Knowledge reference for national forest assessments

The Knowledge Reference for National Forest Assessments is collection of scientific articles prepared specifically for this initiative. They cover a wide range of activities regarding the setting up and carrying out an assessment of the forest resources at the national level.

The Knowledge Reference provides an invaluable resource for various stakeholders within the government, private and academia related to the forest sector. It is used by FAO to support  the development and implemention of national forest assessments in member countries, and can be used for free, as teaching material.

You can download the full document or individual chapters. In addition you can test your knowledge with Self Study Exercises.

an initiative in collaboration with the Swedish University of Agricultural Sciences





download the full document or each individual chapter at the following links:



Self Study Exercises

 This section contains study questions related to the content of each chapter. They are aimed at testing the reader's comprehension of the material.

Rationale and policy influence


  • Discuss the interest of different stakeholders in learning more about forests. Do some stakeholders seem not to want better information?

  • Which are the five most important forest policy issues that need to be discussed?

  • Which ten types of information are needed in the first hand?

  • How can forest policy formulation and information collection best be linked in your country? 

Organization and implementation


  • What role does the NFA have in your country? (discuss and relate it to the issues discussed in section 2)?

  • Which organizational and implementational aspects on the NFA point towards using simplicity as a guiding principle for design, data collection and analysis procedures?

  • List and briefly describe the important steps in the implementation of the NFA cycle. 

  • In your country, what existing ”capacity centers” would be important partners for the NFA in the event that all the required capacities are not available in-house?

  • In your country, which environment would be adequate for the NFA organization? (In the event that that has already been established, discuss the advantages and disadvantages of the current arrangement.)

Sampling Design


  1. Describe the differences, advantages and disadvantages of simple random, systematic, stratified and cluster sampling designs.
  2. Explain why a stratified sampling design may be superior to a simple random or systematic sampling design. Describe ancillary data that may be useful for constructing strata.
  3. What role does spatial correlation among observations or measurements of forest attributes play in the selection of a sampling design and estimation of population variances?
  4. Describe the criteria and information necessary to determine an appropriate sample size.
  5. Identify sampling issues and constraints unique to inventories in tropical forests.


  1. Simple random sampling designs are the easiest to implement but may feature gaps in coverage.  Systematic sampling designs are also fairly easy to implement and are of two kinds: (i) aligned designs for which plots are established at grid intersections or at the centers of polygons that tessellate the population, and (2) unaligned designs for which plots are established at randomly selected locations within the polygons.  Systematic designs provide good spatial balance and coverage, but are more complex and risk of alignment with geographic features such as roads, rivers, or topographic features.  Stratified designs are also more complex but permit optimization of estimates relative to desired properties such as unequal importance of strata and uncertainty estimates.  Within strata, simple random or systematic sampling designs are typically used.  Cluster sampling designs group selected numbers of plots in close geographical proximity to minimize costs of travel between plots.

  2. Stratified sampling designs permit optimization of sampling relative to multiple properties and may feature different sampling designs and different sampling intensities within different strata.  Commonly used ancillary data used as the basis of stratifications include political, climatic, land-use, and topographic maps.  Maps of forest/non-forest, forest type, and growing stock volume obtained from remotely sensed data have also been used as a source of stratification information.  If change estimation is important, then stratifications that do not change over time are preferable.

  3. Spatial correlation among observations for plots of the same cluster should be considered when selecting plot configurations and the arrangement of plots within clusters.  Sampling is less efficient when the distance between plots is less than the range of spatial correlation because less new information is obtained from measurement of successive plots.  In addition, variance estimation becomes more complex when spatial correlation must be accommodated.

  4. The primary criterion is the precision of estimates with greater sample sizes producing greater precision.  Three important items of information are necessary to determine a sample size that satisfies precision requirements: (i) desired precision, (ii) confidence level, and (iii) sampling (plot-to-plot) variability (iv) available resources including financial resources .  Often sample size must be balanced against the cost of sampling.

  5. Multiple issues must be considered:  (i) plot configuration and sampling intensity in forests that are both more dense and more diverse than boreal and temperate forests, (ii) greater sampling costs due for remote areas and areas with difficult access, and (iii) integration of ground sampling with acquisition of remotely sensed data.

Observations and Measurements


  1. Explain why a major statistical planning criterion for the choice of a plot design is to capture as much of the given variability of the target variable as possible inside each observation.
  2. List some target variables that could be estimated based on one-dimensional line elements as observation units.
  3. Explain the rationale of a nested plot design, in which trees of different diameter classes are included in sub-plots of different area size (smaller trees in small plots, large trees in large plots).
  4. If an NFA is being carried out for the first time, what sources of information might form a suitable basis for a decision on plot design options?
  5. A decision-maker contests the reliability of the results in an inventory report on the grounds that only 0.001% of the country’s forest area was observed in the field. How can the reliability of the results be defended?


  1. If it is possible to capture a large portion of the variability inside each observation, the distribution of observations becomes narrower and the standard error is decreasing (means higher precision of estimates)
  2. (1) The length of linear features (road networks, forest border, tree rows, …) based on line intersect sampling, or (2) the relative share or total area of condition classes (forest types, forest- non-forest) based on line intercept sampling.
  3. Natural forests are characterized by a very high density of small trees and a low density of large trees. Assessing all small trees on a large plot area is not efficient. Further, larger trees contribute much more to the total volume or biomass and should therefore have a higher probability to be included in a sample.
  4. Data from ecological research plots might serve as basis for simulations. Experiences from neighboring countries with similar forest types might be another source of information. If no data are available, it is advisable to carry out a pilot study to derive the necessary prior information.
  5. Even if the intensity in terms of observed area is low, the sample size is very high. The estimated standard error that defines the width of the confidence interval is low. This interval indicates the reliability of an estimate.

 Data collection through interviews


Self-Study Exercise 1: Testing the Sampling Design - One of the critical steps in the preparatory phases for the field interview component of any NFA is to test the sampling design. The purpose of such testing is to determine the extent to which a particular sampling design would generate a representative sample of forest users. This exercise describes the basic steps for conducting such a test, based on the recent experience of the NFA in Tanzania. A variation of this test should be performed as a self-study exercise for any prospective NFA project. The project used high-resolution satellite imagery (the panchromatic band of Landsat 7, with a 15-metre spatial resolution) to obtain a better sense of the implications of the proposed sampling design in terms of numbers of likely field interviews. The satellite image was converted to a shape file and imported into ArcGIS. The coordinates for the sampling units in the interview were overlaid in the GIS. Map 1 shows the test results for the area west of Morogoro, Tanzania. This area was selected for the test because it represents a critical case for the sampling design, being much less densely populated than most other areas of the country. If the proposed sampling design performs satisfactorily (i.e.shows that a sufficient number of households are likely to be selected in each reporting unit), it is reasonable to conclude that the design will perform at least as well in other areas. Although the 15-metre spatial resolution did not allow the location of individual dwellings to be positively distinguished, the imagery did provide useful, estimating that the proportion of sampling units would have a high probability of having no household dwellings within them. If many sample units are void of households, there is a risk of not having a representative sample of forest users.

Map 1. Spatial distribution of sampling units in the area West of Morogoro (including the Eastern Arc Conservation area)

Note: the white circles represent the sampling units.

For the area used in this test, it appears that about 15 out of 46 sample units (33 percent) have very little or no human presence, and consequently there is a very low probability of finding any households living within these units. The results indicate a reasonable chance of people living near the vast majority of sampling units in this particular area. These results also indicate that the sampling design seems viable, since the area is less populated than most other parts of the country. However, further empirical tests are recommended, using the same approach presented here. Such tests would seek to answer the specific question of how many households should be sampled in each of the 26 regions of Tanzania, and determine whether the given sample sizes are sufficient to achieve an 8 percent sampling error at the regional level. Additional information is required to determine this point. The following exercise provides a description of such information may be acquired.

Self-Study Exercise 2: Field testing of the interview questionnaire

Three factors, often overlooked in survey work, are very important influences on the quality of interview data: (i) the interview skills of the people conducting the interviews; (ii) the content and clarity of questionnaires; and (iii) the length of the interview. All of these factors may be addressed through careful preparation during the planning stage of the NFA. In this self-study exercise, it is suggested that NFA personnel engage in a process of training and field-testing of interview questionnaires. This process could involve several steps:

1. Invite NFA personnel to a one-day workshop.
2. In the workshop, divide participants into groups to propose variables of interest to be measured through interviews. For simplicity, ask groups to focus on a maximum of two variables each.
3. Ask groups to develop interview questions directed at specific target actors (households or key informants) that can generate measures for the variables of interest.
4. Based on group inputs, compile all proposed interview questions into one interview questionnaire for household interviews and another for key informants.
5. Divide workshop participants into groups of three. One person will act as an interviewer, one as an interviewee, and the third as a silent observer and timekeeper. The purpose of this exercise is to identify problematic questions, suggest improvements, and obtain a sense of the total time needed for each interview.
6. In plenary, go through each questionnaire, one question at a time to review possible suggestions for modifications.
7. Circulate a new version of the questionnaires, and if possibly repeat exercise 5.
8. Ensure that each interview may be completed in no more than 45 minutes. Make necessary adjustments to meet this objective.
9. Repeat exercise 5 in a simple field setting, preferably in a community of forest users with which NFA personnel enjoy a good rapport and where there is a willingness among villagers to engage in a workshop of this sort. Make sure that community members are properly introduced to the purpose of the workshops and that they are duly compensated for their participation.
10. After conducting several ideas in the field, gather all participants to discuss the content of the questionnaires, one question at a time. Make corresponding adjustments to the questionnaires.

Remote Sensing


1. What support can satellite data typically provide for NFAs?
2. How can remote sensing be used in a multi-phase inventory?
3. Why is it difficult to work with remote sensing in northern or tropical countries and what possible solutions do you see?
4. Why is radar data more difficult to use than optical?
5. What are the limits for satellite data in terms of daily repetition rates?
6. Why are high-resolution satellite data in NFAs often sampled?
7. Why might it be necessary to adapt the sampling from remote sensing to the field sampling design?
8. Is it possible to use satellite images in NFAs without computers?
9. Is any pre-processing necessary before starting to use satellite images within a NFA?
10.Who can do the geocoding?


1.  Q. What support can satellite data typically provide for NFAs?

- Map information on forest non-forest distribution, infrastructure, fragmentation and major forest characteristics like crown closure and forest types
- Provide a retrospective monitoring of changes of forest areas
- Relatively fast access to forest condition information
- Rynoptic view (information does not stop at borders)
- Visualisation of the forest situation (supports argumentations)
- Support the field measurement crews to find the location of terrestrial measurement samples
- Support for the architecture of terrestrial sampling design by pre-stratification
- Improvement  estimation quality by post-stratification
- Reduce sampling density without reducing estimation quality
- Regionalisation of terrestrial measured or modelled forest parameters based on regression methods like kNN and others

2. Q. How can remote sensing be used in a multi-phase inventory?

- Stratificaion
- Sampling design
- Assessment of forest parameter by regressions (e.g. use crown closure and forest type information from remote sensing to predict wood volume)

3. Q. Why is it difficult to work with remote sensing in northern or tropical countries and what kind of possible solutions do you see.

- Difficult data take due to the weather situation, high cloud cover percentage
- Take satellite data which have a high repetition rate and a large area coverage e.g. metrological satellite data like AVHRR or earth observation satellites which provide daily data of the same area like SPOT Vegetation,  Meris and Modis.
- Radar data for forest area estimations region with low topographic impact

4. Q. Why is RADAR data more difficult to use than optical? Complex to process information

- In mountainous areas large amount of information can be lost due to radar shadowing

5. Q. What are the limits for satellite data with daily repetition rate?

- These data have normally a lower spatial resolution.
- It will be more difficult to get the correct forest area because small forest areas below e.g. 1 ha might be lost.
- Regressions between terrestrial sample measurements and satellite data might get looser due to lower spatial resolution

6. Q. Why are high resolution satellite data in NFAs often sampled?

- It is often not possible to get a full coverage of a country (especially large country) within reasonable time with high resolution satellite data.
- The very high resolution data are costly.

7. Q. Is it necessary to adapt the sampling from remote sensing to the field sampling design?

- Yes, because only if sampling from remote sensing is adapted to field sampling the full benefit of a combined approach is possible (regressions in a multi-phase inventory)

8. Q. Is it possible to use satellite images in NFAs without computers?

- Yes, because the image can be used for photo interpretation

9. Q. Do I need to take care of any pre-processing before I use satellite images within a NFA?

- Yes, at minimum geocoding. That means the image has to be rectified and referenced to a geographical reference system.

10. Q. Who can do the geocoding?

- It is possible to order geocoded images with UTM coordinates. Companies can help to transfer this to national geographical reference system.

Information management


  1. The knowledge ecosystem concept includes “competition”. What international treaties/agreements does your country subscribe to that would require your NFA to produce reports?
  2. Which agencies/units were involved at each stage of the process to transform forest plot data into the entry for your country in FAO’s 2010 global assessment, and what programs and systems were used?
  3. Give three examples of system failures that have been reported in your country (or a country of your choice) and list the stated causes.
  4. A donor agency is funding development of an information system for your NFA and you have to perform a requirements analysis for the system. From the following list of system design considerations, rank the top five issues for your system, giving reasons.
  5. Which of the following is most limiting to development of your countries’ NFA information system: technical interoperability, semantic interoperability, political/human interoperability, inter-community interoperability, legal interoperability or international interoperability.


1. This will vary by country.  For example, as far back as 1998, Australia’s State of the Forests Report listed 17 International forest-related agreements, forums or statements of relevance to Australia (

- Food and Agriculture Organization of the United Nations, 1945
- Rio Declaration and Agenda 21, 1992
- Statement of Forest Principles, 1992
- United Nations Framework Convention on Climate Change, 1992
- United Nations Framework Convention on Biological Diversity, 1992
- Commission for Sustainable Development, 1992
- Montreal Process and Santiago Declaration, 1994
- General Agreement in Tariffs and Trade (GATT), 1947, and World Trade Organisation, 1995
- Convention concerning the Protection of the World Cultural and Natural Heritage, 1972 (World Heritage Convention)
- Convention on Wetlands of International Importance etc, 1971 (Ramsar Convention)
- Man and the Biosphere Programme, 1971
- Convention on the Conservation of Migratory Species of Wild Animals, 1979 (Bonn Convention)
- Convention on International Trade in Endangered Species of Wild Fauna and Flora, 1973 (Washington)
- The Convention on Conservation of Nature in the South Pacific, 1976 (Apia Convention)
- International Tropical Timber Agreement, 1983
- Convention for the Protection of the Natural Resources and the Environment of the South Pacific Region, 1986, Noumea
- CAMBA (1986) and JAMBA (1974) Agreements (bilateral agreements with China and Japan, respectively, that reinforce the Ramsar Convention

2. Discovering the answer to this question can be difficult, but can be pursued along the following lines 1) Each country nominates an official correspondent, whose duties include (see ):

- process and submit national data to FRA 2010, including the co-ordination of inputs from different national institutions as well as taking national reporting to other international processes into account;
- act as point of contact for identification of national specialists for the remote sensing survey and selected special studies which form part of FRA 2010; 
- verify and validate national information for FRA 2010 before publication; 

Contact information for each official correspondent and their alternate is listed at  and ; in many cases the home page of their organization is listed. 2) The FRA 2010 ( ) indicates that “... detailed guidelines, specifications and reporting formats were provided. The reporting format required countries to provide the full reference for original data sources and an indication of the reliability of the data for each of these, as well as definitions of terminology. Separate sections in these reports deal with analysis of data, including any assumptions made and the methodologies used for estimations and projections of data to the four reference years (1990, 2000, 2005 and 2010); calibration of data to the official land area as held by FAO; and reclassification of data to the classes used in FRA 2010.” 3) The country reporting to FRA 2010 consists of 17 national reporting tables (see ).  Full details of the process followed by each country can be obtained by following links at .  Note that data sources listed are often earlier publications, which must be consulted in turn.   In some cases, the actual systems involved cannot be determined.

3. This can be pursued by entering the following search terms into Google: information system fail|failure your_country_name

- by substituting “developing countries” for your_country_name, more general studies can be located:
- by including the search term forestry, agriculture or environment, more specific examples can be found. 

In addition to finding specific cases, more general issues can be explored: issues include (Heeks 2002: - defining and measuring success and failure; extent of success/failure 

- design-actuality gaps; hard/soft gaps   

4. Each situation will differ.  A suggested approach is to first read section 4.1.1 for a description of Requirements Analysis,  also referring to . You could also develop a Knowledge Ecosystem of your situation (section 5.2), to help guide your answer.

Secondly, decide on the method of ranking: what criteria will you use (e.g. difficulty of meeting the requirement with existing technology/personnel/institutional arrangements/funding)?

Finally, evaluate each of the terms, based on its description in the chapter, in relation to your actual situation.  

5. Each situation will differ.  Your answer should follow on from the analysis for question 4 above, focusing specifically on interoperability issues after reading the article:Miller, Paul. 2000. “Interoperability. What is it and Why should I want it?” Ariadne Issue 24, 21-Jun-2000 (Accessed October 1, 2011). Following this more in-depth analysis of interoperability, you may wish to revisit your rankings in question 4: as Miller indicates, “there are several aspects to consider in moving towards interoperability, of which the most usually cited one of technology is normally the most straightforward to solve.”

Modeling for Estimation and Monitoring



B = basal area (of a tree or trees in a plot)
BAF = basal area factor (in Bitterlich sampling)
BEF = biomass expansion factor
CWD = coarse woody debris
D = stem diameter of a tree at a given reference height (typically 1.3 m)
H = tree height
Lidar = light detection and ranging (aka laser scanning)

Exercise 1. Your task is to estimate total stem volume for a fixed area plot in an inventory. The example assumes that there is only one species in the plot, and that a single volume equation is adequate.

The area of the plot is 600 m2.

You have measured the diameter (D) at breast height for all trees with a height greater than 1.3 m.

You have also measured the height of eight trees for the purpose of constructing of a height-diameter model and the prediction of height for trees with no measured height.

Trees selected for a height measurement are highlighted (bold) in the data given below.

There are 42 trees in the plot. The diameter (D) at breast height was measured to the nearest 0.5 cm, but the data were rounded to the nearest 2-cm class. The recorded values of D are as follows:

D = {18, 18, 20, 22, 22, 22, 22, 22, 22, 24, 26, 26, 28, 28, 28, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 32, 32, 34, 34, 36, 36}

Q1.0: Compute the basal area (B) in square metres per hectare from the given data of D and plot size (give the result to the nearest 0.1 m2).

Q1.1: Has the rounding of D introduced a bias in the estimate of B?

Q1.2: What is the magnitude of the relative bias (i.e. bias in percent of the estimate of B) introduced by rounding measurements of D in B? Pick the most appropriate answer from the following list of relative bias: -5%, -2%, 0%, 2%, 5%.

Heights of the eight measured trees were measured to the nearest 10 cm, but only recorded to the nearest 0.5 m. The height data were:

H ={26., 27.5, 29.5, 30., 30., 31., 31.5, 31.5}

To predict the expected height (eH) for trees with no height measurement you opt for the following height-diameter model [1]:

eH =b0 +b1*loge[D]

Estimate via ordinary least squares the regression parameters b0 and b1.

Q1.3: Do you think the rounding rule applied to D has an effect on your estimates of b0 and b1?

With the estimates of b0 and b1, compute the expected height of all plot trees (call them eH; notice: the expected height of a measured tree is the measured height). Round all expected heights to the nearest 0.5 m.

Compute the expected total stem volume of the 42 trees (eV) using the following volume-equation (D in cm, H in m)[2]:

eV = 3.03 * 10-5 * D**1.7 * eH**1.3

Round each tree’s volume estimate to the nearest 0.02 m3.

Q1.4: In your opinion, does the above rounding rules for D and H introduce a bias in the estimate of the mean tree height (i.e. mean of eH)?

Q1.5: Does the rounding of D and H introduce a bias into the expected total volume (eV)?

Exercise 2.

You are tasked with estimating the total above ground biomass for a species AA in a newly inventoried forest. The inventory provides you with the diameter at breast height for all trees of species AA with a height larger than or equal to 1.3 m. You have identified the following four above ground biomass (AGBM in kg oven-dry mass) equations as suitable candidates [3].

D is diameter at breast height (in cm).

EQ1: AGBM = 0.0983 * D**2.3773

EQ2: AGBM = 0.0617 * D**2.5328

EQ3: AGBM = 0.0842 * D**2.5715

EQ4: AGBM = 0.0629 * D**2.6606

To help you decide which equation is most suitable, you have estimated AGBM for ten trees sampled at random from the inventory sample.

The diameter (D cm) and above ground oven-dry biomass (AGBM kg) of your ten trees are as follows:

Tree D   AGBM
no. cm   kg
1 3.1   1.52
2 9.3   26.26
3 11.2   41.26
4 13.6   69.10
5 13.9   70.44
6 15.3   91.72
7 19.4   161.68
8 28.9   493.56
9 36.3   840.06
10 40.0   1115.20

Q2.1 Based on this information, which of the above four equations appears to be most suitable for use? Explain your choice of equation.

Exercise 3.

Your task is to estimate total tree stem volume of trees in the NFI plots of your country. You have made observations of diameter at breast height (D) and height (H) of all trees in all measured NFI plots. For species AA, BB and CC you are using volume equation models that can estimate the total stem volume from H and D. However, for species DD you do not have a model for volume estimation. For this exercise, assume that you have only observed these four species in your NFI plots. How would you go about estimating volume for species DD in this situation? Please explain your suggested approach. What factors might prevent you from reaching a decision? In the event that no decision is possible, what additional information might be required to reach a decision and estimate the volume for trees of species DD?

Exercise 4.

You are part of an NFI/NFA team responsible for taking field measurements in NFI plots. Stakeholders of the NFI are keenly interested in estimating ecosystem carbon content. A funded request is put forward to select data in the NFI plots to estimate carbon content in forest floor litter. How would you respond to this request? If a decision is taken to meet this request what field procedure would you recommend?

Exercise 5. A NFA client/stakeholder has asked you to make predictions of total above ground biomass of live trees within a 1000 km2 region with approximately 60 percent forest cover. There are only 25 NFI plots in this region. The biomass estimates from these 25 plots are highly variable. A direct estimate of biomass for the region based on the 25 samples would have a very low precision. You have access to national archives of remotely sensed data. What course of action would you embark on in this situation?

[1] Taken from Loetsch, Zöhrer and Haller. 1971. Forest inventory, Volume 2. BLV, p. 130.
[2] Adapted and modified from Brackett. 1973. Notes of tarif tree volume computation. State of Washington, Department of National Resources .Resource Management Report No. 24. Converted to SI-units.
[3] From Ter-Mikaelian and Korzukhin. 1997. Biomass equations for sixty-five North American tree species. Forest Ecology and Management, 97(1): 1–24.


Answers and intermediate results to Excercise 1:

Estimates of regression parameters on rounded data:

b0 = 5.54, b1 = 4.46.

Predicted tree heights (rounded to nearest 0.5 m):

eH = {19., 19., 19.5, 20., 20., 20., 20., 20., 20., 20.5, 20.5, 20.5, 21., 21., 21., 21., 21., 21., 21., 21.5, 21.5, 21., 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 22., 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 22., 22., 22., 22.}

Expected total volume of the 42 trees (using above equation for V, the recorded values of D, eH, and rounding each tree’s volume to the nearest 0.02 m3): eV =40.88 m3.

AQ1.0: 44.7 m2 ha-1

AQ1.1: Yes, the rounding rules for diameter introduces a bias in mean height of the 42 trees. The rounding introduces a negative bias (estimated mean height is less than actual mean height).

AQ1.2:  -2% (the student will have to assume a uniform distribution of rounding errors within each D-class to arrive at the correct answer).

AQ1.3: the coefficients b0 and b1 are both underestimated (i.e. numerically smaller than the coefficients derived from non-rounded measurements of D).

AQ1.4: Yes. The mean height is actually overestimated by 12 cm.

AQ1.5: The volume is, by chance, nearly unbiased (bias is approximately 0.1%) assuming correct models. Opposite bias in eH and D cancels (in this example).

Answer to Exercise 2:

Q2.1: When bias is the overriding concern (the 10 observations are viewed as a small yet representative sample of the population) EQ4 is most suitable. When using EQ4 the average residual (estimated AGBM minus observed AGBM) is -0.84 kg, the overall lowest average residual. For EQ4 A two-sided t-test under the null hypothesis of a mean residual value of zero yields a t-value of -0.16 with a P-value under H0 of 0.872. The runner-up equation is EQ3 with a mean residual value of -5.61 kg, a t-test value of -1.58 and a P-value under H0 of 0.148. In fact, a t-test under the null hypothesis: residuals from EQ3 arise from the same distribution as residuals from EQ4 cannot be rejected (t-test: mean difference = -4.77 kg, t = -0.77, P(t > -0.77|  H0) = 0.46).

When root-mean-square error (RMSE) is the main concern it is EQ3 that has the lowest RMSE of 12.0 kg. The RMSE of EQ4 is 15.2.

Conclusion: given the low bias of EQ4 and relative close values of RMSE obtained with equations 3 and 4 it is EQ4 that should be favored.

The test results clearly show that neither EQ1 nor EQ2 should be considered. One could argue for a model that is a compromise (average) between the implicit models in EQs 3 and 4.

The astute student may argue that the residuals are not iid which would bias the above test-results. However, given the sample size of 10 there is no suitable (refined) test-alternative.

Suitable answers to Exercise 3:

Step 1. Find out what you can about growth form, ecology, and taxonomy for species AA, BB, CC, and DD. Is species DD similar to any of the alternatives (AA, BB, CC)? If so, maybe this suggests to adopt the volume model for the most similar species. Try to find as much information you can about branching habits and crown shapes in the four species. Species with similar branching habits and crown shapes often have similar stem form and H:D relationships. Local knowledge may be illicited in this step and prove helpful.

Step 2. Make a scatterplot of H plotted against D for each species (identify each species in the plot). Is the relation between H and D for species DD similar to that of the other tree species? The species with relationship between H and D most similar to that of D may provide the most appropriate volume model.

Step 3. If I can’t make a decision (model choice) after having gone through steps 1 and 2, then I might undertake a small field study with in-situ determination of H, D, and stem volume of a dozen or so trees from species DD. You can now gauge which of the models for AA, BB, and CC is most appropriate by comparing model predictions with your own measurements.

Step 4. Compute an approximate volume from values of H and D by assuming a simple geometric shape of the tree.

Step 5. You could contemplate an ‘average’ volume model for species DD (for pair-wise values of H and D compute the volume for species AA, BB, and CC and take the average, then fit a model for species DD predicting stem volume from H and D). But you will have to argue for why this approach is better than any of the others!

Suitable answers to Exercise 4:

The NFI plots may or may not be suitable for this request type. The amount of forest litter may undergo large seasonal fluctuations. If NFI plots are visited at different times of the year the data will reflect this seasonal variation which will undermine the quality of the data. In some situations, the amount of forest litter (dry weight per unit area) may be almost constant throughout the year (there is an equilibrium between addition of new litter and decomposition of older litter). In those cases, a sample of litter taken on a particular day is ‘as good’ as a sample taken on any other day. Most likely the NFI plots will be located in both types of forests. If sampling is decided then an efficient way to collect data is to gather litter in four 1-m2 plots at predetermined locations near but outside the actual NFI plot (you don’t want to disturb the growth on these plots), for example. If the client insists on sampling of carbon in NFI plots where forest litter fluctuates through the year, it should be discussed and the consequences (on data quality) made clear to the client. It may be necessary to sample at times of maximum and/or minimum litter.

Acceptable answer to Exercise 5:

I would try to find a model to explain biomass per ha (Y) from one or more ancillary variables (X) in the remotely sensed data with a spatial resolution (pixel size) compatible with the size of the NFI plots for which I have a biomass estimate. The 25 plots may suffice to establish a single promising model to be used for all pixels in the region. In this case I would opt for a model-assisted estimation of the precision of the estimate of biomass. A purely model-based estimate of precision is likely to underestimate the precision of the estimated biomass.

Alternatively, I may find that there are different forest types in the region (strata), each requiring a separate model. My 25 plots will not be sufficient in this case, not even if I tried advanced modelling with random (strata) effects. In this situation I may decide to use additional NFI plots outside the region but otherwise likely to be from the same set of forest types as found in the region of interest. Once I have the required models (after appropriate model-search and model-selection routines as described in most standard textbooks of statistics) I will embark on a small-area estimation procedure and also document model-properties in such a way that any user of my model(s) is empowered to make qualified inference about the quality of predictions, potential of bias, application domain, and other possible issues of interest to the analyst. Finally I would use the model(s) to predict biomass for each pixel in the region of interest. Then I would attempt, either alone or with the assistance of an expert, to estimate the variance of this regional estimate of biomass. In this endeavor I would favor a model-assisted approach to estimation. Since this exercise involves spatial predictions, I expect to have to deal with the issue of spatial correlation in both X and Y before I can arrive at an estimate of variance.



1. What is the role of scenario modelling in the preparation process of the National Forest Programme (NFP)?
2. What is the role of national forest monitoring and assessment (NFA) in the preparation process of NFP, in particular in relation to scenario modelling?
3. List trends and other potential change factors affecting the demand for wood and other forest resources in your country.
4. List trends and other potential change factors affecting the supply of wood and other forest resources in your country.
5. What types of scenarios, approaches for scenario modelling and actual scenario models (software tools) would be applicable for your country?


1. Analytic and transparent study of options and their impacts.
2. Data on forest resources and their development as well as on operating environment.
3. Future use of wood-based products and forest-based products and services depend on demography, socio-economic situation, substitutes etc.
4. Future supply of wood and other forest resources depend on forest resources and their development under ecological conditions, land and forest ownership and their needs, values and interests, socio-economic constraints etc.
5. Select from supply-driven/demand-driven, research-initiated/policy-targeted, extrapolation/state-transition models/simulation models.


last updated:  Tuesday, July 19, 2016