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The assessment of the current annual increment of forest standing volume (

The assessment of current annual increment of forest standing volume (

However, the growth dynamics of a given forest stand is not easy to be reliably assessed on one single occasion,

Several methods have been proposed for inventorying _{st}). By measuring the forest standing volume of a given stand (_{st}), the current annual increment of the stand is then straightforwardly calculated as (

where (

where _{j} is the percentage current annual increment of forest standing volume, referred to the _{j} is the forest standing volume, referred to the

All the approaches applied for estimating

where

On a short-term perspective, _{j}, _{j} and _{j} referred to that class (

Usually, _{j} is estimated with reference to the _{j} is estimated with reference to the

A suitable approach to such an end is to rely on general models established to predict

In order to circumvent the estimation of

where

The parameters _{st}. On the other hand, assuming that only

However, this formula again poses the question of estimating

Simplified approaches for an approximate estimation of the annual increment of tree height in a given forest stand can be exploited when direct mensuration is impossible and general prediction models are not available. A suitable approach is based on the difference between the heights assessed on the height curve (

This approach has been adopted to some extent,

The height curve is established on the basis of the sample trees from the stand of interest. However, it is well known that the more an even-aged forest is mature, the more the height curve is flattened (

Here we report the results of a comparison of _{st} assessment by _{st} is also estimated by the conventional K400 criterion (

The study site is located within a silver fir (

The measurements were carried out in a 0.5 ha plot representative of the average conditions of the stand. The dbh of all the trees with dbh >12.5 cm was measured (

Annual stem growth ring count and width measurement (with a precision of 1/100 mm) were carried out on the last ten rings of each sampled core by the LINTAB system (RinnTec) associated with TSAP software (http://www.rinntech.de/content/view/16/47/lang,english/). _{10}/10 where _{10} is the increment of the radius occurred in the last 10 years. The ^{-1}) to the

with ^{2} = 0.67 and SEE = 0.071 cm yr^{-1}. The recruitment period, _{j }= 5/_{j}, where _{j} is the current annual dbh increment predicted by the

_{10}/10, where _{10} is the stem length corresponding to the height increment in the last 10 years. The ^{-1}) to the

with ^{2} = 0.59 and SEE = 0.05 m yr^{-1}. The conventional height curve was established by the scatterplot of the heights

_{j} was estimated by _{j} = 2/_{j}) ). For all cases _{j} was obtained by _{j} was obtained either directly applying

At the time of inventory, the average tree age was about 60 years; the number of trees per hectare was 336; beech was present with 40 individuals per hectare, ^{3} ha^{-1}, of which 93% was due to the silver fir.

The examined stand is characterized by ^{-1} for the smallest dbh class (15 cm) and from 0.80 to 0.89 cm yr^{-1} for the largest one (80 cm). Correspondingly, the period for a tree of a given dbh class to move onto the next dbh class ranges, on average, from 16 years for the 15-cm dbh class down to 6 years for the 80-cm dbh class. Measured ^{-1} for the smallest dbh classes and from 0.15 to 0.21 m yr^{-1} for the largest ones (31-35 m).

_{j} values estimated for each dbh class by the three compared approaches and by the K400 criterion. As expected, _{j} decreases with increasing dbh. Both simplified approaches adopted to assess _{j}, for all the dbh classes as per the approach based on the conventional height curve and for the classes below 60-65 cm as per the approach based on the dynamic height curve. The differences between the simplified approaches and the benchmark approach are larger for the smaller dbh classes and become smaller for the larger ones. Distinctively, _{j} ranges from 7.4% with respect to the 15-cm dbh class down to 2.6% with respect to the 80-cm dbh class for the benchmark approach, while it varies, respectively, from 6.7% to 2.6% according to the dynamic height curve approach and from 6.2% to 2.5% according to the conventional height curve approach. The percentage current annual increment of forest volume at stand level is equal to 3.8% for the benchmak approach, to 3.6% for the dynamic height curve approach, and to 3.4% for the conventional height curve approach. Hence, the dynamic height curve approach gives smaller differences (less than half) than the conventional one as to the benchmark. Distinctively, the _{st} assessment by the dynamic height curve approach can be considered fairly accurate. On the contrary, the K400 criterion brings to a relevant underestimation of _{st} (2.7%).

The ^{3 }ha^{-1 }yr^{-1} for the benchmark approach to 21.9 m^{3 }ha^{-1 }yr^{-1} for the dynamic height curve approach, to 20.8 m^{3 }ha^{-1 }yr^{-1} for the conventional height curve approach and to 16.5 m^{3 }ha^{-1 }yr^{-1} for the K400 approach. As expected, similarly to what observed for the ^{3 }ha^{-1 }yr^{-1 }for the benchmark approach, a value of 3.6 m^{3 }ha^{-1 }yr^{-1} for the dynamic height curve approach, a value of 3.5 m^{3 }ha^{-1 }yr^{-1} for the conventional height curve approach and a value of 2.9 m^{3 }ha^{-1 }yr^{-1} for the K400 criterion.

_{j}, the approach based on the dynamic height curve underestimates the _{j} values up to dbh of 75 cm, while the conventional height curve approach underestimates the _{j} values for all the dbh classes and provides

In this study, two simplified approaches to assess the current annual height increment within the framework of the estimation of

Theoretically, both the simplified approaches are relatively easy to be implemented. However, the dynamic height curve approach is applicable only when an established diameter-height-age model is available and valid for the stand of interest, or when stands of various ages with composition, site fertility and silvicultural treatment similar to those of the stand of interest are available.

Alternatively, the approach based on the conventional height curve can be applied: in this case, underestimation as broad as 9% may be expected as concerns the assessment of the _{st} underestimation of nearly 1/3 in the examined case study. In the light of this, when no other practical tools are available, the

Further considerations can be drawn from the test carried out. From a general point of view, longitudinal and radial stem growth show different patterns (

As a matter of fact, objective decisions need objective information (

Within this framework, the eqns. 2, 4 and 7 are suitable for assessing the percentage current annual increment of forest standing volume within sample plots under practical forest inventory purposes on a single occasion, both on a stand-wise level (forest inventory by compartments) or within assessments at larger scales. The simplicity of such formulas is attractive, though they are characterized by several limitations: for instance, the procedure does not take into account tree mortality. However, it gives reasonable predictions on a short-term perspective, when tree mortality can be neglected, leading to a suitable assessment of the current productivity of the considered forest stands. Obviously, the obtained figures are relative to the stands measured and cannot be extrapolated for long periods or to other stands: in this respect, only proper growth and yield models should be exploited (for reference,

As for

This study was partially developed within the scope of research project “FUME - Forest fires under climate, social and economic changes in Europe, the Mediterranean and other fire-affected areas of the world”, European Commission FP7-ENV-2009, Grant Agreement Number 243888.

We thank the company “La Foresta s.r.l. di Serra San Bruno” for the willingness shown during the surveys in the field.

We also thank four anonymous reviewers for their helpful suggestions on an earlier draft of this paper.

^{th}edn). McGraw-Hill, New York, USA.

^{rd}edn). Prentice-Hall International, New York, USA.

Tree dbh distribution in the examined stand.

Current annual increment of dbh

Current annual increment of tree height

Scatter-plot of measured height

Trends of percentage current annual increment of volume calculated in the examined stand according to the three approaches compared for assessing

Descriptive statistics of the attributes measured on the sampled trees. (SD): standard deviation; (SE): standard error.

Attribute | mean | SD | Skewness | SkewnessSE | Kurtosis | KurtosisSE |
---|---|---|---|---|---|---|

dbh (cm) | 37.4 | 11.3 | 0.85 | 0.25 | 0.91 | 0.50 |

current annual increment of dbh (cm yr^{-1}) |
0.60 | 0.12 | 0.37 | 0.25 | -0.61 | 0.50 |

height (m) | 26.9 | 3.41 | 0.05 | 0.25 | -0.05 | 0.50 |

current annual increment of height (m yr^{-1}) |
0.28 | 0.07 | -0.06 | 0.25 | -0.40 | 0.50 |

Significance of the

Paired comparison | T | Z |
---|---|---|

dynamic height curve approach - benchmark approach | 7.07(p<0.01) | -3.30(p<0.01) |

conventional height curve approach - benchmark approach | 9.38(p<0.01) | -3.30(p<0.01) |

dbh class(cm) | Benchmark approach for assessing ^{3 }ha^{-1 }yr^{-1}) |
Dynamic height curve approach for assessing ^{3 }ha^{-1 }yr^{-1}) |
Conventional height curve approach for assessing ^{3 }ha^{-1 }yr^{-1}) |
K400criterion(m^{3 }ha^{-1 }yr^{-1}) |
---|---|---|---|---|

15 | 0.14 | 0.13 | 0.11 | 0.08 |

20 | 0.33 | 0.30 | 0.28 | 0.21 |

25 | 0.62 | 0.59 | 0.55 | 0.42 |

30 | 1.04 | 0.99 | 0.93 | 0.74 |

35 | 1.71 | 1.62 | 1.53 | 1.24 |

40 | 3.12 | 2.98 | 2.82 | 2.30 |

45 | 3.34 | 3.19 | 3.04 | 2.50 |

50 | 3.80 | 3.65 | 3.47 | 2.89 |

55 | 3.05 | 2.94 | 2.81 | 2.35 |

60 | 1.90 | 1.84 | 1.76 | 1.48 |

65 | 1.85 | 1.80 | 1.72 | 1.46 |

70 | 1.04 | 1.02 | 0.98 | 0.83 |

75 | 0.39 | 0.38 | 0.36 | 0.31 |

80 | 0.43 | 0.42 | 0.41 | 0.35 |

Schneider’s coefficient

dbh class(cm) | Benchmark approach | Dynamic height curve approach | Conventional height curve approach |
---|---|---|---|

15 | 688 | 628 | 575 |

20 | 620 | 578 | 537 |

25 | 587 | 553 | 518 |

30 | 567 | 537 | 505 |

35 | 553 | 525 | 497 |

40 | 543 | 517 | 490 |

45 | 534 | 511 | 485 |

50 | 527 | 506 | 481 |

55 | 520 | 501 | 478 |

60 | 514 | 498 | 475 |

65 | 509 | 495 | 473 |

70 | 504 | 492 | 471 |

75 | 499 | 490 | 469 |

80 | 495 | 488 | 467 |