General Forestry for APPSC Forest Section Officer · Chapter 12

Forest Mensuration, Remote Sensing and GIS, Working Plans and Sampling

What to remember

Mensuration measures trees and stands. Diameter at breast height (DBH) is taken at 1.37 m above ground. Basal area = π/4 × D². Volume of a tree = basal area × height × form factor.
Remote sensing and GIS map forest cover from satellite images. Healthy plants reflect strongly in near-infrared and absorb red light, so NDVI = (NIR − Red) / (NIR + Red) is high for dense green forest.
A working plan is the written scheme of management of a forest for a fixed period (usually 10 years). Its basic units are the working circle and the compartment. Sampling lets us estimate the whole forest by measuring small plots.

1. Measuring a tree

Diameter and girth. In India diameter or girth is measured at breast height = 1.37 m (4.5 feet) above the ground on the uphill side. Girth = π × diameter. Instruments:

Calliper (tree calliper): two arms slide on a scale; gives diameter directly.
Diameter tape (π-tape): tape marked so that a girth reading is converted to diameter.
Girth tape: measures girth.
Biltmore stick and Spiegel relascope: indirect methods; the relascope also measures upper-stem diameters and heights.

Special cases: for a tree with buttresses, measure above the buttress; for a forked tree below breast height, measure each stem.

Height. Instruments are the Abney level, clinometer, Haga altimeter, Blume-Leiss hypsometer and Christen hypsometer. Principle: similar triangles or trigonometry.

Height = (horizontal distance × tan θ) + observer eye height (when the angle is measured upward to the top from level ground).

Example: at 20 m from the tree base, the angle to the top is 45°. Tan 45° = 1, so height above eye = 20 m; if the eye height is 1.5 m, total height = 21.5 m.

Basal area (BA) = π/4 × D² = 0.7854 × D². With D in metres, BA is in square metres. Example: D = 0.40 m gives BA = 0.7854 × 0.16 = 0.1257 m².

Stand basal area per hectare = sum of the basal areas of all trees in the plot, scaled to one hectare.

2. Volume of trees and logs

Formula	Expression	Use
Huber	V = A_m × L (mid-section area × length)	Easiest for logs
Smalian	V = (A₁ + A₂)/2 × L (end areas)	Logs when ends are accessible
Newton	V = (A₁ + 4A_m + A₂)/6 × L	Most accurate
Quarter girth	V = (G/4)² × L	Timber trade (G = mid-girth)
Form factor	V = BA × H × F	Standing tree

Newton's formula is the most accurate of the three, because it uses both end sections and the middle.

Form factor (F) = actual volume / volume of a cylinder of the same breast-height basal area and height. Typical solids: cylinder F = 1, paraboloid F = 0.5, cone F = 0.33, neiloid F = 0.25. Form quotient = diameter at half height / DBH.

Worked example 1: Mid-girth of a log is 1.2 m; length 10 m. Quarter girth = 0.3 m; V = 0.09 × 10 = 0.9 m³.

Worked example 2: Huber: mid-section area 0.2 m², length 6 m: V = 1.2 m³.

Worked example 3: Smalian: A₁ = 0.30 m², A₂ = 0.10 m², L = 5 m: V = 0.2 × 5 = 1.0 m³.

Worked example 4: BA = 0.1 m², H = 20 m, F = 0.5: V = 1.0 m³.

Stacked wood. Firewood and small timber are measured in stacks. The unit is the stere (1 m³ of stack). Solid volume = stack volume × stacking coefficient, which is less than 1 because of air gaps.

Volume tables give the volume of a standing tree from easy measurements (DBH, or DBH and height). A *local volume table* uses DBH only; a *standard* (general) one uses DBH and height; a *form-class table* also uses form class.

3. Growth and increment

Current annual increment (CAI) = growth in one year.
Mean annual increment (MAI) = total volume at age ÷ age.
MAI is at its maximum when CAI = MAI (the curves cross). This age is the rotation of maximum volume production.
Increment is measured by an increment borer, which extracts a pencil-thin core to count annual rings and measure width.
Site quality is judged by the height of dominant trees at a standard age; the result is the *site index* (site quality class).
Yield tables give expected volume per hectare for a given species, age and site quality. Stand tables give the number of trees by diameter class.
Crown density and stocking: how closely trees occupy the area.

Example: At 20 years volume is 200 m³/ha, so MAI = 10 m³/ha/yr. At 21 years it is 215 m³; CAI = 15 m³.

4. Sampling in forest inventory

A *complete enumeration* measures every tree (used for valuable species or small areas). A *sample* measures a part and estimates the whole.

Method	How plots are chosen	Remark
Simple random	Every plot has equal chance	Needs a full list
Systematic	Plots at fixed intervals	Easy in field; common
Stratified	Forest divided into similar strata first	Reduces error
Cluster	Plots grouped together	Saves travel time
Multistage	Samples in stages	Used in national inventories

Sampling intensity = (area sampled / total area) × 100. Example: 20 plots of 0.1 ha in a 200 ha forest sample 2 ha, so intensity = 1%.
Plot shapes: circular, square, rectangular, strips. A circular plot of 0.1 ha (1,000 m²) has radius = √(1,000/π) ≈ 17.84 m.
Statistics: mean = Σx/n; standard deviation (SD); standard error SE = SD/√n; coefficient of variation CV = (SD/mean) × 100. Larger sample size n reduces the standard error.
Estimate of the total = mean per hectare × total area.

Example: Mean volume = 80 m³/ha from sample plots. Forest area 500 ha gives estimated total = 40,000 m³.

5. Remote sensing

Remote sensing collects information about the Earth without touching it, using electromagnetic radiation from sensors on satellites, aircraft or drones.

Spectral behaviour: healthy vegetation absorbs blue and red light for photosynthesis, reflects green strongly, and reflects near-infrared (NIR) very strongly. Water absorbs NIR and looks dark. Dry soil reflects more in the visible range.
NDVI = (NIR − Red) / (NIR + Red). Its value lies between −1 and +1; dense green vegetation gives high positive values (for example 0.6 to 0.9), water gives negative or near-zero values.
Resolution has four kinds: spatial (size of one pixel on the ground), spectral (number and width of bands), radiometric (number of brightness levels) and temporal (how often the same place is revisited).
Passive sensors use sunlight (optical sensors); active sensors send their own signal (radar, LiDAR). Radar can see through clouds, which is useful during the monsoon.
Indian programme: ISRO's IRS series, Resourcesat, Cartosat and RISAT (radar). The National Remote Sensing Centre is in Hyderabad. The Forest Survey of India (Dehradun) uses satellite images to prepare the India State of Forest Report, normally every two years.
Uses in forestry: forest cover mapping, change detection (deforestation), fire detection, burnt-area mapping, plantation monitoring, biomass estimation and habitat mapping.
Image interpretation uses tone, texture, shape, size, pattern, shadow and association.

6. GIS and GPS

Geographic Information System (GIS) stores, analyses and displays spatial data with attributes. Data types:

Vector: points (a tree, a camera trap), lines (road, stream), polygons (a compartment, a lake).
Raster: grid of cells (satellite image, digital elevation model, DEM).
Overlay analysis combines layers (for example forest type + slope + roads) to select sites or prioritise fire-prone areas.
GPS gives location from satellites. The US system is NAVSTAR GPS; India has NavIC (also called IRNSS). A fix needs signals from at least four satellites (three for position, one for time). Common datum: WGS 84.
Toposheets of the Survey of India are used as base maps; common scales are 1:50,000 and 1:25,000.

Map scale = map distance / ground distance. On a 1:50,000 map, 1 cm = 0.5 km, and 1 cm² = 0.25 km² = 25 ha. Example: a forest block of 8 cm² on a 1:50,000 map has area 8 × 25 = 200 ha.

7. Working plans

A working plan is a written scheme of management for a forest area that ensures continuity of policy and action, based on sound silviculture and the needs of the area. A plan is prepared by a Working Plan Officer and approved by the Government (in India with guidance from the National Working Plan Code, which has been revised since it was first issued).

Units

Working circle: a group of forest areas managed under one objective and one silvicultural system (for example Teak Working Circle, Bamboo Working Circle, Protection Working Circle).
Felling series: group of compartments that are harvested in turn.
Compartment: permanent unit of area, numbered and bounded, used for records.
Block: group of compartments (a larger unit).

Plan period is typically 10 years (a revision comes at the end). The plan has two parts: facts and analysis (area, soil, climate, growing stock, past management), then prescriptions for management (objectives, working circles, silviculture, yield, protection, staff).

Regulation of yield and rotation. *Rotation* is the planned number of years between formation and final felling. Types: physical, technical, financial (economic) and rotation of maximum volume production. Normal forest is an ideal forest with normal age-class distribution, normal growing stock and normal increment.

Annual coupe (area method) = total area / rotation. Example: 400 ha, rotation 80 years: coupe = 5 ha per year.
Von Mantel's formula (volume method): Annual yield = 2 × Growing stock / Rotation. Example: growing stock 40,000 m³, rotation 80 years: yield = 1,000 m³ per year.
In a normal forest with equal annual yield, Normal growing stock = Annual yield × Rotation / 2.

Exam traps

Breast height in India is 1.37 m, not 1.5 m.
Quarter girth uses (G/4)²; it is not the same as π/4 × D².
Huber uses mid-section area; Smalian uses the two end areas; Newton uses all three.
MAI is highest when CAI equals MAI, not when CAI is highest.
NDVI uses NIR minus red in the numerator.
Radar (active) sees through cloud; optical (passive) does not.
Working circle is a management unit; compartment is a permanent record unit.
Von Mantel has 2 in the numerator; area coupe has no 2.

One-liners

1. Breast height in India: 1.37 m.
2. Basal area = 0.7854 × D².
3. Form factor of a cylinder is 1; paraboloid 0.5; cone 0.33.
4. Newton's formula uses A₁, A_m and A₂ with weights 1, 4, 1.
5. CAI = MAI at the culmination of MAI.
6. Increment borer extracts a core to count rings.
7. NDVI ranges from −1 to +1.
8. NavIC is India's regional navigation system.
9. NRSC is at Hyderabad.
10. The Forest Survey of India brings out the State of Forest Report.
11. The Survey of India toposheet 1:50,000: 1 cm = 0.5 km.
12. Standard error = SD / √n.

Practice questions

In India, the standard breast height for measuring tree diameter is:
1. 1.00 m above ground
2. 1.37 m above ground
3. 2.00 m above ground
4. 1.50 m above ground
Answer
B. 1.37 m above ground
Breast height = 1.37 m (4.5 ft).
Which instrument gives the diameter of a tree directly from two sliding arms?
1. Haga altimeter
2. Increment borer
3. Tree calliper
4. Abney level
Answer
C. Tree calliper
A calliper reads diameter directly; Abney level and Haga altimeter measure angles or heights.
An increment borer is used to:
1. Extract a core to count annual rings
2. Measure tree height
3. Measure slope of ground
4. Measure stack volume
Answer
A. Extract a core to count annual rings
The core shows ring width and age.
The basal area of a tree with diameter 0.40 m is about:
1. 0.063 m2
2. 0.503 m2
3. 0.251 m2
4. 0.126 m2
Answer
D. 0.126 m2
BA = 0.7854 x 0.40^2 = 0.1257 m2.
A log has mid-girth 1.6 m and length 5 m. Its volume by the quarter-girth formula is:
1. 0.4 m3
2. 2.0 m3
3. 0.8 m3
4. 1.6 m3
Answer
C. 0.8 m3
(1.6/4)^2 x 5 = 0.16 x 5 = 0.8.
A log has mid-section area 0.25 m2 and length 8 m. Volume by Huber's formula is:
1. 1.0 m3
2. 2.0 m3
3. 0.5 m3
4. 4.0 m3
Answer
B. 2.0 m3
V = 0.25 x 8 = 2.0.
A log has end areas 0.40 m2 and 0.20 m2 and length 10 m. Volume by Smalian's formula is:
1. 4.0 m3
2. 2.0 m3
3. 6.0 m3
4. 3.0 m3
Answer
D. 3.0 m3
V = (0.40 + 0.20)/2 x 10 = 3.0.
A log has areas A1 = 0.30, Am = 0.25 and A2 = 0.20 m2 and length 12 m. Volume by Newton's formula is:
1. 4.5 m3
2. 2.7 m3
3. 3.0 m3
4. 3.6 m3
Answer
C. 3.0 m3
(0.30 + 4 x 0.25 + 0.20)/6 x 12 = (1.5/6) x 12 = 3.0.
A tree has basal area 0.2 m2, height 25 m and form factor 0.6. Its volume is:
1. 1.2 m3
2. 3.0 m3
3. 5.0 m3
4. 2.5 m3
Answer
B. 3.0 m3
V = 0.2 x 25 x 0.6 = 3.0.
A tree has volume 1.5 m3, basal area 0.15 m2 and height 20 m. Its form factor is:
1. 0.5
2. 0.3
3. 0.2
4. 0.75
Answer
A. 0.5
F = 1.5 / (0.15 x 20) = 1.5/3 = 0.5.
From a point 25 m away on level ground, the angle to a tree top is 45 degrees and eye height is 1.6 m. The tree height is:
1. 25.0 m
2. 26.6 m
3. 23.4 m
4. 51.6 m
Answer
B. 26.6 m
Height = 25 x tan 45 + 1.6 = 26.6.
The form factor of a perfect cylinder is:
1. 1.0
2. 0.33
3. 0.5
4. 0.25
Answer
A. 1.0
Cylinder 1, paraboloid 0.5, cone about 0.33, neiloid 0.25.
The mean annual increment is at its maximum when:
1. The tree is a seedling
2. CAI is zero
3. CAI equals MAI
4. CAI is at its peak
Answer
C. CAI equals MAI
The CAI curve cuts the MAI curve at its maximum.
A stand has 360 m3/ha at 30 years. Its mean annual increment is:
1. 3 m3/ha/year
2. 10 m3/ha/year
3. 30 m3/ha/year
4. 12 m3/ha/year
Answer
D. 12 m3/ha/year
MAI = 360 / 30 = 12.
Site index of a forest is based on:
1. Height of dominant trees at a standard age
2. Girth of the smallest tree
3. Number of tree species
4. Rainfall alone
Answer
A. Height of dominant trees at a standard age
Site quality is judged by dominant height at a fixed age.
In which sampling method are plots placed at fixed intervals?
1. Simple random sampling
2. Systematic sampling
3. Stratified sampling
4. Cluster sampling
Answer
B. Systematic sampling
Systematic sampling uses a regular grid or interval.
Dividing a forest into similar groups before sampling is called:
1. Systematic sampling
2. Cluster sampling
3. Stratified sampling
4. Complete enumeration
Answer
C. Stratified sampling
Strata are formed first, then samples drawn within each.
25 plots of 0.2 ha are laid in a 500 ha forest. The sampling intensity is:
1. 5%
2. 0.5%
3. 2%
4. 1%
Answer
D. 1%
Sampled area = 5 ha; 5/500 x 100 = 1%.
A sample has standard deviation 20 and 25 plots. The standard error of the mean is:
1. 0.8
2. 5
3. 20
4. 4
Answer
D. 4
SE = SD / sqrt(n) = 20/5 = 4.
Mean volume is 50 and standard deviation is 10. The coefficient of variation is:
1. 20%
2. 10%
3. 5%
4. 50%
Answer
A. 20%
CV = 10/50 x 100 = 20%.
The radius of a circular sample plot of 1,000 m2 (0.1 ha) is about:
1. 31.62 m
2. 10.00 m
3. 17.84 m
4. 8.92 m
Answer
C. 17.84 m
r = sqrt(1000/pi) = 17.84 m.
Healthy green vegetation reflects very strongly in which region of the spectrum?
1. Red
2. Near-infrared
3. Blue
4. Thermal infrared
Answer
B. Near-infrared
Chlorophyll absorbs red and blue; leaf structure reflects NIR strongly.
If NIR reflectance is 0.6 and red reflectance is 0.2, NDVI is:
1. 2.0
2. 0.4
3. 0.75
4. 0.5
Answer
D. 0.5
NDVI = (0.6 - 0.2)/(0.6 + 0.2) = 0.4/0.8 = 0.5.
Which type of sensor can see through clouds during the monsoon?
1. Optical passive sensor
2. Visible colour camera
3. Radar (active microwave)
4. Thermal camera only
Answer
C. Radar (active microwave)
Radar uses microwaves that pass through cloud.
Spatial resolution of a satellite image refers to:
1. Number of bands
2. Ground size of one pixel
3. Number of brightness levels
4. Revisit time
Answer
B. Ground size of one pixel
Spectral, radiometric and temporal are the other resolutions.
The National Remote Sensing Centre of India is located at:
1. Hyderabad
2. Bengaluru
3. Pune
4. Dehradun
Answer
A. Hyderabad
NRSC is at Hyderabad; FSI is at Dehradun.
The minimum number of GPS satellites needed for a three-dimensional position fix is:
1. Four
2. Three
3. Six
4. Two
Answer
A. Four
Three for position and one for time.
In a GIS, a forest compartment is best stored as a:
1. Point
2. Polygon
3. Line
4. Pixel of a DEM only
Answer
B. Polygon
Areas are stored as polygons in vector data.
A digital elevation model is an example of:
1. Vector point data
2. Raster data
3. Attribute table only
4. Vector line data
Answer
B. Raster data
A DEM is a grid of elevation values.
On a 1:50,000 toposheet, a distance of 6 cm on the map equals on the ground:
1. 0.3 km
2. 30 km
3. 3 km
4. 6 km
Answer
C. 3 km
6 x 50,000 = 300,000 cm = 3 km.
A forest block measures 12 cm2 on a 1:50,000 map. Its ground area is:
1. 30 ha
2. 120 ha
3. 600 ha
4. 300 ha
Answer
D. 300 ha
1 cm2 = 25 ha; 12 x 25 = 300 ha.
A group of forest areas managed with one objective and one silvicultural system is a:
1. Working circle
2. Beat
3. Compartment
4. Block
Answer
A. Working circle
That is the definition of a working circle.
The permanent numbered unit of area used for management records is the:
1. Felling series
2. Working circle
3. Range
4. Compartment
Answer
D. Compartment
The compartment is the permanent record unit.
A working plan period is commonly:
1. 3 years
2. 50 years
3. 10 years
4. 1 year
Answer
C. 10 years
Most plans run for ten years and are then revised.
A forest of 600 ha has a rotation of 60 years. The annual coupe under the area method is:
1. 36 ha
2. 20 ha
3. 10 ha
4. 5 ha
Answer
C. 10 ha
600/60 = 10 ha per year.
By Von Mantel's formula, a forest with growing stock 30,000 m3 and rotation 60 years has annual yield:
1. 1,000 m3
2. 1,800 m3
3. 2,000 m3
4. 500 m3
Answer
A. 1,000 m3
Yield = 2 x 30,000 / 60 = 1,000.
In a normal forest with annual yield 500 m3 and rotation 80 years, the normal growing stock (yield x rotation / 2) is:
1. 40,000 m3
2. 20,000 m3
3. 10,000 m3
4. 6,250 m3
Answer
B. 20,000 m3
500 x 80 / 2 = 20,000.
The India State of Forest Report is prepared by the:
1. National Remote Sensing Centre
2. Survey of India
3. Wildlife Institute of India
4. Forest Survey of India
Answer
D. Forest Survey of India
FSI at Dehradun prepares it using satellite data.
India's regional satellite navigation system is:
1. Galileo
2. NAVSTAR
3. GLONASS
4. NavIC
Answer
D. NavIC
NavIC (IRNSS) is Indian; NAVSTAR is the US GPS.
Which log volume formula uses the end areas and the middle area?
1. Newton's formula
2. Smalian's formula
3. Huber's formula
4. Quarter-girth formula
Answer
A. Newton's formula
Newton: (A1 + 4Am + A2)/6 x L.
Consider the statements: 1. Optical satellite sensors are passive. 2. Radar sensors are active. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Optical sensors use sunlight; radar emits its own signal.
Consider the statements: 1. In a working plan the compartment is a permanent unit. 2. Working circles are fixed only by geography, not by objective. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Working circles are formed by management objective and system.
Consider the statements: 1. Mean annual increment is the total volume divided by age. 2. MAI is maximum when CAI is zero. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
MAI is maximum when CAI equals MAI.
Consider the statements: 1. Standard error decreases as the sample size increases. 2. Von Mantel's formula has growing stock divided by rotation without a factor of 2. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
SE = SD/sqrt(n); Von Mantel's yield = 2 x GS / R.
Consider the statements: 1. Basal area is pi/4 x D squared. 2. Breast height in India is 1.5 m. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Breast height in India is 1.37 m.

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