2
— —
The Bacala Early Warning System
(BEWS)*
This essay describes the development of BEWS, illustrates the use of BEWS, provides what-if scenarios, and provides recommendations concerning the future development of the model.
Table of Contents
The Situation in 1999 2
Data 3
The power function 4
Disclaimer: What BEWS is and What it is not 6
The Calculator 6
USING the calculator 12
Interpreting the results 15
The c-value 18
Future Developments: BEWS II+ 24
Other uses for the Calculator 18
Acknowledgements 26
References 26
* Developed by Rob Scagel, Pacific Phytometric Consultants
"Models are how we think, they are how we understand how the world works. As we go through life we build these very complex pictures in our minds of how the world works, and we're constantly referring back to them — matching incoming data against our models. That's how we make sense of things. One of the most important use for models is in sorting incoming information to decide if it is important or not".
Richard Maybury. 1999
The Situation in 1999
Doug Bacala is the Silviculture audit forester for the BC Ministry of Forests, Squamish Forest District. As a part of Doug's mandate he would like to be able to determine, at some point prior to the legally mandated survey date, whether a plantation is likely to pass a future survey. This has all the risks and thrills of counting your chickens before they are hatched!
Doug phrased this very elegantly. The days of "I think your plantation is not growing well enough " have passed and must be replaced with "the data indicates that the growth of your plantation too slow and likely will not achieve early free growing".
The input for the decision model is:
1. Total height growth at a particular age
2. Current height increment
These data should be readily available from survey data. Given these two inputs and a growth curve, it should be possible to determine whether the current height growth is sufficient to surpass a future height goal.
The analytic translation of Doug's request is:
Given survey results for total height and height increment at the fourth year I would like to develop the following statements:
"The average height growth for Fdc on this block was x+/- sd with a current annual increments of x +/- sd. As a results we expect that 75% of the Fdc will achieve the minimum heights of 150cm required for the IDFww [01] by the early free growing date of 6 years".
This modelling approach would be a suppliment to developming growth normals - a process underway in Squamish District and the subject of another essay
Data
What was uncertain was the nature of growth in early plantations. Over the past 20 years we have developed many growth curves for early plantation performance. In nearly every trial we have collected and analyzed data I have been very pleased with how well a power function fits the data. The power function appears to be an excellent generalization for early plantation growth.
In addition, we discovered that electing the planting height as the height-intercept provided additional fit.
We resurrected ** data sets encompassing ** trees and determined the parameters for best fitting power function through the average height/ age. The results are presented in Appendix I.
Given that the power function fit the data so well we tested it on operational normals being developed in Squamish District and for several clients in Northern Alberta.
The power function
The power function, using a c-value of 1.4, is illustrated below. It is important to compare the function to the linear growth curve. Both the linear and power function were forced to share the same height-intercept — the height at planting. Based on the power function the initial growth is slower than expected for linear growth. We refer to this as the "lag phase". The lag phase would correspond to planting checking, Assart effect, and frost damage experienced in young plantations. Eventually the growth based on the power function catches up to and exceeds that expected for linear growth, after which point the two curves continue to diverge. In the example given below there is more than a 150cm difference in height growth between the curves by age 10.
The c-value
The correct parameterization of the c-value is essential for the working of BEWS. An understanding of the effect of different c-values can be gained by leaving all other parameters of BEWS fixed and simply adjusting the C-value.
Below is an example for . Here we have adjusted the c-value from 1, the linear growth, through to higher powers. Note in particular the increasing lag with the higher the selected c-value. Note also decreasing length of time to achieve a minimum height of 400cm given an increasing c-value.
Disclaimer: What BEWS is and What it is not
Lets be clear about exactly what BEWS is and how it was intended to be used. BEWS deals with population parameters. It about predicting the average growth of a plantation. BEWS is not about prediciting the growth of individual trees.
The Calculator
BEWS consists of a single Excel97 workbook with six worksheets. The different worksheets contain the reference growth data, estimated equations, and fitted data (GroData).
A listing of the legisltated minimum height growth for each species/ ecosystem/ biogeoclimatic zone combination in the Submaritime biogeoclimatic zones. The table also includes the legislated regeneration delay from the BC MOF Forest Practices Code (Stocking).
A pivot table summary of the stocking information from BC MOF Forest Practices Code (StockingSum). This is an important table in its own right as it allows the user to examine the variation of legislated minimum heights over different species, site associations,and biogeoclimatic zones. This table constitutes and important source of information for beginning to revise the Forest Practices Code minimum heights as height growth normals are developed.
A list of the morphological sizes accepted by the BC MOF Nursery Administration Office (Morph). Currently only the target seedling heights have been included.
And the two calculators. The generic BEWS.
And the more detailed, but constrained BEWS II.
USING the calculator
The current version of the calculator is to be considered a prototype. It is written in Microsoft Office '97, Excel. The core of the calculator are two pivot tables that access stocking information and stock type size. The calculator has not been protected in any manner so please practice safe computing - make backups of the original calculator.
There are several conventions used in this spreadsheet. Any shaded cell is a calculation and should not be touched, ever. The only areas in which you are permitted to enter data are unshaded cells prefixed with a =>. Shaded cells indicated by a => are multiple choice. All the data required data inputs are on the right side of the calculator (political dextrorotatory)
A. Define the biogeoclimatic subzone and species being managed.
1. Select the appropriate biogeoclimatic subzone from the pop-down list. (IDFww)
2. Select the appropriate site association from the pop-down list (01)
3. Select the appropriate species from the pop-down list (Fdc)
This gives you the appropriate survey statistics contained in the Stocking Standards Guidelines from the Forest Practices Code. In the example illustrated above:
· Minimum height (MinHgt) is 150cm
· Regeneration delay (RegenDel) is 4 years
· Early free growing (EFG) is 9 years after logging
· Late free growing (LFG) is 15 years after logging
· Earliest age (EarlyAge) of planted seedling is 5 years.
· Latest age (LateAge) of planted seedling is 11 years.
At this point we have only created the lookup tables for the Submaritime Biogeoclimatic zones in Squamish District.
B. Define the planting stock being used.
4. Select the appropriate species (Fdc)
5. Select the appropriate stock type (615A)
6. Select the stock type age (1+0)
This gives you the target morphology for the stock type. In the example the target height for a Fdc PSB 615 1+0 is 45cm. The morphological parameters are taken from the BC MOF 1998 Nursery stock standards. Don't know which stock type to select? Try the 415B 1+0.
C. Define the growth rate.
7. Select a growth rate parameter (1.4).
This is the most arbitrary aspect of the calculator. Unless you have height increment data there is nothing to stop you from using any growth rate parameter in order to justify your conclusion - clearly an inadequacy in a audit calculator. There are several work-arounds:
1. Choose a c value of 1.4 to 1.6. C-values in this range have been determined to be common for many areas in the Submaritime.
2. Consider the current height increment data and trial a range of c-values until you achieve a close fit to the actual height and height increment.
Interpreting the results
In the example we set up above we are trying to determine the growth rates required to achieve early free growing for Fdc PSB 615B seedlings planted in the IDFww[01]. We are allowed, by law, regeneration delay of up to four years, however in this ecosystem if you don't get it planted within 6-months of harvesting you might as well give up trying to achieve timely reforestation. The legislated minimum height is 150cm.
BEWS calculates growth curves (top graph) and height increment curves (bottom graphs). The calculations are displayed in tabular form on the right. The highlighted green cells are the legislated minimum heights under the early-free growing criteria and the late free-growing criteria.
At planting the trees are, on average, 45cm tall — common height for Fdc PSB 615B 1+0. In order to meet the early free-growing criteria this stock type must achieve at least an 11cm height increment in the first growing season. However notice that only a 4cm height increment is required if late free-growing is your management target.
Let us assume that a survey was conducted when the plantation was three-years old. The average height of the plantation was 80cm tall and had a height increment of 15cm. Comparing this value to the tabled values in BEWS for the third year (96cm tall, 22cm height increment) the plantation would not be expected to achieve early free-growing but it is growing nearly 30% better than a plantation that would achieve late free-growing.
As an alternative interpretation let us assume that the survey results showed average height of 100cm and 25cm height increments. Clearly this plantation exceeds that required for achieveing minimum heights and the only threat to failure to achieve early free-growing would be based on height above competing vegetation.
Other uses for the Calculator
BEWSII is specifically hardwired to the stocking standards of the Forest Practices Code and the stock type specification adopted by the BC Ministry of Forests Nursery Administration office. A limited amount of what-if scenarios can be developed using BEWS II by choosing different species and stock types for a particular biogeoclimatic zone and site association.
A more generic version of the the calculator, BEWS, has been written to provide the testing of what-if scenarios. BEWS allows you to choose your own target height, target age, and stock type size as well as your own survey results.
The what-if scenarios that we have examined are:
1. Effects of stock type size on meeting legislated early free growing dates.
2. Determining growth rates necessary to achieve heights greater than the minimum legislated heights but 150% greater than expected brush
3. Determining growth rates necessary to achieve legislated minimum heights at times different than those dictated by the early and late-free growing assessment.
Consider the example below. We have originally parameterized BEWS for the same data presented in BEWS II. Theses examples are not meant to offer profound insite into regeneration silviculture but to encourage the user to develop their own what-if scenarios.
Survey results indicated that the average height of a 3-year old plantation was 80cm with a 15cm height increment. We would like to know the growth trajectory for these seedlings given a c-value of 1.4. Note that we have imputed a Min of 80cm and a RegenDel of 6 years in order to simulate the survey results. We have also modified the LFG to 11 to force the two curves to compare plantation ages of 3 and 5-years. The results appear to confirm that a c-value of 1.4 was correct as the estimate and actual height increments are 15cm.
Given these data what would the c-value to be in order to achieve 150cm at 5-years? By a trial and error we arrive at a c-value of 2.15 — an unusually high, and probably impossible c-value based on our entraining data.
Future Developments: BEWS II+
BEWS II is under active development. There are several key features that we wish to build into the model:
1. Diameter growth. We will determine whether we can use a general nonlinear equation to describe diameter growth. This can be achieved using similar historical data as we used to adopt the power function for height. The initial version of this incorporation will be a strictly diameter by age relationship. Later we will develop a height by diameter graph over a number of ages. This is not an endorsement for HD-ratio.
2. Vegetation growth. Data from research trials suggests that the generalized power function that works so well for conifer seedling growth can also be used for some of the major competing vegetation assessment. For small shrubs and herbs it appears that a logistic function, or one of the other asymptotic equations may be a more parsimonious description.
3. Incorporation of current height increment. The current version of BEWS II allows the user to select their own c-value. This is an admitted short-coming of BEWS II and one which leaves the model open to abuse. We propose to force the user to enter the current height increment which, in turn, will calculate the appropriate c-value.
4. Reprogramming as a stand alone VisualBasic application. Although BEWS functions well as an Excel application it is somewhat idiosyncratic in this computing environment. Reprogramming BEWS as a stand-alone application would improve its portability. Currently BEWS uses formatting features restricted to Office97 and Office2000. Maintaining backward compatibility with earlier version of Excel may not be possible.