavelet Neural Networks

Ajla Kulaglic Agricultural and Environmental Informatics Research

Center Istanbul Technical University

Istanbul, Turkey kulaglic@itu.edu.tr

Burak Berk Üstündağ Agricultural and Environmental Informatics Research

Center Istanbul Technical University

Istanbul, Turkey berk@berk.tc

Abstract— The main purpose of the presented study is to examine the usability of a Wavelet Neural Network (WNN) model for soil moisture estimation. In this study, the wavelet transformations and neural networks have been employed to estimate the daily soil moisture. Collected data have been decomposed into wavelet sub-time series using Discrete Wavelet Transformation (DWT) with Haar mother wavelets. The sub-time series have been selected as the inputs of neural network for estimation performance. Decomposition is done on different type of data. At the same time, those decomposed sub-time series data are used like inputs to the Time-Delay Neural Network (TDNN). The selection of sub-time series has effect on the output data also. Soil moisture values at different depths are estimated using inverse discrete wavelet transformation (IDWT). DWT and IDWT are applied with the quadrature mirror filters of decomposition and synthesis filters. Also, it is shown that selection of sub-time series has impact on the neural network model’s performance. Consequently, the most appropriate wavelet-NN configuration is determined for each station which means of selecting the appropriate mother wavelet, number of scales and the neural network type. The main point, in WNN type configuration is the wavelet decomposition and usage of sub-time series as inputs of neural network. The results have been provided with the error metrics of the Root Mean Square Error (RMSE) and Coefficient of Efficiency (CE) by comparing the real and estimated values.

Keywords—TARBIL; soil mositure estimation, time-delay neural network, LANDSAT8; NDVI; synthetic NDVI; fractional vegetation cover; data fusion

I. INTRODUCTION Soil moisture represents dynamic land surface variables. It

demonstrates spatial variation as a function of vegetation, land use as well as topographic position [1,2]. On the other hand, soil moisture content is directly relevant to important parameters of agricultural applications. In order to find optimal irrigation schedule with respect to phenological requirements of the plant it is important to analyze soil moisture behavior. Due to rapid population growth, industrialization and economic development, available water resource have decreased from 4000m3 to 1500m3 level per capita/year within last 60years. As one of the countries with limited fresh water resources; 73.2% of total water supply Turkey uses for agricultural irrigation [3].

In this study, a Wavelet-Neural Network is presented for daily soil moisture estimation using wavelet time sub-series of meteorological variables.

Simple/multiple regression models were typical models that were used for forecasting statistical time series models [4 and 5]. These models assumed that data are stationary with ability to capture non-stationaries and non-linarites in meteorological data. Forecasting using a decomposition of data is more useful in providing information and forecasts regarding to component of a time series [5, 6, 7, and 8]. Decomposition approaches seek to decompose a time series into its major subcomponents [5]. Wavelet transformation represents useful decomposition method maintaining useful information in both the time and frequency domain. Wavelet transformation has shown their excellent performance in non-stationary signal analysis [5]. It provides useful decompositions of original time series so that wavelet transformed data improves the ability of a forecasting model.

Neural networks (NNs) also showed great ability for modeling and forecasting non-linear and non-stationary data. In recent years, neural networks (NNs) have been applied to a wide range of problems for estimations and have produced improved accuracy when compared to traditional statistical methods. [9,10,11,12,13]. The advantages of ANNs are reflected in (a) their ability to learn from examples which allows network to learn and adapt to changes, (b) their adaptability to represent change of problem environments, (c) not requiring a prior knowledge, (d) their inherent property of nonlinearity [5,12].

Collected data from TARBIL network have been decomposed into wavelet sub-time series using Discrete Wavelet Transformation (DWT). These time-series have constituted the inputs of neural network for estimation of soil moisture profile. Decomposition has been done on different type of data (precipitation, parcel based evapotranspiration, sNDVI, irrigation and soil moisture).

Decomposed inputs precipitation, irrigation, parcel based evapotranspiration are used together with sNDVI as inputs of a multiple-input time-delay neural network for soil moisture profile estimation at 15cm and 45cm depths. Proposed model can be performed through 4-layer time-delay neural network with observed and forecasted meteorological parameters as

part of inputs. Multiple-type time series data are used in one single time-delay neural network.

The paper is organizes as follows, after introduction study area and data preprocessing is explained. Wavelet transformation, neural network and used wavelet neural network is explained. At the end, result and conclusion are presented and explained.

II. MATERIALS AND METHODS

A. Study area The data have been provided from monitoring station

network of Turkish Agricultural Monitoring and Information Systems Project (TARBIL). Until today there are 300 available working stations installed next to agricultural fields. Agro-meteorological stations have sensors that collect meteorological parameters at different height levels up to 10m, soil moisture and temperature measurements, phenological parameters (biometric and spectral measurements) and digital images of the crop fields at different zoom rates. Agro-meteorological parameters together with digital images are recorded with sampling period ranging from 10 to 30 minutes. The most number of stations are located in Şanlıurfa, South-Eastern part of Turkey. The Şanlıurfa province has characteristics of typical arid and semi-arid continental climate. The Table I shows the mean monthly meteorological temperature and rain collected by Turkish State Meteorological Service [26] for the period 1954-2013.

B. Agro-meteorological data Meteorological data from observed stations were collected

and preprocessed. Cumulative precipitation and parcel based evapotranspiration are used as inputs of a multiple-input time-delay neural network. Evapotranspiration (ET) is computed using Peanman-Monteith method [15]. This method uses the daily mean temperature, wind speed, relative humidity and solar radiation to compute ET (1). The strong correlation among evapotranspiration and soil moisture is shown in [16].

)1((

)(

a

s

a

scan

rr

reeGR

ET

a

++Δ

−+−Δ=

γ

ρρλ (1)

where Rn represents the net radiation, G soil heat flux, (es-ea) vapor pressure deficit computed using (2) and (3), ρa is mean air density at constant pressure, cp specific heat on the air, (cp=1.005KJ/kg °C), ∆ represents saturation vapor pressure temperature relationship, γ is the psychometrics constant given by (5), rs is surface resistance and ra is aerodynamic resistances.

)23727.17

exp(*6108.0 += TT

se (2)

100* RHee sa = (3)

2)273(*4098

Tes

+=Δ (4)

λεγ

*)*( Pcp= (5)

In equation (3) RH represents relative humidity. P in (5) represent atmospheric pressure (P=101,3 kPa), cp specific heat, ε ratio between molecular weight for water vapor/dry air and λ is latent heat of vaporization given as a function of the air temperature (6).

)*014425.033517.15(1

T−=λ (6)

C. Synthetic NDVI Synthetic NDVI (sNDVI) values are generated based on

Fractional Vegetation Cover (FVC) extracted from digital images and NDVI data obtained from satellite images. The application is divided in two parts. First, we find the right model and second, the temporal gaps between acquired images are filled.

FVC extraction is done as described in the method proposed in [17]. Red (R), Green (G) and Blue (B) bands are transformed to Hue (H), Saturation (S) and Intensity (I) according to Castelman [18], where hue values correspond to green color are centered at 120°.

Normalized Difference Vegetation Index (NDVI) represent satellite-based index used to represent vegetation conditions. NDVI measurements and acquisition methods have been used to monitor vegetation and its changes [19, 20, 21, and 22]. It has been shown that NDVI indices are closely related to precipitation, temperature and soil moisture [23].

In presented study we used 11 LANDSAT8 images recorded over Şanliurfa province from April 2013 until October 2013 (Fig. 1). Acquisition dates of each image, together with its NDVI value of one used parcel are given in Table II. LANDSAT8 operates in the visible, near-infrared, short wave infrared and thermal infrared spectrum providing 30m multi-spectral spatial resolution images.

Images that cover the area of our interest are cloud free. Each pixel in the satellite image is converted to radiance using linear transformation (Eq. 10).

Gain

BiasDNRad Band

BandBandBand += (10)

whereas BandDN stands for the cell value digital number, BandBias is the bias value for a specific band and BandGain is the value for a specific band.

NDVI is defined as it is shown in equation (11) by contrasting visible and near-infrared bands.

RadRad

RadRad

REDNIRREDNIRNDVI

+−= (11)

Table I: Mean climate data in Şanlıurfa Province Şanlıurfa

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Long term average values (1954-2013)

Avg. temp.

(°C)

5.6 6.9 10.9 16.1 22.1 28.2 31.9 31.2 26.7 20.2 12.7 7.5

Avg. max.

Temp. (°C)

10.0 11.9 16.5 22.2 28.6 34.7 38.7 38.2 33.8 26.9 18.5 11.9

Avg. min.

temp.(°C)

2.2 2.9 6.1 10.5 15.5 20.8 24.3 24.0 20.0 14.7 8.4 4.1

Avg. sun. dur.

(hours)

4.1 5.1 6.2 7.5 10.1 12.2 12.3 11.3 10.1 8.6 5.5 4.0

Avg. # of

rainy days

12.3

11.2 10.9 9.6 6.7 1.6 0.3 0.2 0.9 5.0 8.1 11.3

Mont. rainfall (kg/m2)

87.3 71.0 62.7 48.5 28.9 3.8 0.7 0.8 2.6 25.2 45.9 81.6

Long term maximum and minimum temperature Max. temp. (°C)

21.6 22.7 29.5 36.4 40.0 44.0 46.8 46.2 42.0 37.0 29.4 26.0

Min. temp. (°C)

-8.0 -9.6 -7.3 -3.2 6.0 10.0 15.6 16.0 11.2 2.5 -2.7 -6.4

Satellite images from the previous year where used in this

study. The first image was acquired on 25th April 2013. Parcels mean NDVI values are extracted from available satellite images. Continuously recorded digital images are used to compute FVC of agricultural parcel. Parcel based FVC values are computed continuously, while parcel based NDVI values are computed when satellite image is available. Linear regression is used for modeling the relationship between parcel based NDVI and parcel based FVC values.

When new satellite image arrives, the parcel based NDVI values are computed and the proposed model is updated. As the number of satellite images increases the model is updated. The coefficient correlation R2 between FVC and NDVI, after using all available satellite images, is 0.98 and mean absolute error is 0.03.

In the Fig. 2 (X, Y, date, NDVI) represents mean NDVI values extracted from available satellite image of parcel (X,Y); while (Xi, Yi, t, FVC) represents fractional vegetation cover extracted from digital images of agricultural parcel (Xi, Yi); i refers to agricultural parcel (station number). (Xi,Yi) are elements of (X,Y).

D. Wavelet transformation Wavelet transformation demonstrates a good local

representation of signal in the time and frequency domain. Comparing with Fourier transformation where time information is lost, wavelet transformation represents more

effective mathematical tool. Wavelet transformations allow us to use long-time intervals for low frequency information and shorter intervals for high frequency information [5]. The wavelet transformation is defined as the sum over all time of the signal multiple by scale and shifted versions of wavelet function ψ

dxa

bxxfa

baW )()(1),(* −= ∫

+∞

∞−ψ (12)

Where a represents scale parameter, b position parameter and * correspond to the complex conjugate number. Computing wavelet coefficient at every possible scale generates a lot of data. Using discrete wavelet transformation (DWT), where dyadic scales and positions are chosen the analysis becomes more efficient and accurate [6].

Fig. 1 Data acquisition area used in this study

Table II Landsat 8 Images acquisition date and NDVI values for one selected parcel

Fig. 2 Synthetic NDVI generation model

Fig. 3 Wavelet sub-time series components

Collected data from TARBIL network have been decomposed into wavelet sub-time series using DWT with Haar mother wavelets. The time series passes through two filters and are decomposed into two wavelet sub-time series components (Fig. 3). The DWT converts a signal into father and mother wavelets. Father wavelets ((A) components) represent the high-scale, low frequency components. Mother wavelets ((D) components) are representations of the low-scale and high frequency components. The DWs has a distinct contribution to the original time series [6]. Decomposition is done on different type of data. At the same time, those decomposed sub-time series data are used like inputs to the Neural Network (NN) for estimation performance.

E. Artificial Neural Network Neural networks (NNs) approach provides solutions to the

problem based on input and output variables in a complex system. The main advantage of neural network is that they can

learn from examples which allows network to learn and adapt to changes [12, 24]. NNs may be described as a network of interconnected nodes (neurons). Number of neurons in the input and output layer of NN is specified by the problem to which network is constructed. In this study different types of data are applied together with their past values in a time window into a NN structure. The 4-layers neural network, with two hidden layers is constructed. Proposed neural network scheme is shown in Fig. 4.

F. Wavelet-Neural Network The main purpose of wavelet-NN is the estimation of daily

soil moisture profile using the sub-series components obtained using discrete wavelet transformation on input variables (Fig. 5). For this purpose, firstly original data are decomposed into discrete wavelets by DWT. Secondly; the DWs are selected as the inputs of NNs for the soil moisture estimation. The main idea in wavelet-NN model is the wavelet decomposition of the time series data and the application of the DWs as inputs of NN model.

Fig. 4 Time-delay neural network for data fusion

Fig. 5 The Wavelet-Neural Network model

Date NDVI

1 4/25/2013 0.266878

2 5/27/2013 0.14046

3 6/12/2013 0.14239

4 6/28/2013 0.14445

5 7/14/2013 0.21344

6 7/30/2013 0.31403

7 8/15/2013 0.34826

8 8/31/2013 0.31266

9 9/16/2013 0.28847

10 10/2/2013 0.24951

11 10/18/2013 0.28579

III. RESULTS The daily meteorological data are collected and evaluated

from the agro-meteorological stations placed next to the reference agricultural parcels. A 4-layer NN structure with two hidden layer is employed. In this study 4 different types of data are used together. Temporal ground measurement data together with remotely sensed spatial data are used to predict soil moisture profiles. Multiple-time series data and feedback from the past estimated values of the soil moisture at different depths are decomposed using DWT and used like inputs of the time delay neural network (TDNN). The architecture of the network consists of an input layer (precipitation, evapotranspiration, irrigation and sNDVI) and output layer of two neurons (corresponding to SM15 and SM45). Before employing the NNs, the selected input data were decomposed using DWT and divided into two sets; training and testing. A training set is used for constructing the neural network while testing set is used to estimate model performance in the network. Input data has significant impact on the obtained results of the trained network [25]. Training is performed using back-propagation training method.The network is trained with existing soil moisture values, the output values are for SM (t), while SM (t-T) is applied to the input. The 72hours meteorological data from observed agricultural parcels are collected with 24hours time-delay (T=24hours). After training is done and network is constructed, the trained model is validated. Test data are not used in training of the network. The study results show that soil moisture at levels of 15cm and 45cm can be obtained reasonably by using the proposed method. The obtained Root Mean Square Errors (RMSEs) (Eq. 13) for soil moisture at 15cm and 45cm for training sets are 8,89cb and 6,07cb;respectively. The RMSEs for testing set are 10,19cb and 9,41cb respectively.

∑=

−=n

iii XX

nRMSE

1

2)ˆ(1 (13)

Coefficient of efficiency (CE) (Eq. 14) describes the predictive accuracy of used model. For soil moisture estimation at 15cm CE is 98% for training set and testing set; and for soil moisture estimation at 45cm the CE is 98% for training set and 96% for testing set.

2

1

1

2

)ˆ(

)ˆ(1

XX

XXCE n

ii

n

iii

−

−−=∑

∑

=

= (14)

On the figures below (Fig. 6, Fig. 7) the soil moisture measured and estimated at 15cm and 45cm for training and testing data sets are presented.

(a)

(b)

Fig. 6 Soil moisture estimation for training set (a) at 15cm and (b) at 45cm

(a)

(b)

Fig. 7 Soil moisture estimation for test set (a) at 15cm and (b) at 45cm

IV. CONCLUSION A multiple parameter wavelet time-delay neural network is

used for estimation of soil moisture profile at different depths. The data has been trained by two different reference soil moisture references in proposed network scheme. The amount of depth could be increase (15cm, 30cm, 45cm, 60cm…etc.) by having related outputs. Synthetic NDVI model is constructed depending on linear relationship between digital images derived FVC and satellite images derived NDVI. sNDVI values together with meteorological data are decomposed and used as input of the 4-layer TDNN. Although soil type may have an impact on the soil moisture estimation, the vegetation indices such as FVC, green leaf area index,

sNDVI has positive addition to solution of spatial distribution of soil structure. Error rate, in the boundary of soil structure change, may require additional data in similar manner in order to limit parcel based error.

On the other hand, using decomposed input values the estimation of soil moisture become more accurate compared with results obtained from the original inputs [16]. The sub-series included in the network input layer bring a new perspective in the discussions about NNs.

We have shown that soil moisture estimation error at different depths is reduces when DWT is used. The results of daily soil moisture estimation data indicate that the performances of wavelet neural network models are more effective than the NN models.

Training data are chosen at locations from which we acquire both remote sensing data and temporal ground monitoring station data.

The proposed model can be used for estimation of soil moisture both in time and space where we do not have sensors during the long term operational phase. This model is intended to serve as additional method to obtain reliable values of soil moisture. The proposed data fusion method can be applied to past time-window for nowcasting of soil moisture at pre-trained depths.

V. REFERENCES [1] A. Iodice, A. Natale, D. Riccio, “Polarmetric Two-Scale Model for Soil

Moisture Retrieval via Dual-Pol HH-VV SAR Data, IEEE Journal of selected topics in applied earth observations and remote sensing, vol. 6, no. 3, June 2013

[2] W.Y. Chung, J.F. Villaverde, J. Tan, “Wireless Sensor Network Based Soil Moisture Monitoring System Design”, Position Papers of the 2013 Federated Conference on Computer Science and Information Systems pp.79-82

[3] http://www.climateadaptation.eu/turkey/fresh-water-resources/ last visit: 18.06.2014

[4] A. N. Flores, E. Istanbulluoglu, R. L. Bras, E. Entekhabi, “A framework for the prediction of soil moisture”, Department of Civil and Environmental Engineering, MIT, Cambridge

[5] T.W. Kim, J.B. Valdes, “Nonlinear Model for Drought Forecasting Based on a Conjunction of Wavelet Transforms and Neural Network, Journal of hydrologic engineering, 2003.8:319-328

[6] T. Parta, H.K. Cigizoglu, “Prediction of daily precipitation using wavelet-neural networks”, Hydrological Sciences Journal, 54:2, 234-246, DOI: 10.1623/hysj.54.2.234

[7] Z. Bashir, M. El-Hawary, “Short Term Load Forecasting by using Wavelet Neural Networks, 0-7803-5957-7/00, 2000 IEE, pp. 163-166

[8] C.Stolojescu, I. Railean, S. Moga, P. Lenca, A. Isar, “A Wavelet Based Prediction Method for Time Series”

[9] U. Okkan, “Wavelet neural network model for reservoir inflow prediction”, Scientia Iranica A (2012) 19(6), 1445-1455, doi:10.1016/j.scient.2012.10.009

[10] L.F. Ortega “A Neuro-wavelet Method for the Forecasting of Financial Time Series”, Proceedings of the World Congress on Engineering and Computer Science 2012 vol I WCECS 2012, October 24-26, 2012, San Francisco, USA

[11] Z.Y. Dong, B.L. Zahng, Q. Huang, “Adaptive Neural Network Short Term Load Forecasting with Wavelet Decompositions, 2001 IEEE Porto Power Tech Conference

[12] H. Han, P. Felker, “Estimation of daily soil water evaporation using an artificial neural network”, Journal of Arid Environments, 1997, 37:251-260

[13] H.K. Cigizoglu, “Estimation, forecasting and extrapolation of river flows by artificial neural networks, Hydrological Sciences Journal, 48:3, 349-361, DOI: 10.1623/hysj.48.3.349.45288

[14] T. Lakhankar, H. Ghedira, M. Temimi, M. Sengupta, R. Khanbilvardi, R. Blake, “Non-Parametric Methods for Soil Moisture Retrieval from Satellite Remote Sensing Data”, Remote Sensing 2009,1,3-21; doi:10.3390/rs1010003

[15] R. G. Allen, L. S. Pereira, D.Raes, M. Smith, “Crop Evapotranspiration Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage”, 1998, Paper 56

[16] A. Kulaglic, B.B. Üstündağ, S. Bagis, “Spatiotemporal Soil Moisture Estimation for Agricultural Drought Risk Management”, Agro-Geoinformatics, Second International Conference, 2013

[17] G. Pan, F. Li, G.Sun, “Digital camera based measurement of crop cover for wheat yield prediction”, Geoscience and Remote Sensing Symposium, 2007

[18] K. R. Castleman, “Digital Image Processing” Prentice-Hall, Upper Saddle River, NJ, 1999.

[19] J. H. Kastens, T. L. Kastens, D. L. Kastens, K. P. Price, E. A. Martinko, R. Y. Lee, “Image masking for crop yield forecasting using AVHRR NDVI time series imagery.” Remote Sensing of Environment, 99(3), 2005, pp. 341-356.

[20] G. Asrar, M. Fuchs, E. T. Kanemasu, J. L. Hatfield, “Estimating absorbed photosynthetic radiation and leaf area index from spectral reflectance in wheat” Agronomy journal , 76, 1984, pp. 300–306

[21] C. J. Tucker, "Red and photographic infrared linear combinations for monitoring vegetation", Remote sensing of Environment 8.2, 1979, pp.127-150.

[22] C. J. Tucker, C. L. Vanpraet, E. Boerwinkel, A. Gaston, “Satellite remote sensing of total dry matter production in the Senegales Sahel”, Remote Sensing of Environment 13, 1983, pp. 461-474

[23] J. Wang, P.M. Rich, K.P. Price “Temporal response of NDVI to precipitation and temperature to central Great Plains, USA”, International Journal of Remote Sensing, 24:11, 2003, pp. 2345-2364

[24] M. Mukhlisin, A. El-Shafie, M. R. Taha, “Regularized versus non-regularized neural network model for prediction of saturated soil-water content on weathered granite soil formation”, Neural Comput&Applic (2012) 21:543-553

[25] R.Z. Al-Saffar, S.I. Khattab, S.T. Yousif, “Prediction of Soil’s Compaction Parameter Using Artificial Neural Network”, Al-Rafidain Engineering, vol.21 no.3, June 2013,

[26] http://www.mgm.gov.tr/veridegerlendirme/il-ve-ilceler-

istatistik.aspx?m=SANLIURFA last visit: 02.07.2014