Modeling dead wood in Fennoscandian old-growth forests dominated by Norway spruce

2004 ◽  
Vol 34 (5) ◽  
pp. 1025-1034 ◽  
Author(s):  
Thomas Ranius ◽  
Bengt Gunnar Jonsson ◽  
Nicholas Kruys
Keyword(s):  
Norway Spruce ◽  
Residence Time ◽  
Tree Mortality ◽  
Woody Debris ◽  
National Forest Inventory ◽  
Mortality Data ◽  
Negative Exponential Distribution ◽  
Computer Simulation Program ◽  
Number Of Stems ◽  
Negative Exponential

If equilibrium is assumed in unmanaged forests, the volume of coarse woody debris (CWD), VCWD, may be calculated from (i) the volume of living trees, Vliving, (ii) average volume of a dead stem in relation to when it was alive, k, (iii) tree mortality rate, m, and (iv) residence time of CWD, t, by the equation VCWD = Vlivingkmt. We parameterized this equation with data from Norway spruce (Picea abies (L.) Karst.) dominated forests in Fennoscandia. The Vliving was assumed to be directly proportional to forest productivity. Tree mortality data were from the National Forest Inventory, while it was difficult to find quantitative data on k and t. The predicted amounts (74–138 m3/ha, with larger amounts in the south) and size distribution (a negative exponential distribution of the number of stems) of CWD corresponded fairly well to averages from field inventories. By using a computer simulation program, the variability in tree mortality, density of living trees, and residence time of CWD were considered. In the simulations, the amount of CWD varied widely between 1-ha plots, especially for individual decay classes. Therefore, this model could be used to predict averages from larger landscapes unaffected by large disturbances, while no model can predict the amount of CWD at individual plots.

Time since death and fall of Norway spruce logs in old-growth and selectively cut boreal forest

2002 ◽  
Vol 32 (10) ◽  
pp. 1801-1812 ◽  
Author(s):  
Ken Olaf Storaunet ◽  
Jørund Rolstad
Keyword(s):  
Norway Spruce ◽  
Classification Systems ◽  
Time Since Death ◽  
Forest Stands ◽  
Old Growth ◽  
South Central ◽  
Decay Class ◽  
Negative Exponential Distribution ◽  
Decomposition Time ◽  
Negative Exponential

To estimate the age of Norway spruce (Picea abies (L.) Karst.) logs by means of decay classes, and to assess how long it takes for downed logs to decompose, we dated logs dendrochronologically by applying 5- and 8-grade decay classification systems. Study sites were chosen in old-growth and previously selectively cut forest stands in boreal south-central Scandinavia; 113 logs were dated to the number of years since death, 120 were dated to the number of years since fall, and 61 logs were dated to both. The number of years from death to fall showed a negative exponential distribution, with a mean of 22 years and a range of 0–91 years. Decay classes of logs (8-grade scale) reflected time since fall (R2 = 0.58) better than time since death (R2 = 0.27) in a linear regression model. This result is due to the lower decomposition rate of standing snags. Therefore, the decomposition time of logs should be divided into two periods: time from death to fall, which varies considerably, and time after fall, which appears to follow a linear relationship with decay class. The model predicted that it takes 100 years after fall for downed logs to decompose completely (reaching decay class 8) in old-growth stands. Logs in selectively cut stands appeared to decompose faster (64 years), which is explained by a sample shortage of old logs resulting from previous cuttings. We conclude that the decomposition time of downed logs may be severely underestimated when data is retrospectively compiled from previously logged forest stands.

Modeling the decay of coarse woody debris in a subalpine Norway spruce forest of the West Carpathians, Poland

2008 ◽  
Vol 38 (3) ◽  
pp. 415-428 ◽  
Author(s):  
Jan Holeksa ◽  
Tomasz Zielonka ◽  
Magdalena Żywiec
Keyword(s):  
Decay Rate ◽  
Norway Spruce ◽  
Residence Time ◽  
Coarse Woody Debris ◽  
Woody Debris ◽  
Subalpine Forest ◽  
Residence Times ◽  
Stem Size ◽  
The Mean ◽  
Total Residence Time

Coarse woody debris (CWD) is an important structural element in forests. Its role depends on the species, size, position, and decay rate. This paper reports an attempt to determine the total residence time of CWD across all decay classes and also within successive decay classes. We simulated the process of CWD decomposition for stem size and position (snags versus logs), using matrices of the transition of CWD between decay classes. The study was based on a sample of 2785 Norway spruce snags and logs measured twice over a 10  year period in a Carpathian subalpine forest. The revealed pattern of decomposition depended highly on CWD size. When log numbers were considered, the mean total residence time increased from 71 years for small logs (diameter < 23 cm) to 90 years for medium-sized logs (23–35 cm), and to 113 years for large logs (>35 cm). In terms of volume, the mean total residence times of logs were 47, 49, and 63 years for the three diameter categories. Still shorter were the mean total residence times for log mass: 34, 41, and 41 years for the three diameter categories. The pattern of decomposition depended highly on the CWD attributes taken into consideration. The differences in decay rate between log diameter categories are considerable when the number of logs is taken into account, but they practically vanish when log mass is considered.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

Ehrenfest urn models

1965 ◽  
Vol 2 (02) ◽  
pp. 352-376 ◽  
Author(s):  
Samuel Karlin ◽  
James McGregor
Keyword(s):  
Exponential Distribution ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Urn Models ◽  
Time Intervals ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 &lt;p&lt; 1).

scholarly journals Traffic Characteristics for A Freeway Normal Section at Baghdad City

2018 ◽  
Vol 7 (4.20) ◽  
pp. 283
Author(s):  
Jalal T. S. Al-Obaedi ◽  
Muhanad Al-temimy ◽  
Amal Ali
Keyword(s):  
Traffic Flow ◽  
Research Work ◽  
Distribution Data ◽  
Lane Changing ◽  
Traffic Characteristics ◽  
Traffic Lane ◽  
Video Recordings ◽  
Negative Exponential Distribution ◽  
Headway Distribution ◽  
Negative Exponential

Traffic characteristics at highway sections are usually varying based on many factors including type of highways, geometric design and drivers’ behavior at a given area (country).  This paper focuses on finding the characteristics for traffic on selected normal freeway section at Baghdad city.  Video recordings and speed gun are used to collect data from a basic freeway section within Mohammed Al-Qassim freeway that represents the busiest freeway at the city.  The estimated characteristics include the distribution of traffic among the available lanes, desired speed of traffic, lane-changing frequency, and headway distribution.  For traffic distribution, it is found that traffic concentrates more in off side lane compared with other lanes for moderate to high flow rates.  Regression models have been developed based on the available lane distribution data.  The lane found to be increased with the increasing of traffic flow and the desired speeds found to be normally distributed.  Examining the headway data shows that the shifted negative exponential distribution can be used to represent the headway distribution for low to intermediate traffic flow only.  The findings of this work provides a good database for traffic characteristics for Iraqi highways as little effort has been given in previous research work.  

scholarly journals Stochastic Analysis of a Computer System with Unit Wise Cold Standby Redundancy and Failure of Service Facility

2020 ◽  
Vol 5 (3) ◽  
pp. 529-543
Author(s):  
R. K. Yadav ◽  
S. C. Malik
Keyword(s):  
Computer System ◽  
Probability Density Functions ◽  
Software Components ◽  
Treatment Rate ◽  
Repair Rate ◽  
Service Facility ◽  
Negative Exponential Distribution ◽  
Cold Standby ◽  
Negative Exponential ◽  
Similar Unit

Here, we analyze stochastically a computer system by taking one more similar unit (called computer system) in cold standby redundancy. The computer system consists of hardware and software components together. The provision of a single service facility has been made for repairing hardware and up-grading the software. The failure of the service facility is considered which resumes the jobs with full efficiency as new after availing treatment. The failure rates of hardware and software components as well as failure rate of the service facility are taken as constant and thus follow negative exponential distribution. The treatment rate of the service facility, repair rate of the hardware and up-gradation rate of the software follow arbitrary distributions with different probability density functions. Efforts have been made to determine reliability measures in steady state by using SMP and RPT. The behavior of MTSF, availability and also the profit function is observed graphically for some particular situations of the parameters.

scholarly journals Zur Auswirkung der Hangneigungskorrektur auf Schätzwerte im Schweizerischen Landesforstinventar (LFI) | Investigation of the effect of the slope correction method as applied in the Swiss National Forest Inventory of estimates

2001 ◽  
Vol 152 (6) ◽  
pp. 215-225 ◽  
Author(s):  
Michael Köhl ◽  
Peter Brassel
Keyword(s):  
Forest Inventory ◽  
Basal Area ◽  
Correction Method ◽  
National Forest Inventory ◽  
National Forest ◽  
Average Deviation ◽  
Forest Inventories ◽  
Slope Correction ◽  
Number Of Stems ◽  
Elliptical Area

For forest inventories on slopes, it is necessary to correct the test areas, because the circular areas, when projected, become elliptical. Based on 93 samples from the Swiss National Forest Inventory (FNI), it was determined whether the simplified method, which increases the radius to match that of the elliptical area, leads to a distortion of the results. An average deviation of 2% was found between the FNI estimated values and the actual values for the basal area and the number of stems. For estimations of smaller units, greater distortions of the results are expected.

scholarly journals Time since death and decay rate constants of Norway spruce and European larch deadwood in subalpine forests determined using dendrochronology and radiocarbon dating

2015 ◽  
Vol 12 (17) ◽  
pp. 14797-14832 ◽  
Author(s):  
M. Petrillo ◽  
P. Cherubini ◽  
G. Fravolini ◽  
J. Ascher ◽  
M. Schärer ◽  
...  
Keyword(s):  
Decay Rate ◽  
Tree Rings ◽  
Rate Constants ◽  
Radiocarbon Dating ◽  
Woody Debris ◽  
Visual Assessment ◽  
Exponential Model ◽  
Alpine Valley ◽  
Species Specific ◽  
Negative Exponential

Abstract. Due to the large size and highly heterogeneous spatial distribution of deadwood, the time scales involved in the coarse woody debris (CWD) decay of Picea abies (L.) Karst. and Larix decidua Mill. in Alpine forests have been poorly investigated and are largely unknown. We investigated the CWD decay dynamics in an Alpine valley in Italy using the five-decay class system commonly employed for forest surveys, based on a macromorphological and visual assessment. For the decay classes 1 to 3, most of the dendrochronological samples were cross-dated to assess the time that had elapsed since tree death, but for decay classes 4 and 5 (poorly preserved tree rings) and some others not having enough tree rings, radiocarbon dating was used. In addition, density, cellulose and lignin data were measured for the dated CWD. The decay rate constants for spruce and larch were estimated on the basis of the density loss using a single negative exponential model. In the decay classes 1 to 3, the ages of the CWD were similar varying between 1 and 54 years for spruce and 3 and 40 years for larch with no significant differences between the classes; classes 1–3 are therefore not indicative for deadwood age. We found, however, distinct tree species-specific differences in decay classes 4 and 5, with larch CWD reaching an average age of 210 years in class 5 and spruce only 77 years. The mean CWD rate constants were 0.012 to 0.018 yr−1 for spruce and 0.005 to 0.012 yr−1 for larch. Cellulose and lignin time trends half-lives (using a multiple-exponential model) could be derived on the basis of the ages of the CWD. The half-lives for cellulose were 21 yr for spruce and 50 yr for larch. The half-life of lignin is considerably higher and may be more than 100 years in larch CWD.

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