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a Inst. for Forestry and Game Management, Gaverstraat 4, B-9500 Geraardsbergen, Belgium
b Dep. of Soil Management and Soil Care, Ghent Univ., Coupure 653, B-9000 Gent, Belgium
c Lab. for Forest, Nature and Landscape Research, Katholieke Univ. Leuven, Vital Decosterstraat 102, B-3000 Leuven, Belgium
* Corresponding author (bruno.devos{at}lin.vlaanderen.be)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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b) measurements. The predictive quality of 12 published PTFs was evaluated using an independent dataset of forest soils (1614 samples) from Flanders, Belgium. For all samples, PTF accuracy and precision was calculated, and for topsoil and subsoil samples separately. All functions were found to produce a systematic underestimation of predicted b, with mean prediction errors (MPEs) ranging between –0.01 and –0.51 Mg m–3. Most PTFs performed differently when applied to topsoil or subsoil data. Prediction of topsoil b showed the highest prediction error. The evaluation demonstrated the poor performance of some published PTFs, and raised concern that the predictive ability of even the better models may not be adequate. Therefore, two candidate PTFs were recalibrated and validated. With recalibration, accuracy improved considerably and showed a near-zero bias, but precision increased only slightly. The best fitted empirical model was based on loss-on-ignition (LOI): b = 1.775 – 0.173(LOI)1/2. Its predictive capacity was not significantly better than the Adams physical two-component model b = 100/{(LOI/0.312) + [(100 – LOI)/1.661]}. For the prediction of b in forest soils, LOI was two times more important than texture variables, and LOI alone accounted for >55% of the total variation. The lowest root mean squared prediction error (RMSPE) was 0.16 Mg m–3 for LOI-based, and 0.21 Mg m–3 for texture-based models. Separate calibration of topsoil and subsoil layers did not enhance the predictive capacity significantly.
Abbreviations: b, bulk density • CI, confidence interval • LOI, loss-on-ignition • MPE, mean prediction error • MSPE, mean squared prediction error • OM, organic matter • PTF, pedotransfer function • RMSPE, root mean squared prediction error • RSE, residual standard error
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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b is the mass of an oven-dry sample of undisturbed soil per unit bulk volume (ISSS Working Group, 1998, p. 153). This important physical soil property is essential for weight-to-volume or area conversions and is indispensable for the assessment of soil carbon stocks and nutrient pools (Tamminen and Starr, 1994). Bulk density is needed for estimating soil water retention characteristics, and is a required input parameter for water, sediment, and nutrient transport models (Boucneau et al., 1998). Furthermore, it is an indicator of soil compaction, porosity, and site productivity (Tamminen and Starr, 1994), and has been found to correlate negatively with root density and tree growth (Salifu et al., 1999). It is considered a key property that characterizes soil structure in general.
Bulk density has been found to correlate strongly with organic matter (OM) and soil texture (Adams, 1973; Alexander, 1980; Harrison and Bocock, 1981; Huntington et al., 1989; Manrique and Jones, 1991; Salifu et al., 1999). In uncultivated soils, like most forest soils, OM has a dominating effect on b (Curtis and Post, 1964; Jeffrey, 1970; Adams, 1973) and acts as its main predictor. In soil samples where OM is a minor component, texture or other variables can more significantly contribute to b (Manrique and Jones, 1991).
Bulk density has been found to vary with depth (Harrison and Bocock, 1981; Huntington et al., 1989; Leonavi
iut
, 2000), soil group (Alexander, 1980; Manrique and Jones, 1991; Salifu et al., 1999), land use, and vegetation (Harrison and Bocock, 1981).
Field sampling and direct measurement of b is considered labor intensive, expensive, time consuming, and frequently tedious (Harrison and Bocock, 1981; Boucneau et al., 1998; Kaur et al., 2002). Consequently, b data obtained by direct measurements are often lacking in soil databases. To overcome this problem, PTFs based on OM and soil texture are frequently used to estimate b (Boucneau et al., 1998; Kaur et al., 2002). Since LOI is an easy and low-cost method for determination of OM, it is widely applied as a PTF predictor to estimate b.
Only a few attempts have been made to validate existing PTFs of b using independent datasets. Boucneau et al. (1998) tested class and continuous PTFs on 182 soil samples of arable land in Belgium, and Kaur et al. (2002) evaluated continuous PTFs on 224 soil samples of four watersheds (arable land, pine forest, oak forest, and barren) in the Almora district in India. No references have been found reporting on the validation based on forest soil samples only.
Kaur et al. (2002) found a very limited predictive potential of published b PTFs due to their development on specific soils and/or ecosystems, use of an indirectly computed OM content as a predictor variable, poor predictive potential of developed regression models, and subjective errors. Harrison and Bocock (1981) recommended, that to obtain a high accuracy and great precision in estimating soil b, an equation specific for each range of soils of relevance to a particular research program should be used rather than to rely on general PTFs.
Hence, the objectives of this paper are to (i) test the performance of 12 published continuous PTFs using a forest soil dataset of 1614 measured b values, (ii) evaluate each function using several validation indices to select the best candidate models in terms of accuracy, precision and operability; (iii) assess the improvement when the selected candidate functions are recalibrated; (iv) evaluate the influence of the addition of predictors on the prediction error; and (v) analyze if separate recalibration on topsoil and subsoil samples is worthwhile.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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b database contains information of 217 forest soil survey plots located within the Flanders region. Coordinates of the sampled locations range from 50°42' to 51°27' N and 2°40' to 5°41' E. On all plots, undisturbed and disturbed soil samples of each observed horizon were taken for physical and chemical analysis. Data on measured b (down to a depth of 1.2 m) are available for 532 pedons (1614 undisturbed samples) encompassing the major Belgian soil types. The sampled soils were classified according to the Soil Survey Staff (2003) as Spodosols, Entisols (suborders Psamments, Fluvents, and Aquents), Alfisols, and Inceptisols. They belong to the following World Reference Base soil groups: Podzols, Arenosols, Luvisols, Albeluvisols, Cambisols, Fluvisols, Gleysols, Regosols, and Anthrosols (FAO, 2001). Most encountered USDA texture classes are sand (27% of total), loamy sand (26%), sandy loam (20%), and silt loam (17.5%).
Sample depths range from 0.5 to 120 cm, with an average of 50 cm (median 43 cm). Validation of the 12 published PTFs was done using the total dataset first. In a second analysis, the b dataset was split into two subsets: topsoil samples (mainly A horizon) and subsoil samples (E, B, and C horizons). Average sampling depth for topsoil samples was 10 cm within a depth interval of 0.5 to 40 cm. Some descriptive statistics of the basic soil properties are listed in Table 1.
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Sampling and Analysis
Sampling for b was done by the core method using standard sharpened steel cylinders of 100 cm3 volume (d = 53 mm, h = 50 mm). A dedicated ring holder (Eijkelkamp Agrisearch Equipment, Giesbeek, the Netherlands) was used for the core sampling after application of a Riverside auger to prepare a sampling platform at a predetermined depth within a specific horizon. In hard layers, a percussion-free hammer was used for hammering the ring holder with a minimum of vibration into the ground.
The soil-filled cylinder was carefully removed from the ring holder and the soil extending beyond both cylinder ends was trimmed flush using a sharp knife. Cylinders with stones, charcoal, or roots larger than 2 mm in diameter were rejected and resampled in the same horizon. Protective plastic covers prevented samples from drying out. The cylinders were transported in special cases to the laboratory to minimize disturbance.
In the laboratory, samples were stored at 2°C before analysis. Bulk density was measured after determination of the soil moisture retention curve at eight matric potentials. The samples were oven dried (105°C) until constant weight (>24 h).
Soil physicochemical analysis was done using disturbed samples of the same horizons. The disturbed samples were dried, ground, and passed through a 2-mm sieve.
Organic matter content was estimated by measurement of LOI at 550°C for 3 h on a 3-g oven-dry sample. Errors in estimation of OM by LOI were rather small because most soils are low in pH (almost no inorganic carbon) and rather low in clay content.
Texture was determined using a laser diffraction method (LDM), calibrated, and validated using standard pipetting and sieving procedures (ISO 11277) after application of the same pretreatment. Coefficients of variation of clay, silt, and sand fraction determination using LDM were below 5, 5, and 2%, respectively.
Published and Model Type Pedotransfer Functions
A literature review resulted in 12 different continuous PTFs (Table 2). These PTFs could be grouped in five model types (A–E). Type A are functions where the predictor variables are log transformed, while a square root transformation is applied to Type B. In both cases, the response variable (b) is not transformed. In Type C, the reciprocal of the b, called specific volume, is used. The Stewart/Adams equation used in Adams (1973) and Rawls and Brakensiek (1985), based on mineral and organic b parameters, conforms to the equation used by Honeysett and Ratkowsky (1989).
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Table 3 lists basic information about the type of soils, sample depths, and horizons examined in each study, the observed b range, the method used for determination of the predictor variable, the applied b determination method, and the water potential of the reported b values.
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. These are defined as:
b,i and
are the observed and predicted b values, respectively; n the number of observations; and var and cov the variance and the covariance function, respectively. The MPE allows the evaluation of a positive or negative bias of a PTF, indicating an average tendency for overestimation or underestimation, respectively. The SDPE shows the random variation of the predictions after correction for the global bias. It is affected by four sources of uncertainty: (i) the limited precision of the model, (ii) local deviations of the model from the real situation, (iii) the inherent variability of the property measured, and (iv) the measurement error. The RMSPE is a measure of the overall error of the prediction. It is the square root of the mean square prediction error (MSPE). For large n, MSPE equals the sum of MPE2 (accuracy error) and SDPE2 (precision error) as shown in Eq. [5].
The ratios MPE2/MSPE and SDPE2/MSPE give the relative contribution of accuracy and precision to the total prediction error. The MPE, SDPE, and MSPE should be as small as possible. A graph of the MPE2 vs. SDPE2 of the evaluated models reveals the best models located near the origin. The prediction coefficient of determination is a measure of the strength of the linear relationship between measurements and predictions, and indicates the fraction of the variation that is shared between them. Bootstrapping was used as a resampling technique to obtain confidence intervals (CIs) for the parameters of interest. In the bootstrap, N new samples, each of the same size as the observed data, are drawn with replacement from the observed data. It was assumed that the validation dataset is representative for the underlying population. For more information on the bootstrapping technique, we refer to Johnson et al. (1990). The applied number of resamples (B) was 1000. Confidence intervals were calculated based on bias-corrected and adjusted (Bca) percentiles at 2.5 and 97.5%, respectively. These are generally more accurate than empirical percentiles (S-Plus, 2000, p. 547). The CIs were used to check if the validation indices were significantly different between PTFs. S-Plus 2000 (professional release 2, Mathsoft Engineering & Education, Inc., Cambridge, MA) was used for all statistical calculations and regression analysis. Stepwise model selection used the Akaike information criterion for the inclusion or rejection of model parameters.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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b. For the total dataset, MPE ranged from –0.01 to –0.51 Mg m–3, with a median value of –0.23 Mg m–3. When the PTFs were applied using topsoil properties only, the bias was even higher with MPE ranging from –0.12 to –0.63 Mg m–3 (median = –0.30 Mg m–3). For subsoil samples, the MPE was between +0.05 and –0.47 Mg m–3 (median = –0.21 Mg m–3). Prediction errors using published PTFs were highest when predicting topsoil b. This is clearly indicated by the RMSPE, which was on average 24% higher in the topsoil than for the overall dataset.
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b. This was not the case for the Leonaviiut and Huntington PTFs, which showed the lowest correlations and thereby an unstable predictability, especially when applied to subsoils.
Figure 1
illustrates the performance of all PTFs. The PTFs with the highest accuracy and precision were those developed by Adams (7C), Rawls and Brakensiek (8C), and Honeysett and Ratkowsky (9C), all belonging to model type C. Their MPEs and RMSPEs were in absolute terms smaller than 0.18 Mg m–3 and 0.26 Mg m–3 respectively (Table 5). The lowest prediction quality was observed for the PTFs of Kaur et al. (12E), Federer (10D), Huntington (11D), and Leonaviiut (3A). The latter function has a low bias and is relatively accurate, especially for subsoils, but shows a high deviation of the prediction error (SDPE), which indicates its lack of precision (Fig. 1).
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b = (0.602 + 0.026 LOI)–1. The recalibrated equation for Model B is
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The intercepts of both models increased after calibration, due to higher subsoil densities in our dataset, while the regression coefficients decreased (Table 2).
After recalibration, the MPE improved from –0.16 Mg m–3 to –0.03 Mg m–3 and from –0.33 Mg m–3 to –0.004 Mg m–3 for models C and B, respectively. Thus, the bias became very small and was not significantly different from zero for Model B (CI95% = [–0.0018, 0.0009]). Model C showed a small negative bias (CI95% = [–0.0043, –0.0015]). The RMSPE improved for Model C from 0.24 Mg m–3 to 0.17 Mg m–3 and from 0.37 Mg m–3 to 0.16 Mg m–3 for Model B. The prediction coefficient of determination remained the same after recalibration.
With recalibration, accuracy was highly improved but precision increased only slightly. After recalibration, more than 97% of the overall prediction error (MSPE) was due to error in precision (SDPE)2. Hence, the SDPE converged to the RMSPE. The SDPEs evolved on average from 0.18 Mg m–3 to 0.16 Mg m–3. For the Adams PTF (7C), precision error did not change with recalibration, in contrast with Rawls (8C) and Honeyset (9C), although belonging to the same model. This shows that the parameter estimates of the Adams PTF were more precise (for our dataset) than those in the other type C PTFs. Comparing Eq. [6] with Model 7C in Table 2 reveals that b of OM was similar in the published and recalibrated Adams function, 0.311 and 0.312 Mg m–3, respectively.
The CIs of the bootstrapped RMSPEs from both candidate functions were identical: (CI95% = [0.15, 0.18]) showing that their performance was not significantly different from each other.
Importance of Texture and Depth as Predictors
The candidate models were extended with the predictor variables texture and depth (Table 4) and calibrated according to the three variable classes using the calibration dataset. The results of the calibration are presented in Table 6.
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Using the same predictors, the B-type models showed the highest goodness of fit. In the stepwise multiple regression, LOI was clearly the most important variable. Sampling depth contributed more significantly in Model B than in Model C, while the Clay fraction was more relevant than sampling depth in Model C (Table 6).
Extending the candidate models with second and third order polynomials did not enhance the coefficient of determination substantially, nor did it enable a substantial reduction of the RSE. Validation of the calibrated models gave the results shown in Fig. 3 . Table 7 summarizes the ranges of the validation indices for the overall performance of the models. The overall bias (MPE) for Model B was not significantly different from zero, but for Model C there was a significant negative bias, although it was very small. The MPE of texture-based models was more than twice as large as of LOI-based models. Only for the C-type model, the bias of texture-based models was significantly different from the LOI-based model.
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total prediction error). Models based on texture alone were significantly less precise than models based on LOI. Models based on all variables did not differ significantly from models based on LOI alone. Moreover, the individual models based within each O, T, or A group did not differ significantly. With recalibration and validation on this dataset, an overall RMSPE lower than 0.16 Mg m–3 could not be obtained. Using cross validation, no further improvement was observed.
As can be seen in Fig. 3, most models tended to overestimate b below 1 Mg m–3. Since b generally increases with depth, the prediction error was analyzed within 10-cm depth intervals. Figure 4
shows that for Model CO, the highest RMSPE (0.26 Mg m–3) was found in the 0- to 10- cm depth interval. Below 10 cm, RMSPE decreased substantially and fluctuated around 0.13 Mg m–3. However, the texture-based Model CT showed the same error in the topsoil, but maintained that error (about 0.23 Mg m–3) in the subsoil. Model CA did not differ significantly from Model CO for all depth intervals.
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This indicated that a LOI-based model was able to predict b more effectively than texture-based models, even when the OM content was low (like in subsoils). The high error in the topsoil was due to other sources of error (sampling method, biotic activity, topsoil compaction, roots, etc.) and could not be reduced by better calibrated models. Therefore, trying to improve the overall performance by a calibration of the models for the topsoil and subsoil samples separately is not worth the effort.
When LOI-based type B models were specifically calibrated for topsoil and subsoil separately, the RMSPE after validation was 0.1585 Mg m–3, while it was 0.1605 Mg m–3 when no specific calibration was applied. A paired t test between the prediction errors (n = 532) showed no significant differences (P = 0.52). In contrast, Model CO performed even worse if calibrated on topsoil and subsoil samples separately. The RMSPE equaled 0.1718 Mg m–3 compared to 0.1655 Mg m–3 when not calibrated specifically. The prediction errors were significantly different (P = 0.03).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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b values in this study is quite large, but originates from a single region. Only Manrique and Jones (1991) used a larger dataset, based on USDA-SCS soil survey data for agricultural soils (Table 2). Although all sampling in this study was done in forests, many sources of variation are introduced by soil type, sampled horizon, sampling depth, type of forest and vegetation, forest management practices, and differences in soil biotic activity. Furthermore, spatial variation in forest soils is considered larger than in cultivated land due to the absence of homogenization by agricultural practices.
The observed overall mean b value of 1.44 Mg m–3 (Table 1) is somewhat higher than mean values for forest soils reported in literature (Table 3). Kaur et al. (2002), Tamminen and Starr (1994), Harrison and Bocock (1981), Salifu et al. (1999), and Prévost (2004) report lower mean values. Manrique and Jones (1991) found values between 1.2 to 1.5 Mg m–3 according to different soil orders. Only Leonaviiut (2000) reports a higher mean b value of 1.68 Mg m–3. This high mean b is mainly explained by the relatively high proportion of subsurface samples in the Lithuanian dataset. In most other datasets, b data from the upper 30 cm (topsoil) prevail.
The topsoil mean b value of 1.23 Mg m–3 (Table 1) for these forest soils is lower than the value of 1.45 Mg m–3 reported by Boucneau et al. (1998) for the topsoil of cultivated land in the same region. However, the subsoil b values in the two studies are comparable (1.51 and 1.50 Mg m–3, respectively). This suggests a land-use impact on b, with organic-rich topsoils in forests tending to have a lower b than agricultural topsoils. In forests, Honeysett and Ratkowsky (1989) found topsoil b between 0.41 and 1.09 Mg m–3, while subsoil b was 0.96 to 1.67 Mg m–3. Similarly, Tamminen and Starr (1994) reported for topsoils b between 0.48 and 1.33 Mg m–3 and 0.98 to 1.67 Mg m–3 for subsoils.
Because of the differences in b between topsoils and subsoils, PTF calibration based on a higher proportion of topsoil samples and applied on topsoil and subsoil samples will lead to an underestimation of b. This explains why we observed a better predictive quality by using the subsurface PTF 2sA provided by Harrison and Bocock (1981) compared with their topsoil PTF 2tA (Table 5). However, their topsoil PTF did not perform well on our topsoil dataset, in contrast to their subsurface PTF applied on our subsoil data.
The 12 investigated PTFs all have limited predictive potential. In general, Type C algorithms performed best. They are based on a two-component physical model, as described by Honeysett and Ratkowsky (1989). The D- and E-type models provided by Federer (1983), Huntington et al. (1989), and Kaur et al. (2002) are truncated at b values of 1.30, 1.22, and 1.38 Mg m–3, respectively (Fig. 1), due to the natural log transformation of the response variable and the specific range of their predictor variables. They exhibited poor performance in this study. The models developed by Leonaviiut (2000) and Adams (1973) tend to overestimate for b values below 1.3 and 1.1 Mg m–3, respectively. In the evaluation of five existing PTFs, Boucneau et al. (1998) calculated MPE values between –0.01 and –0.17 Mg m–3. Kaur et al. (2002) found MPEs ranging from +0.15 to –0.38 Mg m–3, while in our study we observed MPEs between –0.01 and –0.51 Mg m–3. The RMSPE range reported by Kaur et al. (2002) was 0.15 to 0.45 Mg m–3, while in our dataset it ranged from 0.24 to 0.56 Mg m–3. Surprisingly, the highest prediction error was calculated from the most recently developed PTF of Kaur et al. (2002), suggesting that this PTF is not applicable to a wide range of soil types.
Alexander (1980) noted that a MPE of 0.15 Mg m–3 or more may be acceptable, considering that b may increase up to 0.30 Mg m–3 by compaction. Since for any volumetric calculation, b is multiplied by a weight-based concentration, this will lead to an error of 15% or more. For the PTFs evaluated in this study, an average underestimation of 23% may be expected.
It is difficult to make a general statement on the required accuracy of a PTF model. Huang et al. (2003) found that most authors use thresholds for model acceptance between 10 and 20% of the observed mean (b) at 95% confidence intervals (95CI). For instance, Prévost (2004) accepted a relative prediction error of 20% for b.
On the basis of the Table 1 mean values, prediction errors should be in the range of 0.14 to 0.29 Mg m–3 for all soil samples and between 0.12 and 0.25 Mg m–3 for topsoil samples. For studies that require accurate calculations, prediction errors should be below 10%. In such a case, none of the published PTF's can be used without recalibration and local validation. If prediction errors between 10 and 20% are accepted, type C models and the Harrison and Bocock (1981) PTFs can be applied.
Improvement of Pedotransfer Functions after Recalibration
Validation of recalibrated PTFs showed a significant decrease of the overall prediction error (RMSPE), mainly due to the elimination of the bias (accuracy error) after recalibration. Consequently, based on Eq. [5], the remaining error is mainly error in precision (SDPE), and the best fitted models could not reduce this error below 0.16 Mg m–3 for our dataset. This value (RMSPE SDPE) corresponds to the value observed by Kaur et al. (2002) after recalibration (MPE = 0, RMSPE = 0.15 Mg m–3). The smallest RMSPE observed by Boucneau et al. (1998) was 0.13 Mg m–3. This value was observed for arable land, and is consistent with the RMSPE values we observed for deeper soil layers low in OM (Fig. 4).
Alexander (1980) found standard errors of estimation of 0.14 Mg m–3 for upland soils and 0.12 Mg m–3 for alluvial soils. He concluded that b depended on land use, as well as on natural parameters.
It is most likely that natural parameters, such as decompaction by biotic activity of soil fauna and roots, and anthropogenic factors as soil compaction due to harvesting, introduce considerable local variation, especially in the topsoil. Furthermore, there are errors associated with measurement and spatial variability. On one of the experimental plots we performed a variogram analysis based on 191 topsoil b measurements, situated within one forest stand. The nugget value, which is the sum of the measurement error variance (repeatability) and spatial micro-variance (within 1-m distance), was found to be 0.0361 Mg2 m–6, corresponding to a SD of 0.19 Mg m–3. This indicates that the methodological error for b, combined with high spatial variability, is of the same magnitude as the prediction error. Consequently, it is very hard to improve the RMSPE below 0.16 Mg.m–3 in these forest soils, since the prediction error is overwhelmed by methodological errors and intrinsic natural field variation. Without taking these factors into account, the overall prediction error cannot be improved.
Nevertheless, our findings clearly show that recalibration of existing PTFs using a local dataset is worthwhile. The best performing published PTF (7C) still has a lower predictive ability than the worst performing recalibrated texture-based PTF. Therefore, as suggested by Harrison and Bocock (1981), Alexander (1980), Salifu et al. (1999), and Kaur et al. (2002), specific PTFs should preferably be calibrated and validated on a regional basis to enhance the accuracy and precision of b prediction.
Empirical versus Physical Pedotransfer Function Models
The models belonging to Groups B and C performed best in this study. Tamminen and Starr (1994) found the highest correlation coefficients between b and the square root of OM (Group B), but in their study, a natural log transformation of OM (Group D) performed nearly as well. However, since model Group B is less complex and there is no need to truncate upper values as seen occasionally with models D (Fig. 1), it is the preferred empirical model for calibration purposes. Hence, the best-fitted and simplest empirical model within our conditions is Eq. [7].
A more comprehensive model (Honeysett and Ratkowsky, 1989) to analyze the relationship between soil b and organic and mineral soil densities is provided by Model C. From these equations, based on the Stewart/Adams formula, the b of the mineral soil (b,m) and organic matter (b,o) can be calculated separately. According to our data, the b,m is 1.66 Mg m–3. Adams (1973) reported b,m values between 1.27 and 1.54 Mg m–3, Mann (1986) found estimated values between 0.7 and 1.7 Mg m–3, while the b,m chart of Rawls and Brakensiek (1985) ranged between 1.20 and 1.72 Mg m–3. Prévost (2004) found 1.56 Mg m–3 and 1.45 Mg m–3 for the sandy till soils of northern Québec and sandy till loam soils of New Hampshire, respectively. Our b,m value is higher than found by Adams (1973) and Prévost (2004), but lower than the 1.82 Mg m–3 reported by Honeysett and Ratkowsky (1989), and similar to a b,m of 1.64 Mg m–3 used by Post and Kwon (2000) and Guo and Gifford (2002) to calculate soil carbon stocks. All b,m values are less than the limiting bulk densities of 1.80 to 1.90 Mg m–3 referred to by Archer and Marks (1982).
The b,o in our dataset equals 0.312 Mg m–3. This is higher than the average b,o of 0.224 Mg m–3 reported by Rawls and Brakensiek (1985) and used by Mann (1986), Post and Kwon (2000), and Guo and Gifford (2002). It is a factor of two higher than the 0.163 Mg m–3 found by Honeysett and Ratkowsky (1989), and the values of 0.159 Mg m–3 and 0.111 Mg m–3 reported by Prévost (2004). The observed b,o is close to the maximum of the reported range (0.207–0.311 Mg m–3) determined by Adams (1973). As suggested by Prévost (2004), these high b,o values could be in part attributed to the use of a core sampler, which may have compressed organic particles more definitely.
In terms of predictive capacity, the physical two-component model developed by Adams (1973) (Eq. [6]) showed the best performance out of the list of the published PTFs, and performed as well as the best-fitted empirical model. Since it provides extra information, we recommend this PTF for application in research programs.
Impact of Predictors
Adding texture as a predictor has a minor effect on the estimation of b of forest soils. Consistent with the findings of many authors, OM clearly plays a dominant role due to its much lower specific gravity than mineral soil particles and its aggregation effect on soil structure. In our dataset, models based on LOI only account for 55 to 57% of the total variation in b, while texture explains only 20 to 26%. This is probably not unique to forest soils, since Williams (1970) found that 50% of the variation in b in arable and grassland soils at Rothamsted in England could also be accounted for by variation in organic carbon. If only measured or map-derived texture data are available, the use of PTFs for b estimation of forest soils is highly questionable, especially for topsoil layers. Since it is much easier to measure b than texture, field volumetric sampling and b determination is strongly recommended in that case.
Adding clay, sand, and sampling depth improved the models significantly, but only to a small extent (<2%). However, their predictive quality was not significantly better, and therefore use of these variables is not recommended. Simple models based on LOI only are appropriate, parsimonious, and easy to use.
Calibration and Validation Methodology
Separate calibration of horizons or layers did not lead to substantial improvement of the prediction quality. The same horizon may have different characteristics in different pedons, leading to inconsistent predictions, especially when different soil units are involved. Separate calibration of topsoil and subsoil layers generally leads to badly fitted topsoil PTFs due to the high variability (precision error) of b in the more heterogeneous topsoil. Therefore, it is suggested to develop PTFs for the whole pedon and to take calibration and validation samples over all horizons or depths of interest. Since precision error is highest in the topsoil, a higher proportion of subsoil samples (e.g., 3:1), with much lower precision error, is recommended. However, care should be taken that the whole range of the predictor and response variables is covered. During subsequent (cross) validation, the resulting equation should be checked for a near-zero bias and a low SDPE, preferably below 15% of the mean b. In addition, graphical validation of a predicted vs. observed b plot, should show most data points located near the 1:1 line over the whole b range.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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b. This is explained by the fact that most published PTFs are calibrated using a high proportion of topsoil samples which generally have low b. Accuracy error for published PTFs was high, showing that recalibration of suitable functions is worthwhile. The prediction error was highest when the PTFs were used to predict topsoil b. If accurate b values for volumetric calculations are required (errors < 10%), none of the published PTFs can be used without regional recalibration and validation.
Recalibration of existing PTFs leads to a significant decrease of the overall prediction error, mainly due to the elimination of the bias (accuracy error). The remaining overall error in precision could not be reduced below 0.16 Mg m–3, mainly due to the high variability of topsoil samples. The best fitted and most simple empirical model was based on LOI: b = 1.775 – 0.173(LOI)1/2 (R2 = 0.57). However, its predictive capacity was not significant better than the Adams physical two-component model b = 100/{(LOI/0.312) + [(100 – LOI)/1.661]} (R2 = 0.55) yielding an estimate of b = 0.31 and 1.66 Mg m–3 for the organic and mineral component, respectively. Adding texture and sample depth as variables did not enhance their predictive capacity in a significant way. On the basis of our data, separate calibration on topsoil or subsoil data did not improve the overall prediction quality. Therefore, we suggest that researchers calibrate PTFs using samples taken in all horizons or sample depths of interest, with a higher proportion of subsoil samples.
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ACKNOWLEDGMENTS |
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Received for publication January 19, 2004.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSREFERENCES |
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iut, N. 2000. Predicting soil bulk and particle densities by pedotransfer functions from existing soil data in Lithuania. Geografijos metra
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