INTRODUCTION
Presently, the flood spreading systems are using in some regions of Iran to control flood damages and aquifers recharge. By spreading a large volume of floods containing suspension load on the spreading network, it may lead to some differences in soil infiltration. Soil infiltration rate is an important parameter for quantifying runoff, soil water and solute movement and for modeling hydro geologic processes. General idea is that due to the existence of solute and suspended materials in flood water, soil infiltration rate may gradually reduce. Since, direct measurement of soil infiltration is time consuming and expensive, an alternative approach to estimate soil infiltration has been a subject of research efforts and an indirect estimation method which is often regarded as PedoTransfer Function (PTF) approach has been developed. In the PTF method, soil properties such as infiltration rate can be estimated in terms of easily measurable soil physical and chemical properties.
Pedotransfer functions have been used for a wide range of non cultivated soils,
amongst other US soil (Pachepsky et al., 2006)
and Danish soils (Borgesen and Schaap, 2005). Mateosa
and Giráldeza (2005) showed that the total sediment load decreases
with successive irrigations and increases as it moves downstream, while the
bed load decreases. If it is not pay attention to sedimentation of spreading
channels, land and plant cover will degrade, decrease infiltration and increase
soil salinity. Wagner et al. (2001) evaluated
eight wellknown PTFs used for estimation of soil hydraulic conductivity using
detailed measurements of 63 German soil horizons and found that the developed
PTF performed the best for predicting unsaturated hydraulic conductivity. Krogh
et al. (2000) tested 1643 soil samples and showed the clay and organic
matter of soil can explain 90% of Cation Exchangeable Capacity (CEC) differences
by improving of some functions.
Tomessla et al. (2000) used PTFs to estimate
moisture curve of Brazilian soil and showed the improved functions have the
minimum error compared to other common functions. Khodaverdilu
and Homaee (2002) studied 27 soil samples of Karaj series with loamy texture
and showed that the improved PTFs can estimate soil moisture content by 93%
correlation coefficient. To estimate soil water content, Jarvis
et al. (2002) developed PTFs on the arable lands that can explain
more accurate than non arable lands, so that the correlation coefficient increased
from 15 to 35%. Soil Water Characteristic Curve (SWCC) of a silty soil was studied
indirectly using the estimation algorithms known as pedotransfer functions.
The study reveals that the PTFs developed previously to estimate SWCCs match
very well with the experimental results (Thakur et al.,
2007). McBratney et al. (2002) suggest that
this problem can be overcome by using Monte Carlo methods to choose the results
from the Pedotransfer function which gives the least variance.
Ghorbani Dashtaki and Homaee (2004) by improving PTFs
showed that the mean soil particle size, standard error and special gravity
of soil are suitable parameters to estimate soil moisture content. Haung
and Zhang (2005) used the soil particle size as an easily measurable soil
property to improve PTFs for estimation soil moisture curve. Pachepsky
et al. (2006) used the soil structure in PTFs for estimation of soil
hydraulic conductivity. Sten et al. (2001) reviewed
the current status of PTF development, methods to develop PTFs and the accuracy
and uncertainty of various PTFs. Because every PTF is developed on the basis
of a limited database, it exist a lot of uncertainty in applying PTF to different
soil conditions from the soil conditions under which PTFs are developed. Thus,
there is a need to understand the accuracy and the limit of the PTFs developed
in other places in order to apply for soil conditions.
The aim of the present research was to develop the PTFs for estimating soil infiltration rate by the linear and nonlinear regression methods using soil physical data of flood spreading stations of Iran.
MATERIALS AND METHODS
The study area, Iran covers an area of 1,648,000 km^{2} (636,296 mi^{2}) and extends about 2,250 km (1,398 mi) SENW and 1,400 km (870 mi) NESW. Iran has a variable climate. In the Northwest, winters are cold with heavy snowfall and subfreezing temperatures during December and January. Spring and fall are relatively mild, while summers are dry and hot. In the South, winters are mild and the summers are very hot, having average daily temperatures in July exceeding 38°C. On the Khuzestan plain, summer heat is accompanied by high humidity. In general, Iran has an arid climate in which most of the relatively scant annual precipitation falls from October through April. In most of the country, yearly precipitation averages 25 cm or less. The major exceptions are the higher mountain valleys of the Zagros and the Caspian coastal plain, where precipitation averages at least 50 cm annually. In the western part of the caspian, rainfall exceeds 100 cm annually and is distributed relatively evenly throughout the year. This contrasts with some basins of the central plateau that receive 10 cm or less of precipitation annually.
Thirteen flood spreading stations were selected in the country which infiltration rate was measured during 5 years (Fig. 1). The regional soils are classified as Entisols with high percent of gravel and belong to main subgroup of xeroflovents.
Infiltration rate (mm h^{1}) was measured in spreading stations during
five years after construction by double ring method (ASTM
D509302, 2008) in flood spreading lines (Fig. 2).

Fig. 1: 
Location of the flood spreading stations 

Fig. 2: 
Measurement of infiltration rate in a singular point 
Totally, 585 measurements of infiltration rate were investigated. The KolmogorovSmirnov
test (Stephens, 1974) was used to determine the normality
of data obtained. Selected soil properties used as input variables for estimation
of infiltration rate were silt, sand, clay percentage, bulk density, field capacity
and wilting point measured based on NRCS (1992) of USDA
standards.
All stations were classified by Principal Component Analysis (Levesque,
2007) using soil physical data mentioned above. Linear and nonlinear pedo
transfer functions were developed to estimate infiltration rate.
PedoTransfer Function Approach
To develop the PedoTransfer Functions (PTFs) approach to estimate infiltration
rate, this parameter was indirectly estimated from the easily measured soil
properties. Stepwise regression method (Levesque, 2007)
was used to establish the prediction equation for PTFs with α = 0.05.
PTF for Soil Infiltration Rate
The PTFs for soil infiltration rate were explained as below (Eq.
1, 2):
Where 
I 

Soil infiltration rate 
t 

Given variable 
b 
: 
Relation coefficients 
RESULTS
The soil infiltration rate values evaluated and classified into three classes by the application of the cluster and principal component analysis (Fig. 3).
As Fig. 3 and Table 1, the results showed
that factor 1 can explain 42.2% of variance. While factors 2 and 3 explain 14.3
and 10.8%, respectively of variance of the soil physical properties of flood
spreading stations.

Fig. 3: 
Recognizable classes based on eigenvalue of correlation matrix
above 1 
Table 1: 
Eigenvalue of correlation matrix 

Table 3: 
Normalization of functions for independent variables of stations
group 1 

Table 4: 
Coefficients of PTFs to predict infiltration rate in stations
group 2 

Table 5: 
Improved PTFs for predicting infiltration rate in groups 

It should be used the actual value of variables in functions 
Table 2 shows the result of classification flood spreading
stations into three groups based on clustering. There are 8 stations lay in
group 1, 3 in group 2 and 2 in group 3.
The results of the KolmogorovSmirnov test (Stephens, 1974)
showed all data of soil physical properties are abnormal because the test coefficient
was less than 0.05. Table 3 shows the results of normalization
of data for station group 1 for example. Logarithmic and power functions used
for normalization of data.
Linear PTFs
Two models of PTFs for predicting infiltration rate were improved in stations
group 1 based on sand percent and permanent wilting point. To predict infiltration
rate in stations group 2, one model was improved based on silt, sand and field
capacity. An example for group 2 was showed in Table 4.
For stations group 3 another model also developed based on sand. Resulted PTFs for three groups of flood spreading stations were showed in Table 5. These functions are power models in groups 1 and 3, whereas resulted equation for groups 2 is logarithmic.
Nonlinear PTFs
For stations group 1, two models of nonlinear PTFs with one variable improved
based on gravel and sand with R^{2} of 0.14 and 0.16 as Table
6 and related equations were demonstrated in Fig. 4 and
5.

Fig. 4: 
Non linear relation between Infiltration rate and gravel percent
for stations group 1 

Fig. 5: 
Non linear relation between Infiltration rate and sand percent
for stations group 1 
Table 6: 
Nonlinear models developed for estimating infiltration rate
in stations group 1 

There are also three nonlinear PTFs developed for stations group 2 that have
been made from sand, silt and clay factors (Table 6). For
stations group 3 there are developed 2 PTFs with independent variables of sand
for the first equation and silt for the second one.
Table 7: 
Multivariable PTFs to estimate infiltration in the groups 

Multivariable PTFs
Multivariable PTFs were developed to estimate infiltration rate using independent
variables of sand and gravel for group 1 and sand, gravel and silt for group
2 (Table 7). Resulted equations were power models and showed
that soil textural fractions of sand and silt in addition to gravel can affect
the infiltration rate.
DISCUSSION
Although, the literature review showed there were many researches on PTFs,
but their emphasis are generally focused on soil hydraulic conductivity (Pachepsky
et al., 2006; Wagner et al., 2001)
and soil moisture curve (Haung and Zhang, 2005; Ghorbani
Dashtaki and Homaee, 2004; Tomesla et al., 2000)
and there are little researches to predict soil infiltration rate. So, developing
the related functions to estimate infiltration rate by easily measured soil
parameters has a special importance.
Determining coefficients of developed PTFs showed they can not explain all
variance of changes which may be due to the following reasons: Firstly, infiltration
is a complex process and has high variance; secondly there is not a parameter
that can show the effect of soil structure and pores on infiltration rate. This
is in agreement with Sten et al. (2001) that
mentioned there is a lot of uncertainty in applying PTF to different soil conditions.
Resulted regression coefficients at assumed confidence interval of 0.95 obtained
in this research vary 0.16 to 1.00, so the changes have wide variation. It seems
the different properties of flooded surface and flood quality is the reason.
Khodaverdilu and Homaee (2002) obtained 93% correlation coefficient and
Jarvis et al. (2002) calculated 15 to 35%.
The PTFs obtained were mostly based on soil texture. Ghorbani
and Homaee (2004) and Haung and Zhang (2005) used
the soil particle size and Pachepsky et al. (2006)
used the soil structure as an easily measurable soil property to improve PTFs.
CONCLUSION
In this study, developed PTFs vary based on the number of parameters formed them. Most of the developed functions are cubic and one of them is compound. The PTF approach estimates soil infiltration rate parameters indirectly based on the input variables of soil texture and is very efficient way of estimating soil infiltration rate. Determining coefficients of developed PTFs showed they can not explain all variance of changes. It may caused by two reason. Firstly, infiltration is a complex process and has high variance; secondly there is not a parameter that can show the effect of soil structure and pores on infiltration rate.
ACKNOWLEDGMENTS
This study has been supported by Soil Conservation and Watershed Management Research Institute in 2008. Authors wish to thank them for their helpful and constructive comments.