**9. Uncertainty**

**7. Model Validation**

96 Research on Soil Erosion Soil Erosion

*A* ^ *i*

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‐

( )

( )


*A A*

*n p*

where *n* is the number of observations, *p* is the number of parameters in the model, Ai and

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

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.

<sup>ˆ</sup> *<sup>n</sup> i i*

2

å (5)

å (6)


*A A*

<sup>ˆ</sup> *<sup>n</sup> i i*

*n*

1

1

=

<sup>=</sup> -

*i*

=

*i*

=

tive bias and root mean square error have been calculated as follows:

*Bias*

*RMSE*

are observed and predicted soil loss values, respectively.

by Student's Paired-t test or Wilcoxon test.

**8. Sample size**

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