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DIVISION S-5-PEDOLOGY

Effects of Soil Morphology on Hydraulic Properties

II. Hydraulic Pedotransfer Functions

^a College of Natural Resources, Univ. of Wisconsin, Stevens Point, WI 54481 USA
^b Dep. of Soil and Crop Sciences, Texas A&M Univ., College Station, TX 77843-2474 USA

hlin{at}uwsp.edu

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
Pedotransfer functions (PTFs) have gained recognition in recent years as an approach to translate simple soil characteristics found in soil surveys into more complicated model input parameters. However, existing pedotransfer functions have not yet incorporated critical soil structural information. This study showed that soil hydraulic properties could be estimated from morphological features determined in situ (including texture, initial moisture state, pedality, macroporosity, and root density) through a morphology quantification system. Comparison between the class and continuous PTFs developed in this study indicated that the use of quantified morphological properties yielded predictive power similar to that of physical properties in estimating hydraulic conductivity at zero potential; water flow rates in macro-, meso-, and micropores; and a soil structure and texture parameter _macro. The results confirmed that soil structure was crucial in characterizing hydraulic behavior in macropore flow region; whereas texture had major impact on those hydraulic properties controlled by micropores. Depending on the flow domain to be included, estimation of hydraulic properties required the use of different combinations of morphometric indices or physical properties. The PTFs established may be used as starting points for estimating model input parameters.

Abbreviations: PC, principal component • PTF, pedotransfer function

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
THE LACK OF SUFFICIENT FIELD DATA of soil hydraulic properties often limits the application of contaminant transport models. With the increasing popularity of using Geographic Information Systems (GIS) coupled with vadose zone models and soil survey databases for regional-scale assessment of ground- and surface-water pollution potential, the demand for soil hydraulic property data has increased significantly. However, current methods for direct field measurement of soil hydraulic properties are generally regarded as complex, time-consuming, and costly (Mualem, 1986; Bouma, 1989). This has prompted efforts to indirectly estimate hydraulic properties using more readily available soil data such as particle-size distribution, bulk density, and organic matter content (e.g., Rawls and Brakensiek, 1983; Cosby et al., 1984; Vereecken et al., 1989, 1990; van Genuchten et al., 1992). Bouma and van Lanen (1987), Bouma (1989), Wagenet et al. (1991), and others discussed the possibility of using empirical, regression, or functional relationships, called PTFs, to translate simple soil characteristics found in soil surveys into more complicated simulation model input parameters. The PTFs have been attempted for estimating water retention curve, saturated hydraulic conductivity K_sat, unsaturated hydraulic conductivity function, and other soil hydraulic parameters (e.g., Vereecken et al., 1990; Tietje and Tapkenhinrichs, 1993; Wösten et al., 1995; Bell and van Keulen, 1995; Tietje and Hennings, 1996; Batjes, 1996). However, existing pedotransfer functions have not yet incorporated critical soil structural information such as pedality and macroporosity. This, in part, may be due to the lack of a proper means for quantifying soil structure.

In the first part of our study (Lin et al., 1999), we proposed a point scale system as a means for quantifying the descriptors of pedality, macroporosity, root density, initial moisture state, and textural class for field soils. Here, we explore the use of such quantified soil morphology in the development of hydraulic PTFs that translate morphological properties into hydraulic values. Such a quantitative translation may provide access to large existing soil databases (such as National Cooperative Soil Survey databases). Currently, soil profile descriptions are the major source of soil structural information one generally can obtain for a soil series of interest. Thus, utilization of the descriptors of soil structure would be a logical step toward incorporating soil structure into water flow and solute transport models. We compared the predictive power of the PTFs developed from quantified morphometric indices with the PTFs developed from physical properties. We also examined the adequacy of using a lower information level for estimating the hydraulic properties, including the classical approach of using the mass fractions of clay, silt, and sand separates; dry bulk density; and organic C content.

	Materials and methods

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
Soil Data Set
Ninety-six soil horizons of varying texture and structure from the Claypan Area, Blackland Prairies, and Coast Prairie Major Land Resource Areas of Texas were investigated. Using the point scale system developed by Lin et al. (1999), five major soil morphological features—texture, initial moisture state, pedality, macroporosity, and root density—were quantified for each horizon. Meanwhile, basic soil physical properties were also characterized, including particle-size distribution, dry bulk density, and organic C content. Initial soil moisture content was determined gravimetrically from field samples. Soil macroporosity was estimated in situ according to the scheme outlined by Lin et al. (1999). Porosity of very fine size at the root–soil interface was calculated based on root density estimated in the field (Lin et al., 1999). The sample statistics of the soil morphometric indices and physical properties are present in Table 1 . Note that the majority of soil horizons investigated had montmorillonitic or mixed clay mineralogy, thus modifications may be needed if the PTFs developed herein are to be used on soils that are illitic or kaolinitic.

(1)

Flows dominated by gravity have larger values than flows characterized by capillarity (Philip, 1969; Reynolds and Elrick, 1991). In clayey soils, flow dominated by gravity is synonymous with bypass flow. A large _macro indicates a large mean pore dimension effective in transmitting water in macropore flow domain (Lin et al., 1997).

Development of Hydraulic Pedotransfer Functions
Two types of PTFs are distinguished. Those that use continuous variables (e.g., percentage of clay and bulk density) are called continuous PTFs, and those that relate to distinct classes (e.g., textural class and ped grade) are called class PTFs. Both types of PTFs were developed in this study, with a focus on the PTFs constructed from quantified morphological features. The PTFs developed from quantified morphology retain the name class PTFs, although after the quantification of the morphology using the system of Lin et al. (1999) these PTFs appear similar to continuous PTFs. The predictor variables used in developing the class PTFs included: morphometric indices of texture (MI_t); initial moisture state (MI_m); pedality — including ped grade (MI_sg), ped size (MI_ss), and ped shape (MI_st); macroporosity — encompassing macropore quantity (MI_pq), macropore size (MI_ps), and macropore type (MI_pt); and root density — consisting of root abundance (MI_rq) and root size (MI_rs). The predictor variables used in constructing the continuous PTFs were the mass fractions of clay (m_c), silt (m_si), and sand (m_s) separates, organic C content (m_oc), dry bulk density (_d), initial soil gravimetric water content (w_i), field-estimated macroporosity (_macro), and the porosity of very fine size at root–soil interface (_root). Besides the final optimal PTF model, a model at a lower information level was also examined for each of the hydraulic parameters. Those are the models involving only variables that are most readily available at the present time in soil survey databases. For soil morphological properties, these variables are textural class and pedality. For physical properties, they are the mass fractions of clay, silt, and sand separates; organic C content; and dry bulk density.

Multiple regression analyses were performed on the predictor variables and response hydraulic parameters using the Statistical Analysis System (SAS Institute, Cary, NC). To combat the problem of regressing on several highly correlated, so-called multicollinear predictor variables, remedial procedures recommended by Freund and Littell (1991) were followed. First, complete principal components regression was conducted to investigate the structure of the relationships among the predictor variables; second, variable selection was used to find the smallest set of variables needed for estimating the response hydraulic properties.

Principal component analysis (PRINCOMP, SAS Institute) is a multivariate analysis technique that attempts to describe interrelationships among a set of variables. This analysis uses linear transformations of original variables to create a new set of uncorrelated variables, called the principal components (PCs), that can then be used in a regression model. These linear combinations are found by rotating the original variables to a new orientation of the same dimension. The first dimension (first PC) shows the largest variance of the projected data. The second PC displays the next largest variance and is orthogonal to the first, and so on. The eigenvectors for each of the PCs, which relate the components to the original variables, are scaled so that their sum of squares is unity. This allows the determination of which, if any, of the original variables dominates a component. The PCs exhibit no multicollinearity in a regression, and thus important coefficients can be easily determined. If the coefficients of the PCs' transformations imply meaningful interpretation of the components, the PC regression may shed light on the underlying regression relationships.

The most obvious and therefore most frequently used strategy for combating the effect of multicollinearity is to implement a model with fewer independent variables. Since there is no a priori criterion for the selection of variables, it is customary to use an automated, data-driven search procedure to select a suitable subset of variables for a final model. Such a procedure was implemented by RSQUARE selection option in PROC REG in SAS (SAS Institute). An optimum subset model is one that, for a given number of variables, produces the minimum error sum of squares (SSE), or, equivalently, the maximum coefficient of multiple determination (R²). The R² is defined by

(2)

where SSR is the regression sum of squares measuring the variability in the response variable attributed to the model, and SST is the total sum of squares corrected for the mean for the response variable (which measures the total variability in the response variable). The difference between SST and SSR is the error sum of squares SSE, conventionally expressed as

(3)

where O_i are the observed and P_i the predicted values, and n is the number of observations. To compare the goodness of the fit between the models with different numbers of predictor variables, the adjusted R², R²_adj, was calculated, which accounts for the number of parameters (p) in the model (SAS Institute, 1990):

(4)

where i is one if the model includes an intercept, and zero otherwise. The value of R²_adj is always smaller than the corresponding R².

Another popular statistic used to aid selection of a final model is called Mallow's C_p, defined as (Freund and Littell, 1991)

(5)

where MSE is the error mean square for the full model, and SSE_p is the error sum of squares for a model with p parameters (not including the intercept). As more variables are added to a multiple regression, R² will increase, but the C_p usually will first decrease and then increase. Final PTFs in this study were selected using the maximum R²_adj, which gave the smallest C_p. To provide further clues to true optimality, an alternative using both the FORWARD and BACKWARD variable selection methods in PROC REG was also analyzed. The closeness of agreement of the two methods provides some clues to true optimality; if they are identical it is quite likely that optimality has been achieved (Freund and Littell, 1991).

	Results and discussion

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
Principal Component Analysis
The eigenvectors that relate the PCs to the original variables, along with the proportion of total variation in the regression models accounted for by each of the PCs, are given in Tables 2 and 3 for the ten morphometric indices and the eight physical properties, respectively. The eigenvalues indicate that three to five components provide a good summary of the original sets of variables in both cases, implying that the original sets of variables contain redundant information. For the morphometric indices, the first three PCs (PC1–PC3) account for 69% of the standardized variance and the first five PCs explain 84% (Table 2). The corresponding values for the physical properties are 79 and 94%, respectively (Table 3). Subsequent PCs contribute <5% each. Interpretation of those PCs having small variances is not usually useful, thus they are not listed in Tables 2 and 3.

View this table: [in this window] [in a new window]   Table 2 Eigenvectors of the principal components (PCs) of the ten morphometric indices and the proportion of total regression model variation accounted for by each PC (type II sum of squares [SS]/model SS). The PCs having small variances (PC6–PC10) are not listed.

View this table: [in this window] [in a new window]   Table 3 Eigenvectors of the principal components (PCs) of the eight physical properties and the proportion of total regression model variation accounted for by each PC (type II sum of squares [SS]/model SS). The PCs having small variances (PC6–PC8) are not listed.

According to the t statistics for the parameter estimates in the complete PC regression with the morphometric indices, the PC1 is clearly the predominant component for estimating K₀, which accounts for >96% of the variation explained by the model (Table 2). The same is true for v_macro, showing that soil structure (i.e., PC1) is critical in estimating macropore flow rate and the hydraulic parameters dominated by macropore flow such as K₀. The impact of soil structure decreases for estimating v_meso (explaining 69% of the total model variation), and becomes insignificant for predicting v_micro (accounting for only 1.4% of the total model variation). In contrast, the PC3 (texture or nonstructure) explains 55% of the v_micro's model variation, with additional 27 and 12% contributions from the PC2 (very fine porosity) and PC5 (similar to PC3), respectively. The PC3 accounts for only 7% for estimating v_meso and almost none for v_macro. For estimating the soil structure and texture parameter _macro, there appear to be three components of importance. The most important component is PC1, followed by PC3 and PC5. The positive coefficient of the PC1 and the negative coefficients of the PC3 and PC5 indicate that the structureless soils would have small _macro values. This is in agreement with the results reported by Bouwer (1966) and White and Sully (1987, 1992) who found laboratory repacked soils to have lower values than undisturbed field soils.

For the eight physical properties, their PC1 has high positive loadings on the contents of clay separate, organic C, and initial moisture, as well as high negative loadings on sand content and bulk density (Table 3). This component seems to measure soil aggregation. The PC2 is dominated by macroporosity and the porosity of very fine size at the root–soil interface. There are also positive loadings on organic C and sand contents, and small negative loadings on clay and silt contents and bulk density. Thus, the PC2 apparently measures the overall soil porosity, encompassing macro-, meso-, and micropores. The PC3 is dominated by silt content, with smaller negative loading on clay content. It is a measure of soil texture. The PC4 shows a positive relationship with initial moisture content and the very fine porosity at root–soil interface and a negative relationship with macroporosity. This component seems to measure soil wetness and microporosity. Although the PC5 has small eigenvalue, it plays a noticeable role in the regression (Table 3). This component is dominated by bulk density, with smaller positive loadings on organic C, clay content, macroporosity, and negative loading on sand content. It seems to be another measure of soil structure.

The complete PC regression with the physical properties shows that the PC1 (aggregation), PC2 (porosity) and PC4 (wetness and microporosity) are the dominant components for estimating K₀ and v_macro (Table 3). The three combined account for 87% of the variation explained by the PTFs. Soil porosity (PC2) and wetness and microporosity (PC4) explain >80% of the v_meso's model variation, with the PC2 being positive and the PC4 being negative. Soil aggregation and structure (PC1 and PC5) influence negatively on v_micro, while overall porosity (PC2) and texture (PC3) contribute positively to v_micro. Similar to the morphometric indices, estimation of _macro would include three major components associated with structure (PC5), aggregation (PC1), and wetness and microporosity (PC4). The three components combined explain 93% of the model variation.

Pedotransfer Functions
Final PTF models (Table 4) were selected based on the maximum R²_adj with the smallest C_p in the RSQUARE selection procedure. The results from the FORWARD and BACKWARD variable selection methods were almost identical to those of the RSQUARE selection, indicating that true optimality was most likely achieved. Compared with the complete PC regression models, the values of R²_adj of the final PTFs increase slightly (Table 5) . Using these PTFs, the estimated hydraulic parameters agree reasonably well with the observed values. The somewhat smaller R²_adj for v_meso, v_micro, and _macro in both the class and continuous PTFs may be attributed to other factors not accounted for in the original sets of input variables. The use of log-transformed hydraulic properties did not improve the goodness of fit (Table 5).

View this table: [in this window] [in a new window]   Table 4 Parameter coefficients of the final class and continuous pedotransfer functions (PTFs) and their relative importance based on the magnitudes of the type II SS.

Consistent with the principal component analysis, relative importance of the parameter coefficients in the final PTFs once again indicates that soil structure has a dominant effect on K₀ and v_macro, while texture has a major influence on v_micro, and that structure and texture show about equal importance in estimating _macro (Table 4). Macropore quantity (MI_pq) and macropore size (MI_ps), or, in the case of the continuous PTFs, macroporosity (_macro), are among the most important factors for predicting K₀ and v_macro. Texture (MI_t or m_c) is the most significant factor for estimating v_micro. Macropore size and texture, or clay content and bulk density in the case of the continuous PTFs, rank first among those variables selected for estimating _macro.

The relationships between texture and v_macro, v_micro, and _macro in the PTFs imply that, for the soils studied, the fine-textured soils (lower MI_t or m_s) tend to have greater tendency for bypass flow to occur than the coarse-textured soils, leading to higher values of v_macro and _macro and lower values of v_micro in clayey soils than in sandy soils. This is consistent with the observations reported by Lin et al. (1997), who found that larger proportions of water flux under zero potential were transmitted through macropores in clayey soils than in sandy soils. The phenomenon is related to more uniform distribution of pore sizes in sandy soils, which tends to reduce the likelihood of bypass flow.

Lower Information Level Models
Although the mass fractions of clay, silt, and sand separates; dry bulk density; and organic C content have traditionally been used to predict soil hydraulic properties, the use of these five variables in estimating the hydraulic parameters investigated in this study is quite weak except for the v_micro (Table 5). With the exclusion of porosity (_macro and _root) and initial water content (w_i) that closely relates to macroporosity, the R²_adj of the lower information level models decreases by 33 to 78% in comparison with the PTFs established. Only the v_micro has the smallest decrease in R²_adj (9%). Therefore, the classical approach appears reasonable only for estimating the hydraulic properties dominated by micropores, but will suffer when used for predicting the hydraulic parameters controlled by macropores or mesopores. Although organic C content and bulk density partially indicate soil structure, these two properties do not contain sufficient information regarding soil porosity, especially macroporosity. The importance of soil structure and porosity is further illustrated in Fig. 1 , where the multiple regression R²_adj increases most significantly for v_macro with the inclusion of structure-related predictor variables.

View larger version (23K): [in this window] [in a new window]   Fig. 1 Multiple regression R2adj for estimating the macropore flow rate (vmacro), mesopore flow rate (vmeso), micropore flow rate (vmicro), and the soil structure and texture parameter (macro) as a function of graduate inclusion of different physical properties as predictor variables (from mc leftward). See Table 1 for the abbreviations of the variables

	Conclusions

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
The morphology quantification system proposed by Lin et al. (1999) is useful for developing hydraulic PTFs from soil morphological features. The use of such quantified morphology yields comparable predictive power as soil physical properties in estimating several hydraulic parameters. It is clear that soil structure (pedality and porosity) is crucial in characterizing hydraulic behavior in the macropore flow region; whereas texture places major impact on those hydraulic properties controlled by micropores. Consequently, the classical approach of using particle-size distribution, dry bulk density, and organic C content is insufficient for predicting the hydraulic parameters studied, except for micropore flow rate. Macroporosity is an integral part of soil structure, which is deficiently reflected by organic C content and bulk density. Depending on the flow domain to be included, estimation of soil hydraulic parameters requires the use of different combinations of morphometric indices or physical properties. No single morphometric index or physical property appears to provide adequate estimation of the hydraulic parameters studied.

It should be recognized that for any statistical functions, their usefulness is limited to the data population used in the development. The empirical nature of PTFs warrants their best use as starting points for quick and economic estimations of necessary model input parameters, particularly when a large number of hydraulic property data are required. The use of PTFs would be more suitable for regional-scale studies rather than site-specific applications.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
Contribution from the Texas Agric. Exp. Stn., The Texas A&M Univ. System.

Received for publication April 17, 1998.

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 

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This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via ISI Web of Science (16) Citing Articles via Google Scholar Google Scholar Articles by Lin, H.S. Articles by Hallmark, C.T. Search for Related Content PubMed Articles by Lin, H.S. Articles by Hallmark, C.T. GeoRef GeoRef Citation Agricola Articles by Lin, H.S. Articles by Hallmark, C.T.