UNCERTAINTY AND SENSITIVITY ANALYSIS FOR PEDOTRANSFER FUNCTIONS

M. F. Rivera*, C. Fallico, S. Troisi

University of Calabria; Department of Soil Conservation, Italy

The characterization of the soil hydraulic properties results indispensable in numerous hydrological applications and in the studies of many practical problems requiring a large spatial scale. It is notalways possible to perform direct measurements of the soil hydraulic properties, because they are cost and time consumingand highly variable spatially and temporally[1]. Consequently, for their estimate the pedotransfer functions (PTFs) areoften used;these utilize basic information that are translated easily in the simulation model [2]. However, the PTFs models provide predictions, influenced by uncertainties, which originate in the input variables (measurement errors, etc.) and in the simulation model. Many authors analyzed the uncertainty of PTFs and evaluated the effect on the output, using different methods and performing the sensitivity analysis (SA) closely linked to the uncertainty analysis (UA)[3] [4] [5] [6]. Minasny etal.[7] showed that the uncertainty of the PTF model, often produced by internal parameters and by the utilized database, is usually small in comparison to the error produced by the input variables, which influence the output expectationsbya propagation of the initial error. In this studythe Monte Carlo (MC) method was utilized, by assuming the probability distribution of each input variable and by estimating thatof the output variables.N. 30 undisturbed soil samplings were taken on the alluvial area of 800 m2 (40 m x 20m), with a slope of 6 %, in the Turbolo basin, in Calabria (Italy).These samplings, with a diameter of 5.1 cm and height of 5.6 cm, were analyzed in the laboratory by using the gravimetric method. By the RETC code [8], for each sample, or rather for each location,assigned , the following parameters of unsaturated soil was obtained: saturated water content (s), residual water content (r), scaling parameter ()and shape factor (n). These retained independent parameters are in the PTF of Van Genucten model, which represents the retention curve:

(1)

Givenr = 0 and assuming forthe other input parameters a normal distribution, on the basis of the statistical tests (Pearson, Shapiro-Wilk, Kolmogorov-Smirnov) for a confidence level of 95%, the corresponding main statistical parameters are reported in the following Tab. 1:

Tab. 1: Main statistical parameters of the input variables of Eq.(1).

Parameters / s /  / n
Mean / 0.357446071 / 0.334489286 / 3.57264142857143
Median / 0.35471 / 0.323255 / 3.729735
Standard Deviation / 0.028203783 / 0.057598041 / 0.722674
Variance / 0.000795453 / 0.003317534 / 0.522258
Coefficient of Variation / 0.078903605 / 0.172196969 / 0.20228
Skewness / 0.171869081 / 3.868204791 / -1.13398

Successively, the uncertainty analysis (UA) and the sensitivity analysis (SA) were carried out on the model, for a fixed value of pressure head (pF = 2), by using following methods: FAST, Random, Latin Hypercube, Sobol, Morris [9]. The FAST method performs the SA, by estimating the sensitivity indexes like main effects (or first order indexes) and total order indexes, as shown in Tab. 2.

Tab. 2: FAST sensitivity indexes.

(h)
Fast first order indexes / Fast total order Indexes
s / 0.4165 / 0.4509
 / 0.4986 / 0.548171
n / 0.0234 / 0.056612

In Tab. 3, the SA results are reportedfor Random and Latin Hypercube methods; the ranks of the sensitivity indexes are shown in this table, according to Pearson, Spearman, Partial Correlation Coefficient, Partial Rank Correlation Coefficient, Standardised Regression Coefficient, Standardised Rank Regression Coefficient, Smirnov.

Tab. 3: SA for Random (R) and Latin Hypercube (LH) methods (confidence level of 95%).

PEAR / SPEA / PCC / PRCC / SRC / SRRC / Smirnov
R / L H / R / L H / R / L H / R / L H / R / L H / R / L H / R / L H
s / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 1 / 1
 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 2 / 2
n / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3

Also SOBOL method is used and the results are shown in Tab. 4.

Tab. 4: Sensitivity indexes of first and total order for the SOBOL method.

First orderindexes / Total order indexes
(h) / (h)
s / 0.411561 / 0.385032
 / 0.474394 / 0.495524
n / -0.0201 / 0.031638

Finally, in Fig. 1and in Tab. 5 results of Morris method are reported:

Fig. 1: Trend - for Morris. Tab. 5: Morris indexes.

/ (h)
 / 
s / 0.0672 / 0.0093
 / 0.0784 / 0.0189
N / 0.0209 / 0.0058

This analysis was carried out by the SIMLAB 2.2 code [10]. The obtained results shown altogether for the PTF model (1) a non monotonicbehavior.Moreover, referring to the considered model and for the fixed value of pressure head (pF = 2), the most sensitive parameter is clearly the scaling parameter (), followed bythe saturated water content s and successively by the shape factor (n); these results are affected by dry/wet conditions, heterogeneity and texture of considered soil [11] [12].

References

[1] Chirico G.B., H. Medina, N. Romano (2007). Uncertainty in predicting soil hydraulic properties at the hillslope scale with indirect methods. Journal of Hydrology, 334, 405–422.

[2] Bouma J. (1989). Using soil survey data for quantitative land evaluation. Ad.in Soil Science, 9, 177–213.

[3]Vereecken H., J. Diels, J. van Orshoven, J. Feyen, J. Bouma (1992). Functional evaluation of pedotransfer functions for the estimation of soil hydraulic properties. Soil Science Soc. Am. J., 56, 1371–1378.

[4] Schaap M.G. & F.G. Leij (1998). Database-related accuracy and uncertainty of pedotransfer functions. Soil Science, 163, 765–779.

[5] Christiaens K. & J. Fejen (2001). Analysis of uncertainties associated with different methods to determine soil hydraulic properties and their propagation in the distributed hydrological MIKE SHE model. Journal of Hydrology, 246, 63–81.

[6] Minasny B. & A.B. McBratney (2002). Uncertainty analysis for pedotransfer functions. European Journal of Soil Science, 53, 417–429.

[7] Minasny B., A.B. McBratney, K.L. Bristow (1999). Comparison of different approaches to the development of pedotransfer functions for water retention curves. Geoderma, 93, 225–253.

[8] Van Genuchten M.Th., F.J. Leij, S.R. Yates (1991). The RETC Code for Quantifying the Hydraulic Functions of Unsaturated Soils. U.S.A.

[9] Saltelli A., Chan K., Scott E.M. (2000). Sensitivity Analysis. J. WILEY & Sons. England.

[10] Saltelli A., Tarantola S., Campolongo F., Ratto M. (2007). Sensitivity analysis in practice. J. WILEY & Sons. England.

[11] Boateng S. (2001). Evaluation of probabilistic flow in two unsaturated soils. Hydrogeology Journal, 9:543-554.

[12] Rocha D., Abbasi F., Feyen J. (2006). Sensitivity Analysis of Soil Hydraulic Properties on Subsurface Water Flow in Furrows. Journal of Irrigation and Drainage Eng., 418/ ASCE/ July-August.