Published in Soil Sci. Soc. Am. J. 68:943-949 (2004).
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
DIVISION S-7FOREST & RANGE SOILS
Predicting Soil Properties from Organic Matter Content following Mechanical Site Preparation of Forest Soils
Marcel Prévost*
Ministère des Ressources Naturelles, de la Faune et des Parcs, Forêt Québec, Direction de la Recherche Forestière, 2700, rue Einstein, Sainte-Foy, QC, Canada G1P 3W8
* Corresponding author (marcel.prevost{at}mrnfp.gouv.qc.ca).
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ABSTRACT
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The difficulties of sampling forest soils and their high spatial variability make estimation of soil physical properties following forest operations laborious. To develop prediction tools, soils were sampled from two sites located in the boreal forest of northern Québec, Canada. Soil organic matter (OM) content was found to be closely related to bulk density (Db) and porosity after clearcutting and mechanical site preparation (MSP) on these sites. Reasonably good estimates of Db, with an average error of 18 to 20%, can be made from the easily measurable OM concentration and the logarithmic relationships (R2 = 0.731 and 0.847, respectively for the Alma and Chibougamau sites) developed in this study. The organic density approach, recently developed for forest soils in New England, was found to be less precise (R2 = 0.637) than the logarithmic relationships following soil disturbance. For the two sandy till soils in northern Québec, the equation based on this concept best fit the data with a pure OM bulk density (Dbo) of 0.159 Mg m3 and a pure mineral matter bulk density (Dbm) of 1.561 Mg m3. The equations presented in this study also explain between 60 and 70% of the variation in porosity and C/N ratio from OM concentration, with prediction errors of 13 and 24%, respectively. In spite of soil surface disturbance associated with MSP, the easily measurable OM concentration can be used to predict Db, porosity, and C/N ratio.
Abbreviations: Db, bulk density Dbo, pure organic matter bulk density Dbm, pure mineral matter bulk density EU, experimental unit MBIA, mean bias MSP, mechanical site preparation OM, organic matter RMSEP, Root mean square error of prediction
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INTRODUCTION
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ORGANIC MATTER CONTENT and Db are related soil properties that are important to characterize soil disturbance following harvesting and MSP. The pool of several nutrients is closely related to the OM concentration (Armson, 1977). Bulk density is related to other soil physical properties such as texture, structure, air-filled porosity, and water conductivity (Froehlich and McNabb, 1984). Although soil strength (resistance measurements) is presently the simplest and most practicable means of assessing soil physical properties associated with productivity (Powers et al., 1998), Db is often used as an index of soil compaction to quantify harvesting impact on the stony soils of the boreal forest (Corns, 1988; McNabb et al., 2001; Block et al., 2002). In nutrient studies, estimates of Db are also necessary to establish the nutrient pool of a soil layer (grams per square meter of land area, megagrams per hectare) from standard laboratory analyses of concentrations (mg kg1, %).
Theoretically, Db is simple to estimate (oven-dry weight/total volume), but in practice, collection of volumetric samples from forest soils can be very difficult due to rocks, roots, and woody debris (Terry et al., 1981). Furthermore, spatial variability in forest soils is high (Grigal et al., 1991; Järvinen et al., 1993) and the sampling intensity that would be necessary for an adequate estimation frequently exceeds available resources. However, Db and most of the properties affecting root development are closely related to OM concentration, which is determined by loss on ignition of easily collected soil samples. Curtis and Post (1964) developed an empirical relationship of log Db on log OM concentration for till forest soils of Vermont. Federer (1983) and Huntington et al. (1989) obtained similar relationships for forest soils of New Hampshire, which supported the use of OM concentration measurement to estimate Db throughout New England. More recently, Federer et al. (1993) developed a new theoretical expression based on the organic density concept to relate Db and OM concentration. The expression supposes that (i) Dbo and Dbm remain constant in any mixture and (ii) the volumes occupied by the mineral and the organic fractions are additive. The relationship was tested satisfactorily for eight locations in New England, including three sites that had been recently affected by logging disturbance.
Clearcutting and MSP followed by tree planting are widely applied in the boreal forest. In the Canadian boreal forest, the effect of MSP on seedling field performance (Sutton, 1987; Macdonald et al., 1998) and soil properties (Prévost, 1996; Schmidt et al., 1996) received some attention. Although it is recognized that Db is closely related to OM concentration for a given soil, no relationships are available for organic matter-rich till soils in the boreal forest. In this paper, the logarithmic approach and the organic density concept of estimating Db from OM concentration are validated following clearcutting and MSP on two sites of the Canadian boreal forest. Simple relationships between OM concentration and Db, total porosity, and C/N ratio are also developed. A major soil surface disturbance as produced by MSP may greatly affect the physicochemical properties of the soil and change their interrelations. Thus, a further goal of this study was to assess the possibility of developing relationships that would be reliable for both harvest-only and MSP treated areas.
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MATERIALS AND METHODS
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Experimental Sites
Data were collected from two experimental sites, where modified clearcut systems (strip or group seed-tree cuttings) were combined with MSP to promote the natural establishment of black spruce (Picea mariana [Mill.] BSP) seedlings. Both sites were in the black spruce-mosses domain (Saucier et al., 1998) included in the B.1b ChibougamauNatashquan region of the boreal forest (Rowe, 1972); one site is located 120 km north of Alma (49° 48' N lat., 71° 27' W long.) and the other is 80 km southwest of Chibougamau (49° 23' N lat., 74° 52' W long.), Québec, Canada. The regional climate is classified as subpolar subhumid, continental (Robitaille and Saucier, 1998), with 90 frost-free days (Canadian Climate Program, 1982) and an average annual precipitation of 930 mm (one third as snow). Mean daily maximum temperatures are recorded in July (22.1°C) and minimum temperatures in January (24.0°C; Canadian Climate Program, 1993). Soils of the region are developed from deep glacial till and, in both sites, the soil is classified as podzol (Canada Soil Survey Committee, 1992) or Spodosol (Soil Survey Staff, 1998). Both sites were black spruce stands (>90% of basal area) with an ericaceous understorey (Kalmia angustifolia [L.] and Ledum groenlandicum [Retzius]) and a ground cover of feathermoss (Pleurozium schreberi [BSG.} Mitt., Hylocomium splendens [Hedw.] BSG., Polytrichum sp.). The Alma site was described in detail by Prévost (1996) while the Chibougamau site was presented in Prévost (1997).
At Alma, the soil was a loamy sand covered with a Fibrimor layer that was 23 cm in average thickness. The soil moisture regime was classified as moderately to well-drained on 80% of the area, and as imperfectly drained in depressions (according to Saucier et al., 1994). The experimental design for this study was a complete randomized block design with four replications, each containing five soil treatments (50 x 100 m experimental units, EUs): an harvest-only control (no MSP) and four treatments combining two types of MSP (TTS-35H disc trencher [TTS Forest OY, Rajamäki, Finland] and Wadell cone trencher [Storebro International AB, Storebro, Sweden]) and two treatment intensities (single-pass and double-pass). The disc trencher consisted of two free-rotating toothed-discs and the cone trencher consisted of two toothed-cones with a contra-rotation to the direction of the travel. Both trenchers were hydraulically activated to apply downward pressure. These machines cut furrows in the soil and expose mineral soil in a trench bordered by a loosened berm that is elevated above the initial ground surface (Sutton, 1993). The scarification treatments were applied along stream buffer strips, to take advantage of seeding that would come from the strips which is similar to that occurring in strip clearcuts. Each EU was subdivided into two 25 x 100 m subunits, one being allowed to regenerate naturally and the other being planted with 2 + 0 black spruce seedlings.
At Chibougamau, the soil was an imperfectly to well-drained silty sand with a slightly undulating topography. The organic layer was a peaty Fibrimor 20 cm in depth. The MSP treatments were applied around circular groups of seed-trees (30, 40, 50, 60, and 70 m in diameter), which were left uncut. The experimental design consisted of 12 complete randomized blocks, each containing three soil treatments: a harvest-only control (no MSP), a single-pass, and a double-pass passive disc trenching (TTS-35). Each treatment was applied on a truncated pie slice shaped area that had a 40° angle and that extended 100 m from each seed-tree group.
Soil Properties
To evaluate soil properties before MSP, two soil sampling plots were established in each EU. In each plot, two types of samples were collected at three depths, 0 to 10, 10 to 20, and 20 to 30 cm, under the litter layer (L and F horizons) thus including the decomposed humus layer (H horizon, 01 cm). A 130 cm3 undisturbed soil core (5.25 cm diameter, 6.0 cm long) was first collected at each depth with a double-cylinder, hammer-driven core sampler. Bulk samples were collected afterward from the side of the created hole and transported into plastic bags for chemical analyses. Both types of sampling were repeated at each of the two sites at different time intervals following scarification (2, 14, 26, and 38 mo in Alma and 12, 36, and 60 mo in Chibougamau). In scarified EUs, samples were collected at elevated position on the trench profile, while avoiding the bottom of the furrow and undisturbed areas to estimate soil properties in the best planting microsite (Örlander et al., 1990).
Undisturbed core samples were first water saturated from the bottom and weighed. Samples were oven-dried at 105°C for 24 h and weighed again to determine dry weight. Total pore space was estimated by the difference between the saturated weight and the dry weight, removing the density of water as 1.0 g cm3. The dry weight and total pore space were expressed on a volume basis to determine Db and total porosity (Armson, 1977). Values of Db were not corrected for stone content, that is, for particles >2 mm, but cores found to contain stones >10 mm were discarded. Bulk samples were air dried and sieved (2 mm). The Bouyoucos method was used to determine soil textural classes. The OM concentration was obtained by loss on ignition (Nelson and Sommers, 1982) and total C was estimated by dividing this concentration by a factor of 1.724, assuming that inorganic C is insignificant in these acidic soils (pH around 4). The Kjeldahl method (after grinding to 0.5 mm) was used to mineralize the organic matter (Thomas et al., 1967) to determine organic N + NH4N by colorimetry with a Lachat Flow Injection Analyzer (model 8000, Lachat Instruments, Milwaukee, WI), while NO3N was also estimated by colorimetry on 2 M KCl extracts (Kalra and Maynard, 1991). The pH was determined on a 0.01 M CaCl2 solution, while extractable P was measured by the Bray2 method. Exchangeable Ca was measured by plasma-atomic emission spectrometry on 1 M CH3COONH4 extracts (McKeague, 1978).
Data Analysis
All statistical analyses were performed with the SAS software (SAS Institute, 1996). The CORR procedure was used to obtain Pearson correlation coefficients between OM concentration and other parameters. For each site, data of all treatments and all sampling dates were pooled for the regression analyses. The STEPWISE procedure, with the stepwise selection method applying a same significance level = 0.05, for entry and for staying into the model, was used to select among three expressions of the independent variable (OM, ln OM, and [ln OM]2) and obtain the regression coefficients (a, b, c, and d) for the best fit of the model:
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where OM is the organic matter concentration (g OM g1 of soil). The response variable Y was first analyzed without transformation and thereafter using a logarithmic transformation (ln Y). The model having the higher R2 was retained. The accuracy of equations was evaluated with the statistical terms MBIA (mean bias) and RMSEP (root mean square error of prediction):
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where, Yip is the predicted value, Yio, the observed value, N, the number of observations and p, the number of adjusted regression coefficients. These statistical terms are recognized as being valuable to estimate model performance from data that were used to obtain regression coefficients. The nonlinear regression (MODEL procedure), with the Marquardt iteration method, was used to estimate parameters of the Federer et al. (1993) equation:
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where Db is the soil bulk density, Dbm is the bulk density of the mineral fraction, and Dbo is the bulk density of the organic fraction.
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RESULTS AND DISCUSSION
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Relationships between Organic Matter Concentration and Other Variables
The two soils were of coarse texture with only small differences in particle-size distribution (Table 1). This result reflects the crystalline nature of the bedrock from which the till was derived. The ranges of Db values were also comparable for the two sites (0.10 to 1.90 and 0.11 to 1.96 Mg m3, respectively for Alma and Chibougamau), as were ranges of porosity values (32 to 91 and 33 to 96%). Both sites had a wide range of OM concentration values (0.003 to 0.903 and 0.004 to 0.894 g g1), the organic matter content of these forest soils decreasing with depth of sampling (not shown). As a whole, the ranges of C/N ratios were also comparable for the two sites (12 to 81 and 12 to 67), but the average C/N ratio was higher in unscarified EUs at Alma (42) than in other EUs (29). For both sites, pH, extractable P, and exchangeable Ca appeared to be in the normal ranges for till soils of the boreal forest (Schmidt et al., 1996).
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Table 1. Mean, minimum (Min.), and maximum (Max.) values of soil properties related to harvesting and mechanical site preparation (MSP) at the Alma and Chibougamau sites.
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Organic matter concentration is related to most of the variables describing chemical properties of the two forest soils under study (Table 2). The highest linear correlation is with the C/N ratio (r = 0.72 and 0.68, respectively at Alma and Chibougamau) and exchangeable Ca (0.72 and 0.66), while OM concentration is little correlated with soil pH (0.46 for the two sites) and extractable P (0.31 and 0.29). Among the physical properties, Db (0.64 and 0.75) and porosity (0.58 and 0.75) are highly correlated with OM concentration at both sites, while clay content is little related to OM concentration (r = 0.21 and 0.32). Sand and silt contents of both sites are not related (p = 0.180 to 0.659) to OM concentration. Generally, the correlation coefficients between OM concentration and other soil properties are slightly higher for the silty sand of Chibougamau than for the loamy sand of Alma. These slight differences are not attributed to sampling and analysis procedures, as they were the same for the two sites. They may be related to the higher level of soil disturbance at Alma causing more data variability.
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Table 2. Pearson correlation coefficients (r) and corresponding p values between organic matter (OM) concentration (g g1) and other soil properties, at the Alma and Chibougamau sites.
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The relationships between OM concentration and the three response variables Db, porosity, and C/N ratio, were found to be independent of sampling depth. Data for the three soil layers were thus pooled to fit equations for a full range of OM concentration values. Furthermore, a soil treatment effect on the observed relationships was not detected when samples were stratified into harvest-only control and MSP treated areas (dots and circles, Fig. 1)
. For the three response variables, logarithmic equations best fit the data (Table 3) as was reported in the literature (Curtis and Post, 1964; Federer, 1983; Huntington et al., 1989). For every dependent variable, the first term to be included into the equation using the STEPWISE procedure was the same for the two sites. This result suggests that the main tendency was similar between sites and that it would be possible to develop single relationships for the two sites.
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Table 3. Regression coefficients (a, b, c, and d) between the independent variable organic matter (OM) concentration (g g1) and the response variables bulk density (Db, Mg m3), total porosity (%), and C/N ratio, for the Alma and Chibougamau sites. The fitted curves are illustrated by solid lines in Fig. 1.
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Table 4. Relationships between bulk density (Db, Mg m3) and OM concentration (g g1) using the logarithmic approach and the organic density approach.
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The logarithmic model explains 73 and 85% of Db variation, at the Alma and Chibougamau sites respectively (Table 3). Data from both sites were best fit with ln Db as the response variable and with OM as the first independent variable to be included into the model, the linear effect being notable for low organic matter contents (Fig. 1). The inclusion of ln OM into the models only increased the explained variation by 5%, while (ln OM)2 did not improve the model R2 in either case, although it was found significant for the Alma site. Curtis and Post (1964) showed that a relationship using ln OM and (ln OM)2 explained the variation in Db from some Vermont soils very well. In the present study, the equations using ln OM and (ln OM)2 produced approximately the same fit to the pooled data (R2 = 0.767, Table 4) as the relationship including the third term OM (R2 = 0.774, Table 3). However, the logarithmic curves developed by Federer (1983) and Huntington et al. (1989) for forest soils of New Hampshire (Table 4 and Fig. 1) differ in shape from the curves obtained in this study. For given OM concentrations, the former relationships generate lower Db values than the curves produced in the present study. According to Huntington et al. (1989), relatively low Db is characteristic of the generally well-structured and coarse-textured northeastern forest soils. However, these authors had maximum OM concentration values around 0.3, which is low compared with values reaching 0.9 in this study. It is possible that our larger OM concentration range allowed a better fit of high OM concentration values and forced a section of the curve upwards. For OM concentration values of 0.3 and less, which are in the range of Huntington et al. (1989), both curves are quite close to each other. However, the equation obtained by Federer (1983) with OM concentrations ranging from 0.01 to 0.93 for northern New Hampshire soils also underestimates our Db for a given OM concentration value. As a whole, these results indicate that the two studied till soils in the northern black spruce domain have higher Db than forest soils in New Hampshire.
The equation based on the organic density concept fit quite well to the pooled data of the two sites in the present study (R2 = 0.637, Table 4). However, this model explains 13% less of the Db variance than the logarithmic relationship (R2 = 0.767, Table 4). Federer et al. (1993) report that in spite of soil disturbance during harvesting at one site, the DbOM concentration relationship was similar to that obtained in a nearby mature spruce-fir forest and fit the assumption of additive mineral and organic volumes. In the present study, the severe soil disturbance produced during MSP represents a source of error in the organic density model. This approach resulted in a higher Dbo value (Dbo = 0.159 Mg m3 and Dbm = 1.561 Mg m3) for the sandy till soils of northern Québec than for the sandy till loam soils of New Hampshire (Dbo = 0.111 Mg m3 and Dbm = 1.450 Mg m3). This latter curve, taken from Federer et al. (1993), corresponds well to the logarithmic curves that were developed in the present study (Fig. 1). Similar to Federer et al. (1993), Tremblay et al. (2002) obtained 0.12 Mg m3 for Dbo and 1.40 Mg m3 for Dbm, from soils supporting sugar maple (Acer saccharum Marsh) stands and some spruce and fir stands in southern Québec. The Dbo in the present study corresponds to the 0.155 Mg m3 value obtained by Federer et al. (1993) for the data collected by Curtis and Post (1964) from Vermont till soils. It is possible that the relatively high Dbo values observed in the present study could be in part attributed to the use of a core sampler which may have compressed organic particles more definitely.
Similarly to Db, porosity is clearly related to OM concentration (Fig. 1), particularly at the Chibougamau site where the R2 of the fitted model reaches 0.752, compared with 0.561 at Alma (Table 3). For both sites, ln OM was first included into the model and thereafter (ln OM)2 added 2% to the explained variation. The better fit in Chibougamau could be explained by a less severe disturbance as compared with Alma, where the treatment removed 80% of the organic matter content of the microsites without significantly changing the porosity (Prévost, 1996). Furthermore, similarly to Db, prediction of porosity is subject to the intrinsic heterogeneity of forest soils.
The C/N ratioOM concentration relationships are more variable than the DbOM concentration and porosityOM concentration relationships (Table 3 and Fig. 1). The C/N ratio is best explained by ln OM, but contrary to the relationships with Db and porosity, a second term is introduced into the model only for the Alma site ([ln OM]2, partial R2 = 0.071). Surprisingly, the C/N ratio is better predicted for each of the two sites taken separately (R2 = 0.611 and 0.649) rather than for the pooled data (R2 = 0.603). By disturbing surface horizons, MSP produced immediate site-specific changes in C and N concentrations. For example, MSP decreased the C/N ratio by exposing mineral horizons to the surface in Alma (Prévost, 1996), while the treatment little modified this ratio in Chibougamau. Furthermore, subsequent dynamic processes such as OM decomposition and N mineralization may add to data variability by modifying these concentrations in different ways. The accelerated OM decomposition following MSP is likely to decrease the C/N ratio with time, as observed in Alberta by Schmidt et al. (1996). At the Alma site, the buried bag method has indicated that organic matter mineralization was not accelerated during the first year following MSP (Prévost, 1996). Unfortunately, N mineralization was not studied afterward and it is thus impossible to relate the mineralization rate to the observed C/N ratio values.
Adequacy of the Regression Models
In their current practice, both managers and researchers have to characterize forest site condition and thus they need a good estimate of the mean of the principal soil properties. The MBIA statistic shows that the logarithmic equations presented in this study allow to predict Db, porosity and the C/N ratio from OM concentration practically without bias (Table 5). This is an indication that the accuracy of prediction will increase with the number of soil samples and that the estimation of the mean should be reliable.
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Table 5. Some statistics illustrating the error of prediction from logarithmic relationships adjusted for the Alma and Chibougamau sites. The regression coefficients are presented in Table 3 and the resulting curves are illustrated by solid lines in Fig. 1.
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The accuracy of the Db estimate from OM concentration is slightly better for the Chibougamau site than for the site at Alma (Table 5). The RMSEP statistic establishes the mean error of prediction of individual Db values to 0.204 and 0.229, respectively, which corresponds to 17.5 and 20.4% of actual values. Considering that direct Db measurement is very laborious for forest soils, this accuracy appears to be acceptable for most applications. For example, the approach could be considered to be sufficiently precise to detect significant Db differences between sites or changes in Db following MSP. Similarly, Federer (1983) obtained Db estimates within 20% of the observed values in 115 of 130 tested samples in a northern New Hampshire site. This result justified the author to use a single equation developed from this site throughout New England.
The visual analysis of residuals confirmed the absence of a bias in Db prediction from OM concentration (not shown), although it indicated that the absolute error slightly increases with Db, particularly for samples above 0.8 Mg m3. Such a result was noted by Huntington et al. (1989) for low OM concentrations (<0.08 g g1), primarily in the 10- to 20- and 20+-cm depth strata. In the present study, the lack of fit to high Db values (Fig. 1) can be explained by the high variability of Db (0.45 to 1.96 Mg m3) at low OM concentrations (<0.10 g g1). Other soil factors such as texture, structure, and rock content greatly affect Db, particularly at low OM concentration. However, the relative error of estimate (percentage of observed Db) is around 20% for the entire OM concentration range, since Db decreases with increasing OM concentration. These results, together with similarities between the presented relationships and those found in the literature, support the use of OM concentration to obtain reliable Db estimates following MSP on sandy till soils in the boreal forest.
Between 60 and 70% of porosity variation can be explained using OM concentration and the logarithmic relationships developed in this study (Table 3). For both sites, the RMSEP is around 7% and corresponds to mean errors between 12 and 14% of the observed values (Table 5). The MBIA statistic and residuals (not shown) indicate that porosity estimation is generally without bias. Data from the two sites indicate that the porosityOM concentration and DbOM concentration relationships were clearly defined and changed little during the 5-yr sampling period, suggesting that the soil surface layers rapidly stabilized after treatment. Mechanical site preparation created a variety of seedbeds, from compact mineral soil in the trench to loosened OM-rich seedbeds in adjacent berm (Prévost, 1996). According to Örlander et al. (1990), trenching does not loosen the soil significantly below the surface and the soil loosening that occurs in elevated spots does not last for a long time. In the present study, the rapid soil surface settling could be attributed to the compression by the winter snowpack and to the frequent freezethaw cycles occurring in the shallow depths of the cold soils in the boreal forest. The presented equations are thus generally reliable for any post-cut condition including MSP treated areas.
Similar to Db and porosity, the prediction of the C/N ratio is slightly better for the Chibougamau site than for the Alma site. The RMSEP statistics, around 6 in Chibougamau and 7 in Alma, correspond to mean errors of 20 and 24%, respectively (Table 5). The residuals are independent of the predicted C/N ratio (not shown), soil treatment and site, although MSP modified the C/N ratio at Alma. Following MSP in west-central Alberta, Schmidt et al. (1996) observed that the treatment effect on the C/N ratio was closely related to its effect on the OM content. In the present study, the C/N ratioOM concentration relationship was not affected by MSP.
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CONCLUSIONS
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Among the studied soil properties, Db, total porosity, and C/N ratio were the most closely related to OM concentration following clearcutting and MSP at two sites in the Canadian boreal forest. In spite of soil surface disturbance, a close relationship was found between the easily measurable OM concentration and Db (which is laborious to estimate). The logarithmic relationships presented for the two northern black spruce stands explain nearly 80% of the variation in Db and are valid on both harvest-only and MSP treated areas. The prediction error of 20% for Db is acceptable considering the inherent difficulties of measurement and their associated error in forest soils. An approach using organic density was shown to be less precise (R2 = 0.637) than logarithmic relationships (R2 = 0.767) in this study. Indeed, it appears difficult to totally reconcile the concept of additive mineral and organic densities to the well established effect of soil loosening that is attributed to MSP. Relationships using OM concentration as independent variable and explaining between 60 and 70% of the porosity and C/N ratio variations suggest that they can also be useful for a simple and rapid estimation of these variables.
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ACKNOWLEDGMENTS
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The author thanks Rock Ouimet, Daniel Kneeshaw, and André Plamondon for revising an earlier version of this manuscript. The helpful suggestions of the associate editor and two anonymous reviewers are also acknowledged for improving the manuscript. Finally, the author acknowledges Gilles Audy, Louis Faucher, and Pascal Gagnon for soil sample collection; Carol Deblois and his team for laboratory analyses; and Louis Blais for statistical advice.
Received for publication April 4, 2002.
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