ARTIFICIAL NEURAL NETWORK (ANN) ESTIMATION OF SATURATED
HYDRAULIC CONDUCTIVITY
Wilson Agyei Agyare1, Soojin Park2 and Paul Vlek3
Introduction
Saturated hydraulic conductivity (Ks) among other soil
hydraulic properties are important for initializing climate and
hydrologic models. However, measuring Ks is time consuming
and expensive. Work done in the past to model Ks has been
limited to the use of empirical and physical relationships
referred to as pedotransfer functions (PTFs) and in recent
times Artificial Neural Networks (ANN). ANN is used as a
special class of PTFs to approximate any continuous (nonlinear) function (Pachepsky and Schaap, 2004).
The use of terrain attributes for modelling Ks may serve as a
suitable alternative, as terrain data are fairly easy to collect
compared to intensive soil sampling. The important question
is: will the inclusion of terrain attributes in estimating Ks
improve ANN model performance? Also, some of the
setbacks in the use of ANN are the issue of sensitivity and
amount of input parameter required to make a good estimate.
Study area: The study was carried out at two locations in the
Volta Basin of Ghana namely; Tamale (9°28’N and 0°55’W),
and Ejura (7°19’N and 1°16’W) (See Agyare, 2004).
0 .7
Different input data
Mean R2 value
for training data
Mean R2 value
for test data
0 .6
All parameters (A)
0.60a (0.019)
0.47a (0.020
0 .5
Ten (10) most sensitive parameters (B)
0.58a (0.015)
0.51a (0.022)
0.50a (0.021)
0.15b (0.023
0.07b (0.013
F-statistic (Significance)
85.1 (0.00)
92.0 (0.00)
ab
b
b
b
0 .4
2
Six (6) most sensitive continuous soil parameters (C) 0.56a (0.018)
Using only terrain parameters (D)
T rain in g a n d testin g d ata fro m sa m e site
T rain in g a n d testin g d ata fro m d iffe re n t sites
ab
a
0 .3
Training
Testing
curvature†,
0
10
20
30
Number of input parameters
Figure1A. Variation in R2 for Ks estimation with increasing number of
input parameters using ANN
0.55
B
0.50
R
2
0.45
Training
0.40
Testing
Linear (Training)
0.35
Log. (Testing)
0.30
0
200
400
600
800
1000
1200
Sample data size
Figure1B. ANN training data size effect on R2 for training and test
data for estimating Ks using combined data (Tamale + Ejura)
All parameters (A): Profile
plan curvature, curvature, elevation (m),
wetness index, upslope contribution area (m2), stream power index†, slope gradient
(°), LS factor†, Aspect† (°), pH, Bulk density†* (gcm-1), Organic carbon†* (%), CEC†*
(cmol(+)kg-1), Silt†* (%), Clay†* (%), Sand†* (%),site (Tamale or Ejura), gravel and/or
concretion, soil sampling depth (topsoil or subsoil), soil structural grade (strong),
structural type (sub-angular blocky), and structural size (course); with B and C
indicated by † and *
1CSIR-Savanna
Agricultural Research Institute, Tamale, Ghana
of Geography, Seoul National University, Shilim-Dong, Kwanak-Gu, Seoul, Korea
for Development research, University of Bonn, Bonn, Germany
2Department
0 .2
c
c
0 .1
0 .0
E ju ra to p s o il
E ju ra s u b s o il
T a m a le top so il T a m a le s u b s o il
S ite a n d d ep th o f sa m p lin g
Figure 2. Comparison of R2 for estimated Ks for different testing data
using training data from the same site and different site using ANN
Sensitivity analysis of ANN
Figure 1A depicts a rapid improvement in R2 for both training and testing data for the most
sensitive parameters. The increase then becomes gradual, with the training data attaining
a plateau, whereas with the testing data, R2 declines with additional input parameters.
The R2 for the training data linearly increases as an indication of the increasing ability to
train the ANN as the size of the input data is increased (Figure 1B). However, for the
testing data, the R2 increases at a decreasing rate. This trend indicates that after a certain
maximum training data size there will be no further increase in the ability to estimate.
ANN modeling with soil and terrain parameters
According to Table 1 using only terrain attributes (D) gives an
R2 that is significantly lower than when the other three
parameter groups are used for both training and testing
datasets. Figure 2 illustrates R2, for the different sites by soil
depths when Ks is estimated with testing dataset from the
same or different site as the training dataset. Shown on the
graphs are the Bonferroni mean separation results using a, b,
and c. Also marked on the graphs are standard error bars.
There is higher R2 for testing data when it is from the same
site as the training data. The R2 for the topsoil at the two sites
is significantly higher for situations when the training and
testing data are from the same site but lower when the
testing dataset is from a site different from that of the training
dataset. The R2 for subsoil at both sites were not significantly
different whether the testing and training datasets are from
the same site or not.
3Center
Terrain analysis
ƒPoint elevation data generation using differential GPS
ƒDigital elevation model (DEM) generation
ƒTerrain parameter generation from DEM
Soil sampling and analysis
ƒTransecting: Minpit soil identification and profile description
ƒSample depth: 0 – 15 cm (topsoil) and 30 – 45 cm (subsoil)
ƒDisturbed sample: Particle size distribution (sand, silt and
clay), Organic carbon, CEC and pH
ƒUndisturbed sampling: Saturated hydraulic conductivity (Ks)
and Bulk density
Artificial neural network (ANN)
ƒModel: Multi-Layer Perceptron (MLP) with cross validation
ƒEvaluation: Sensitivity analysis, R2 and NMSE
Statistical analysis: CV, ANOVA, R2
Table 1. Coefficient of determination (R2) for Ks using different data groups from
two sites and sampling depths as input data with standard error in ( )
A
0.53
0.51
0.49
0.47
0.45
0.43
0.41
0.39
0.37
0.35
Methodology
R
R
2
Results and Discussions
Objectives
ƒIdentify sensitive parameters among soil and terrain
parameters, and data size suitable for estimating Ks
ƒEstimate Ks for sites different from those of the training data.
Conclusion
ƒSensitive parameters are important for ANN modeling of Ks
ƒLarge training data set (> 1000) is required for good estimation
of Ks using ANN
ƒIn Ks estimation using ANN, training with dataset from same
environment is important when the topsoil is being considered
ƒInclusion of terrain parameters can improve the estimation of
Ks using ANN, but it can not be relied upon solely as input data.
References
1.Agyare, W.A. 2004. Soil characterization and modelling of
spatial distribution of saturated hydraulic conductivity at two
sites in the Volta Basin of Ghana. Ecology and development
series, No. 17, Cuvillier Verlag, Göttingen, Germany
2. Pachepsky, Y., Schaap, M.G. 2004. Data mining and
exploration techniques. In: Pachepsky Y. and Rawls W.J.
(Eds.), Development of pedotransfer functions in soil hydrology,
Development in soil science. Elsevier, Vol. 30, pp. 21-32