**6. Data Analysis and Modeling**

The slope length factor L, accounts for increases in runoff volume as downslope runoff lengths increase. The slope stepness factor S accounts for increased runoff velocity as slope stepness increases. These factors were obtained from digitized topographic maps of scale

For direct application of the USLE a combined slope length and slope stepness (LS) factor

Crop and management factor is the soil loss from an area with specified cover. *C* is a func‐ tion of landuse conditions such as vegetation type, before and after harvesting, crop resi‐ dues, and crop sequence. Forest management practices create a variety of conditions that influence sheet and rill erosion. The USLE has been used with varying degrees of success to predict these forms of erosion on forest land. Assigning a proper value to cover-manage‐ ment factor (C) in the USLE is a problem, however. An undisturbed, totally covered forest soil usually yields no surface runoff. What erosion does occur on undisturbed forest land comes from stream channels, soil creep, landslide, gullies, and pipes, none of which are evaluated by the USLE. Logging, road building, site preparation, and similar activities that

disturb and destroy cover expose the soil to the erosivity of rainfall and runoff [41].

**3.** forest lands which have had site preparation treatments for re-establishment after har‐

100 – 75 0.0001 – 0.001 70 – 45 0.002 – 0.004 40 – 20 0.003 – 0.009

The conservation practice factor *P*, is determined by the extend of conservation practices such as strip, cropping, contouring, and terracing practices, which tend to decrease the ero‐

**Factor** *C*

0.5 <sup>2</sup> *LS l* = ´ + ´+ ´ (0.0138 0.00965 0.00138 ) *S S* (3)

1:25 000.

94 Research on Soil Erosion Soil Erosion

was evaluated for each sample plots as [1]:

where *l* is runoff length (meter), *S* is slope (percent).

Tree categories of woodland are considered separately:

**Percent of area covered by canopy of trees**

**Table 1.** Factor *C* for undisturbed forest land

**2.** woodland that is grazed, burned, or selectively harvested, and

Factor C for undisturbed forest land may be obtained from Table 1 [9].

sive capabilities of rainfall and runoff. Values of *P* range from zero to one.

**1.** undisturbed forest land,

vest.

The candidate variables modeling are numerous and diverse. Hartanto et al. [14] classified such variables in four groups: Soil characteristics, physiographic properties, climatic proper‐ ties and stand characteristics. The candidate variables of soil loss models can be divided in to two groups:


Altitude, exposition, aspect, slope and exposure length have been used as measures of phys‐ iographic structure. Mean height, mean diameter, crown closure and stand density may have been used as measures of the stand level of structure.

Several possibilities exist to describe stand density. Hamilton [13], Ojansuu et al. [26], Van‐ clay [38], Thus [37], all of whom used *BA*, and [3], who used *N*, have provided examples of models with stand density parameters as explicatory variables in modeling. Since *N* and *BA* were directly determined, and did not rely on functional relationships, as opposed to vol‐ ume (*V*), different stand density indexes [7, 28, 10, 5] may be tested.

The soil loss model should be applicable to different stand structures. Therefore, all varia‐ bles must be tested. Based on the discussion above, the following soil loss models have been generally hypothesized:

$$
\hat{A} = \beta\_0 + \beta\_1 S\_1 + \beta\_2 S\_2 + \beta\_3 S\_3 \tag{4}
$$

where *S <sup>1</sup>* is the physiographic structure (altitude, exposition, aspect, slope and exposure length), *S <sup>2</sup>* is the stand structure (*d* ¯ *<sup>q</sup>*, *h* ¯ *<sup>q</sup>*and crown closure) and *S* 3 is the stand density.

Relationship between magnitude of soil loss obtained from sample plots and stand charac‐ teristics have been used to model soil protection value one of the forest values for quantify‐ ing soil loss by using linear, nonlinear, mixed linear and mixed nonlinear procedures in Regression Analysis Method The significance of parameter estimates was tested by means of *t*=b/ASE, where *b* is the parameter estimate and *ASE* is the asymptotic standard error. The parameters of the model for data have been determined using a software package (e.g. SPPS, SAS). Only were variables which are significant (*P*<0.05) included in the equation. A soil loss model is constructed based on some site and stand characteristics as a predictor and possi‐ ble insignificant predictor are excluded. The predicted variable in the soil loss model is an‐ nual soil loss amount, which resulted in a linear or nonlinear relationship between the dependent and independent variables. The predictors of a soil loss model were chosen from stand level characteristics as well as their transformations. Some of them had to be signifi‐ cant at the 0.05 level without any systematic errors in residuals. The assumption of homo‐ scedasticity has been tested using the Durbin-Watson test.

#### **7. Model Validation**

The soil loss model was evaluated quantitatively by examining the magnitude and distribu‐ tion of residuals to detect any obvious patterns and systematic discrepancies, and by testing for bias and precision to determine the accuracy at model predictions [39, 33, 11, 20]. Rela‐ tive bias and root mean square error have been calculated as follows:

$$Bias = \frac{\sum\_{i=1}^{n} \left(A\_i - \hat{A}\_i\right)}{n} \tag{5}$$

**9. Uncertainty**

**10. Conclusions**

There are many sources of uncertainties related to large scale forestry analyses in general, e.g. related to the inventory of input variables used as basis for the analyses [e.g. 16], to model errors of the numerous functions used for predictions [e.g. 15], to the stochasticity of future condition [e.g. 18, 27] and to the stochasticity of future prices and costs [e.g. 34, 19]. Thus [37], as long as the soil loss models are unbiased, they will not introduce any substan‐

Modeling of Soil Erosion and Its Implication to Forest Management

http://dx.doi.org/10.5772/ 53741

97

Soil loss is an important variable which is used for multiple forest management planning.

Measuring soil loss is costly; however, foresters usually welcome an opportunity to estimate this function (forest value) with an acceptable accuracy. Missing soil losses may be estimat‐ ed using a suitable soil loss equation. Based on a comprehensive data set which includes very different stands, such soil loss equation should be fitted for a major tree species in complex.

The stand position and stand density measures used in this kind of studies and variables entered to the soil loss model are easily obtained and are available in forest inventories. In summary, the suggested or developed soil loss models improve the accuracy of soil loss pre‐ diction, ensure compatibility among the various estimates in a forest management scenario,

Linear, nonlinear or mixed models for prediction of soil loss for stand level, designed for use in large scale forestry scenario models and analyses, may been developed. Although soil loss as a phenomenon is complicated to model, and in spite of several uncertain topics re‐ vealed from the work, the model fit and the validation tests may be turned out satisfactory.

Provided the many uncertainties of large scale forestry scenario analyses in general, soil loss models seem to hold an appropriate level of reliability, and we feel that it can be applied in such analyses. This does not mean that the model cannot be enhanced, however. With new rotations of permanent sample plots measurements, the models should be evaluated and, if

and maintain projections with reasonable biological limits.

necessary, revised or calibrated.

Nuray Misir1\* and Mehmet Misir2

\*Address all correspondence to: nuray@ktu.edu.tr

1 Karadeniz Technical University, Faculty of Forestry, Turkey

**Author details**

tial change with respect to the final uncertainty of large scale forestry analyses.

$$RMSE = \sqrt{\frac{\sum\_{l=1}^{n} \left(A\_{l} - \hat{A}\_{l}\right)^{2}}{n - p}} \tag{6}$$

where *n* is the number of observations, *p* is the number of parameters in the model, Ai and *A* ^ *i* are observed and predicted soil loss values, respectively.

In addition, the models were further validated by an independent control data set. The vali‐ dation of a model should involve independant data. Data were partitioned in two independ‐ ent groups, one for model development of soil loss estimation and the other set for validation. The data set used for model development of soil loss eestimation comprised ap‐ proximately 80% of the plots, while the remaining 20% of plots were used for validation. Al‐ though the number of sample plots determined for development of soil loss estimation was made relatively large in order to provide sufficient data for model development phase, the number of sample plots in the test data still should be large enough for validation and ap‐ propriate statistical test. The deviations between predicted and observed values were tested by Student's Paired-t test or Wilcoxon test.

#### **8. Sample size**

The size of sample plot for sampling can be an advantage or disadvantage to model soil loss. A plot size of 800 m2 means that a relatively large number of the trees are not affected by the forest conditions outside the plot. In other words, a relatively number of trees is affected by the forest conditions inside the plot. In this kind of studies plots that might have been sub‐ jected to any harvesting operation between the measurements were excluded from the data material because of insufficient information about treatments. If the harvest on these plots was a result of "regular" management practices, there were no problems related to the ex‐ clusion [37]. However, if the harvest was a result of an extraordinary situation (i.e. floods), exclusion of the plots may have lead to an underestimated soil loss amount.
