Appendix 1: Simulation study for Europe and CIS

by
Raymond L. Czaplewski and Erkki Tomppo

FRA 2010 will consider the following issues and assessment questions:

1. Biodiversity, climate change, desertification, carbon cycling

2. International economic analyses and forecasting

3. Current extent and condition of forests globally

4. Rapid changes in forest cover and land use, deforestation

a. How much forest is being lost? Gained?

b. Where is forest being lost? Hot spots of deforestation and degradation

c. What are the processes driving rapid changes

i. Land use change, agriculture, urban

ii. Timber harvest

iii. Catastrophic fire, floods

5. Comparisons across different spatial scales among:

a. Broad ecological zones across all continents

b. Broad ecological zones within individual continents

c. Individual countries

This FRA 2010 assessment requires a database of reliable information on the current status of forests, changes in forests between 2000 and 2010, and trends in rates of change over a longer span of time. The database needs information for broad ecological zones within individual continents, which can be grouped into broader geographic regions.

National data presents problems for global assessments at these broad, multinational scales. There are differences among nations in definitions, completeness and timeliness of their national data, even in the developed world (FAO 2000, 2001). In the tropical zone, FRA has supplemented national data with a remote sensing survey that can independently test the accuracy of national data for international analyses (FAO 2001). This survey uses internationally consistent definitions and protocols, which is not the case with all national data.

Remote sensing has its own set of challenges for global analyses. The first complete and acceptably accurate thematic map of global forest cover was first produced in the late 1990's (Loveland, 1999). This map used AVHRR satellite data, which has a spatial resolution of 1-km. However, this coarse scale introduces errors in characterizing the current status of forest cover (Moody and Woodcock 1994), and the changes in forest cover over time.

Landsat satellite data, with 30-m resolution, provide more accurate information on forest cover than AVHRR or MODIS because the spatial resolution is 100-to 1000-times greater. However, the processing burden is approximately 100- to 1000-times greater also. Land cover mapping with Landsat data for the entire the world has not yet been achieved, although there are impressive efforts underway to accomplish this massive task in the future. Measuring changes in forest cover over time (e.g., 1980, 1990, 2000, 2010) with full global coverage of Landsat data is even a larger task. A short-term alternative to full Landsat global coverage is sampling of Landsat scenes. This was first accomplished by FAO in FRA 1990 for the tropical forested zones of the world, with a detailed analysis of changes between 1980 and 1990. In 2001, FRA 2000 produced the first global assessment of changes and trends forest cover between 1980 to 1990, and 1990 to 2000.

Remote sensing technologies have improved significantly since FRA 1990. MODIS data are now available globally at 250-m nadir resolution with much greater spectral resolution than AVHRR. MODIS offers the promise for much better global data compared to AVHRR. IKONOS satellite data have recently become available for the entire world. This and similar commercial satellites offer 1-m resolution, which is similar to high-altitude aerial photography. However, the volume of data needed for full coverage of the world increases another 1000-times relative to Landsat data at 30-m resolution.

The objective of this study is to evaluate the feasibility to improve the FRA 2010 global forest assessment using these new sources of remotely sensed data. Assumptions include:

1. Land cover mapping with full global coverage of the world with coarse resolution satellite data (250-m to 1-km pixels) will improve. This will be accomplished through institutions and programs external to FAO.

2. Consistent land cover mapping with full global coverage of the world with high-resolution satellite data (30-m resolution) will be achieved by 2010 through institutions and programs external to FAO. However, measurement of change in forest cover requires imagery from multiple dates, such as 1980, 1990, 2000 and 2010. It is assumed that full coverage with 30-m satellite data for this time series will not be accomplished by 2010. Therefore, sampling of Landsat scenes for assessments of changes and trends in forest cover will remain relevant for FRA 2010.

3. Very high-resolution satellite data (1-m resolution) can improve accuracy of the FRA 2010 database relative to classifications with 30-m resolution data. This same imagery could provide the statistical linkage between global collection of field data for FRA 2010 and an independent remote sensing survey of the world.

This study uses simulations to evaluate the feasibility of multiple-resolution remote sensing for FRA 2010 objectives. The simulation has several components.

1. Construct a realistic hypothetical population that fully covers a very large region. The selected region was Europe and the Commonwealth of Independent States (CIS). The combined land area² is 2.7-billon hectares, of which 38% is forestland and another 4% is other wooded land.

2. Simulate changes in forest cover in this hypothetical population over a 10-year time interval.

3. Simulate estimates of forest area from satellite data with multiple resolutions (1-km, 30-m and 1-m) for the entire hypothetical population at the beginning (2000) and end of the 10-year time interval (2010).

4. Compare alternative sampling designs to statistically estimate the area of forest cover and changes in forest cover during the 10-year interval.

Predict the statistical precision and cost of these alternative designs for possible use by FRA 2010 in the future

Methods

Construction of a hypothetical population

Full coverage with realistic landscape patterns

The hypothetical population mimics Europe and CIS. This geographic area is composed of ten major ecological zones (Figure 2).

Figure 2: FRA 2000 ecological zones for Europe and CIS (2,268,966-km²).

The statistical efficiencies of alternative sampling designs are affected by the detailed spatial structure of regional and local landscape patterns within a population. The FRA 2000 global forest cover map (FAO 2001) for Europe and CIS was used to add this spatial realism into the hypothetical population. The FRA 2000 map uses 1-km cells classified into one of five categories (Table 12). This map is a modification (Zhu and Waller 2001) of the Global Land Cover Characteristics Database (Loveland et al. 1999) produced by the USGS Eros Data Center.

Figure 3: FRA 2000 global forest cover map. The spatial resolution is 1-km, and contains five categories of forest and other cover (Table 12).

Table 12: FRA 2000 global land cover map legend, definitions and representative land cover types (FAO 2001). Figure 2 gives a broad perspective of this map for Europe and CIS. The spatial resolution is 1-km.

FRA 2000 class	FAO definition	Representative land cover
Closed forest	Land covered by trees with a canopy cover of more than 40 percent and height exceeding 5 m. Includes natural forests and forest plantations.	Temperate broadleaf mixed forest Subtropical/temperate conifer plantation Boreal conifer forest
Open or fragmented forest	Land covered by trees with a canopy cover between 10 and 40 percent and height exceeding 5 m (open forest), or mosaics of forest and nonforest land (fragmented forest). Includes natural forests and forest plantations.	Northern boreal/taiga open conifer or mixed forest
Other wooded land	Land either with a 5 to 10 percent canopy cover of trees exceeding 5 m height, or with a shrub or bush cover of more than 10 percent and height less than 5 m.	Mediterranean closed shrubland
Other land cover	All other land, including grassland, agricultural land, barren land, urban areas.	Grassland, cropland, non-woody wetland, desert, urban
Water	Inland water.	Inland water.

Alternative sampling frames

The hypothetical population³ is divided into two alternative area sampling frames. The first frame uses a 150x150-km Large Sampling Unit (LSU), which is defined as approximately the average size of a non-overlapping Landsat scene at higher latitudes. There are a total of 1627 LSUs (i.e., simulated Landsat scenes) in Europe and CIS. However, 152 LSUs are covered by at least 90% ocean and large water bodies. These are excluded from the sampled population to reduce cost and variance. A total of 1473 LSUs are available for sampling.

The second sampling frame uses a 10x10-km Small Sampling Unit (SSU), which is approximately the field of view for a 1-m resolution image (e.g., IKONOS). There are 284,760 SSUs in the hypothetical population. However, 2265 SSUs are covered with at least 90% ocean or large water bodies, and are excluded from the sampled population. A total of 282,495 SSUs are available for sampling, although only a fraction of these units are actually included in any one sample.

The percent of each land cover category (Table 12) was computed from the FRA 2000 global map (similar to Figure 3)for each simulated LSU and SSU. These percentages simulate future results from a global classification with MODIS data, where MODIS could be used to estimate the proportion of each land cover category in each SSU. This is a pessimistic simulation because MODIS is expected to be more accurate for land cover mapping than AVHRR, and the realized results for FRA 2010 should be somewhat better than predicted by this simulation.

Simulated Landsat data
For statistical estimation purposes in FRA 2010, Landsat could be used to estimate the percentages of each category of land cover in a LSU or SSU. Statistical simulations require known values for all sampling units in the hypothetical population. Classification of each Landsat scene was simulated for the hypothetical population with a statistical calibration procedure, and only the simulated area statistics stored in the simulation database. The database for the hypothetical population stored the following fields for each of the 284,760 simulated SSUs (and the corresponding 1,627 LSUs):

Table 13: Data base used in sampling simulations (284,760 records)

Latitude, Longitude
Identification number for 150x150-km PSU
Identification number for 10x10-km SSU
FRA 2000 Ecological Zone code (10 major zones)
Country code
Total area of SSU (approximately 100-km2)
Area (km2) of large inland water bodies, ocean, and other non-land types
Time 0	Area (km2) from FRA 2000 global forest cover map (FAO 2001), with 1x1-km pixels
	1. Closed Forest (60-100% forest in 1-km pixel)
	2. Open and Fragmented Forest (30-60% forest in 1-km pixel) §
	3. Other Wooded Land
	4. Other Land Cover (includes small inland water bodies)
	Simulated area (km2) expected from classification of 30-m resolution Landsat data using calibration model from 1-km to 30-m resolution. Inputs to the calibration model are the area statistics at time t=0 from fields 1 to 4 at Time 0.
	5. Forest
	6. Other Wooded Land
	7. Other Land Cover (includes small inland water bodies)
	Simulated area (km2) expected from classification of 1-m resolution Ikonos data using calibration model from 30-m to 1-m resolution. Inputs to the calibration model are the area statistics at time t=0 from fields 5 to 6 at Time 0.
	8. Forest
	9. Other Wooded Land
	10. Other Land Cover (includes small inland water bodies)
Time +10	Simulated area (km2) from FRA 2000 global forest cover map using change transition matrix (unique to each individual SSU) using fields 1 to 4 at Time 0.
	11. Closed Forest (60-100% forest in 1-km pixel)
	12. Open and Fragmented Forest (30-60% forest in 1-km pixel) §
	13. Other Wooded Land
	14. Other Land Cover (includes small inland water bodies)
	Simulated area (km2) expected from classification of 30-m resolution Landsat data using calibration model from 1-km to 30-m resolution. Inputs to the calibration model are the area statistics at time t+10 from fields 11 to 14.
	15. Forest
	16. Other Wooded Land
	17. Other Land Cover (includes small inland water bodies)
	Simulated area (km2) expected from classification of 1-m resolution Ikonos data using calibration model from 30-m to 1-m resolution. Inputs to the calibration model are the area statistics at time t+10 from fields 15 to 17.
	18. Forest
	19. Other Wooded Land
	20. Other Land Cover (includes small inland water bodies)
	§The area of "Open and Fragmented Forest" (30-60% forest in 1-km pixel) exists only at the 1-km resolution of the FRA 2000 global forest cover map. Such areas are considered mosaics, which are composed of more specific categories (i.e., Forest, Wooded, and Other Land Cover). These mosaics are classified into the specific categories (i.e., Forest, Wooded, and Other Land Cover) with the simulated 30-m and 1-m resolution remotely sensed data.

The basis for this statistical procedure is the error matrix (Scepan 1999), also known as an "confusion matrix", that was produced for the Global Land Cover Characteristics Database (Loveland et al. 1999). This map is the primary source for the FRA 2000 global land cover map (Zhu and Walter 2001).

Landsat data were simulated for each SSU using the data from the FRA 2000 global land cover map (Zhu and Walter 2001). These data formed the basis of a multivariate calibration model (Czaplewski 1992) that predicts the proportional distribution of Landsat classifications for 30-m pixels as a function of classifications from the 1-km pixels in the FRA global land cover map. This model is given in Table 14A. The model is expressed as conditional probabilities in a probability transition matrix. For example, 65/78=83.33% of the Landsat pixels are expected to be classified as "Closed forest" in a 1-km global map pixel, given that the 1-km pixel is classified as "Closed forest" on the global map (Table 14).

Table 15 gives an example that applies the calibration model for one of the 284,760 SSUs in the hypothetical population.

This calibration model is applied separately to each SSU in the hypothetical population using the unique distribution of global map classes for each SSU. This is an attempt to capture the spatial variability and error structure that exists in the real-world population. It cannot be known how well this simulates the actual spatial variability in the true population. The assumption is that the hypothetical population is sufficiently realistic for simulations and survey planning. FRA 2010 will use real data, not these simulated data, to produce the 2010 global assessment.

Table 14: Global accuracy assessment results for the FRA global land cover map (Zhu and Waller 2001) and derivation of the misclassification calibration model to simulate Landsat classifications.

A. Accuracy assessment results for FRA 2000
				Landsat class
				Closed forest	Open or fragmented forest	Other wooded land	Other land cover	Water	Total sample points
Global Map classification		Closed forest		65	2	3	8		78
		Open or fragmented forest		13	9	3	17		42
		Other wooded land		1	2	6	10		19
		Other land cover		3	8	2	160		173
		Water4						0	0
				82	21	14	195		312
B. Distribution of “Open or Fragmented Forest” at 1-km resolution into Closed Forest (45%), Other Woodland (30%) and Other Land (25%) at 30-m Landsat resolution. These distributions are assumptions used to construct the hypothetical simulation population, and they are not based on data.
Global Map classification	Closed forest		65.90			3.60	8.50		78
	Open or fragmented forest		17.05			5.70	19.25		42
	Other wooded land		1.90			6.60	10.50		19
	Other land cover		6.60			4.40	162.00		173
	Total		91.45			20.30	200.25	0	312
Derived misclassification calibration model used to simulate Landsat classifications. This model is computed from Table 14A and applied to all 284,760 SSUs in the hypothetical population. C. Table 15 gives an example of the calibration model applied to a single SSU.
Global Map classification	Closed forest		89.6%			2.5%	7.9%	0	100%
	Open or fragmented forest		51.4%			8.8%	39.8%	0	100%
	Other wooded land		15.2%			27.1%	57.7%	0	100%
	Other land cover		5.5%			1.9%	92.6%	0	100%
	Water5		0			0	0	100%	100%

Table 15: Example showing application of the calibration model from Table 14 to simulate classification distribution of 30-m Landsat pixels within a single 10x10-km SSU, using the classification distribution of 1-km pixels from the FRA 2000 global land cover map within the same SSU

Classification of 1-km pixels in the single 10x10-km SSU from the global land cover map	Number of 1-km pixels in the SSU	Total Number of simulated 30-m Landsat pixels	Simulated distribution of 30-m Landsat pixels					Distribution of simulated MODIS pixels
			Closed forest	Open or fragmented forest	Other wooded land	Other land cover	Water
Closed forest	30	33334	29852	0	838	2644	0	30%
Open or fragmented forest	55	61111	31386	0	5392	24333	0	55%
Other wooded land	1	1111	169	0	301	641	0	1%
Other land cover	9	10000	550	0	188	9262	0	9%
Water	5	5555	0	0	0	0	5555	5%
Total	100	111111						100%
Simulated number of Landsat pixels in SSU			61956	0	6720	36880	5555	111111
Distribution of simulated Landsat pixels			55.8%	0%	6.0%	33.2%	5%	100%

Simulated IKONOS data

This simulation considers the possibility of using 1-m IKONOS imagery to improve FRA 2010 relative to FRA 2000. 284,760 IKONOS images are be required to fully cover the hypothetical population for Europe and CIS. These images include over 10¹³ 1-m pixels. In practice, the cost of acquiring and processing such a large number of images precludes full coverage. However, a small sample of IKONOS imagery for FRA 2010 is feasible.

Just as simulated Landsat data are needed for all 284,760 SSUs in the hypothetical population, simulated classification data are needed for the same number of IKONOS images. Accuracy assessment data for the National Land Cover Dataset for the USA was used to select parameters in the calibration model (Table 17).

Table 17: Calibration model that simulates classification data from IKONOS using simulated Landsat classifications for 10x10-km SSUs. This model is applied to all 284,760 SSUs in the hypothetical population.

		Simulated IKONOS classification with photo-interpretation
		Closed forest	Other wooded land	Other land cover	Large water bodies
Simulated digital Landsat classification	Closed forest	82.8%	3.0%	14.2%	0%	100%
	Other wooded land	12.0%	58.0%	30.0%	0%	100%
	Other land cover	16.9%	6.0%	77.2%	0%	100%
	Large water bodies	0%	0%	0%	100%	100%

Table 18: Example showing application of the calibration model from Table 17 to simulate the classification distribution of 1-m IKONOS pixels within a single 10x10-km SSU, using the classification distribution of simulated 30-km pixels from Table 15

Simulated classification of 30-m Landsat pixels in the single 10x10-km SSU	Total number of simulated 30-m Landsat pixels	Distributor of simulated 30-m Landsat pixels	Simulated distribution of 1-m IKONOS pixels
			Closed forest	Open or fragmented forest	Other wooded land	Other land cover	Water	Total
Closed forest	61956	55.8%	46169166	0	1659164	7932180	0
Open or fragmented forest	0	0%	0	0	0	0	0
Other wooded land	6720	6.0%	725726	0	3507677	1814316	0
Other land cover	36880	33.2%	5597991	0	1974915	25618780	0
Water	5555	5.00%	0	0	0	0	500000
Total	111111	100.00%	52492883	0	7141755	35365276	500000	100000000
Distribution of simulated IKONOS pixels			52.5%	0%	7.1%	35.4%	5.0%	100.00%

Simulation of changes over 10 years

A primary objective of FRA is estimation of changes in forest cover between decadal assessments. Therefore, a useful simulation must include a component of change. Change was imposed on this hypothetical population through a probability transition matrix, which is similar to the calibration models used above. A transition matrix is composed of the conditional probabilities that a land cover type at time 0 will transition into the same or different cover type at time 10. FRA 2000 estimated such transition matrices for the tropics; however, similar matrices for Europe and CIS are not known. Table 19 is one attempt to create transition matrices that roughly correspond to the net changes estimated for Europe and CIS in FRA 2000. The pattern of change among land cover categories is intended to mimic steady state transitions plus human-induced changes (i.e., variable X in Table 19) that vary spatially.

Table 19: Change transition matrix from time 0 to time 10, applied to classes from 1-km FRA 2000 global land cover map

	Time 10
Time 0	Closed forest	Open Frag. forest	Other wooded land	Other land cover
Closed forest (60-100% forest)	0.985-(X*0.9)	X*0.2+0.005	X*0.3+0.005	X*0.4+0.005	100%
Open/fragmented (30-60% forest)	0.010	0.98*(1-X)	0.005+0.98*X*0.5	0.005+0.98*X*0.5	100%
Other wooded land	0.020	0.120	0.800	0.060	100%
Other land cover	0.020	0.080	0.030	0.870	100%
Percent reduction forest cover =X	0<X<1

The value for X in Table 19 for each SSU varies according to a spatial “change risk” model, which is designed to have realistic spatial variability and result in realistic changes over a 10-year period. There are several multiplicative factors that affect the value of X.

The first factor in the change risk model (X₁) considers the distribution of closed forest and open/fragmented forest within a 50-km radius of the SSU. The assumption is that landscapes of this size that are almost entirely forested (80-100% closed forest) have relatively little exposure to land use changes and land clearing. However, the risk of change is assumed to be relatively high for landscapes that have more open and fragmented forest (e.g., 10-60%) intermingled with significant amounts of closed forest (e.g., 30-70%). As the amount of closed, open and fragmented forest become small in a landscape, then the rate of change in forest cover is assumed to be relative small.

Table 20: Relative index (0<X₁<1) for change risk as a function of landscape patterns within 50-km of a 10x10-km Small Sampling Unit (SSU).

		Percent closed forest within a 50-km radius from the SSU
		0-10%	10-20%	20-30%	30-40%	40-50%	50-60%	60-70%	70-80%	80-90%	90-100
Percent open and fragmented forest within a 50-km radius from the SSU	70-75%	0.12	0.51	0.90	0	0	0	0	0	0	0
	60-70%	0.06	0.36	0.75	1.00	0	0	0	0	0	0
	50-60%	0	0.30	0.60	1.00	1.00	0	0	0	0	0
	40-50%	0	0.15	0.45	0.90	1.00	1.00	0	0	0	0
	30-40%	0	0	0.30	0.75	1.00	1.00	1.00	0	0	0
	20-30%	0	0	0.15	0.60	1.00	1.00	1.00	0.60	0	0
	10-20%	0	0	0	0.51	1.00	1.00	1.00	0.45	0	0
	0-10%	0	0	0	0.39	0.96	1.00	0.75	0.21	0	0

The second factor in the change risk model (X₂) considers the distribution of closed forest and open/fragmented forest within each 10x10-km SSU. This is a much less expansive landscape than considered in the first factor (X₁) above. However, similar assumptions are used to assign a risk of change based on the distribution of closed forest and open/fragmented forest in the SSU (Table 21).

Table 21: Relative index (0<X₂<1) for changes in forest cover as a function of composition within a given 10x10-km SSU.

		Percent closed forest within the SSU
		0-10%	10-20%	20-30%	30-40%	40-50%	50-60%	60-70%	70-80%	80-90%	90-100
Percent open and fragmented forest within the SSU	90-100	0.50	0	0	0	0	0	0	0	0	0
	80-90%	0.48	0.6	0	0	0	0	0	0	0	0
	70-80%	0.44	0.57	0.7	0	0	0	0	0	0	0
	60-70%	0.42	0.52	0.65	0.80	0	0	0	0	0	0
	50-60%	0.40	0.50	0.60	0.75	0.90	0	0	0	0	0
	40-50%	0.35	0.45	0.55	0.70	0.87	1.00	0	0	0	0
	30-40%	0.30	0.40	0.50	0.65	0.82	0.90	0.80	0	0	0
	20-30%	0.25	0.30	0.45	0.6	0.80	0.95	0.75	0.60	0	0
	10-20%	0.17	0.20	0.40	0.57	0.77	0.90	0.70	0.55	0.40	0
	0-10%	0.10	0.15	0.35	0.53	0.72	0.85	0.65	0.47	0.35	0.20

The third factor in the change risk model (X₃) considers different risks for different ecological zones. Again, there is little data available to fit such models. The factors in Table 22 are merely assumptions for the hypothetical population.

Table 22: Change risk factor (X₃) for each ecological zone

Ecological Zone	X3	Ecological Zone	X3
Temperate oceanic forest	0.6	Subtropical humid forest	0.5
Temperate continental forest	0.5	Subtropical dry forest	0.7
Temperate steppe	0.7	Subtropical steppe	0.0
Temperate desert	0.0	Subtropical desert	0.0
Temperate mountain system	0.2	Subtropical mountain system	0.3
Boreal coniferous forest	0.5	Subtropical humid forest	0.5
Boreal tundra woodland	0.2
Boreal mountain system	0.1
Polar	0.0

The fourth and final factor in the change risk model (X₄) considers differences among individual countries. The factors in Table 23 were chosen so that the total change by country in the hypothetical population approximately agrees with national statistics reported by FRA 2000.

Table 23: Change risk factors (X₄) for each country to mimic net changes reported by FRA 2000.

Country	X4	Country	X4	Country	X4
Albania	1.00	Germany	0.40	Portugal	0.00
Armenia	0.20	Greece	0.00	Republic of Moldova	0.90
Austria	0.00	Hungary	0.60	Romania	0.60
Azerbaijan	0.10	Iceland	0.00	Russian Federation	1.00
Belarus	0.10	Ireland	0.00	Slovakia	0.05
Belgium	0.90	Italy	0.40	Slovenia	0.00
Bosnia and Herzegovina	0.15	Kazakhstan	0.10	Spain	0.10
Bulgaria	0.20	Kyrgyzstan	0.10	Sweden	0.10
Croatia	0.20	Latvia	0.00	Switzerland	0.50
Cyprus	0.20	Liechtenstein	0.00	Tajikistan	0.90
Czech Republic	0.60	Lithuania	0.20	The FYR of Macedonia	0.90
Denmark	0.80	Luxembourg	0.10	Turkey	0.90
Estonia	0.00	Malta	0.20	Turkmenistan	0.60
Finland	0.05	Netherlands	0.30	Ukraine	0.80
France	0.10	Norway	0.10	United Kingdom	0.10
Georgia	0.40	Poland	1.00	Uzbekistan	0.60
				Yugoslavia	0.90

The final change model for each individual SSU_i uses X_i=X₁*X₂*X₃*X₄ for that SSU with the transition probabilities from Table 19 to simulate 1-km resolution data at time 10. These estimates are then used with the calibration model in Table 14 to simulate 30-m Landsat data at time 10 for each SSU, and those simulated Landsat data at time 10 are input into the calibration model in Table 17 to simulate 1-m Ikonos data at time 10 for each SSU. Figure 4 shows the spatial distribution of change in the hypothetical population.

Table 24: Statistical summary for hypothetical population by Ecological Zone at time 0, and changes between times 0 and 10

Ecological zone	Total area (km2)	Data source	Forest at time 0 (km2)	Change in forest over 10-years (km2)	Change in forest over 10 years
Subtropical	1,749,103	AVHRR	540,171	42,761	7.92%
		Landsat	366,763	60,933	16.61%
		Ikonos	531,887	40,334	7.58%
Temperate oceanic forest	1,243,743	AVHRR	421,814	28,274	6.70%
		Landsat	312,545	40,165	12.85%
		Ikonos	413,448	26,160	6.33%
Temperate continental forest	3,639,242	AVHRR	1,466,846	8,380	0.57%
		Landsat	1,325,990	2,867	0.22%
		Ikonos	1,479,238	964	0.07%
Temperate steppe	2,112,952	AVHRR	467,237	67,506	14.45%
		Landsat	220,972	99,632	45.09%
		Ikonos	496,868	66,238	13.33%
Temperate desert	2,456,317	AVHRR	459,297	-12,836	-2.79%
		Landsat	143,249	0	0.00%
		Ikonos	502,269	3,838	0.76%
Temperate mountain system	1,391,327	AVHRR	612,993	17,740	2.89%
		Landsat	590,866	24,522	4.15%
		Ikonos	621,190	16,002	2.58%
Boreal coniferous forest	5,866,169	AVHRR	3,673,218	-190,637	-5.19%
		Landsat	4,050,198	-290,480	-7.17%
		Ikonos	3,649,235	-194,697	-5.34%
Boreal tundra woodland	1,331,279	AVHRR	416,959	32,159	7.71%
		Landsat	307,694	45,120	14.66%
		Ikonos	424,360	29,324	6.91%
Boreal mountain system	4,914,168	AVHRR	2,542,564	33,676	1.32%
		Landsat	2,597,905	42,762	1.65%
		Ikonos	2,529,359	27,684	1.09%
Polar	1,895,919	AVHRR	460,565	-8,871	-1.93%
		Landsat	179,772	0	0.00%
		Ikonos	433,447	1,477	0.34%
Total for Europe and CIS	26,600,219	AVHRR	11,091,219	17,442	0.16%
	1,749,103	Landsat	10,103,675	25,521	0.25%
		Ikonos	11,093,925	17,362	0.16%

Figure 4: Simulated changes in forest cover between time 0 and 10 using simulated 1-m Ikonos data

Sample designs

FRA 2000 used a stratified random sample of Landsat scenes for the global tropics. Pre-stratification was based on ecological zones and continents (FAO 1996). Within each stratum, further stratification was introduced to reduce variance. These sub-strata are based on the prevalence of forest cover (10-40%, 40-70%, and 70-100%), which was estimated for every sub-national unit (e.g., state, municipality) in the tropics. The Landsat World Reference System (Landsat path/rows) were superimposed on the sub-national unit boundaries, and each Landsat scene was assigned to a substratum. Sample size in each stratum was proportional to the expected rate of deforestation, which was estimated for each sub-national unit based on the prevalence of forest, human population size, and per capita income.

The FRA 1990 pan-tropical remote sensing survey was planned in 1992. During the past 10 years, better pre-stratification materials have become globally available through coarse-resolution satellite data (AVHRR, and soon, MODIS). Use of Landsat data, with 30-m resolution, has become less expensive and more automated. For example, the USA recently completed its first national land cover map with 1992 Landsat data from 500 scenes, and a project has begun to provide similar global coverage with Landsat⁶. Also, satellite data with 1-m resolution are also available for consideration in global applications. These developments offer new options for FRA 2010. Multi-resolution satellite data would work well with multi-stage sampling. Double-sampling for regression with remotely sensed data could improve efficiency by correlating high-resolution, but expensive, estimates of forest cover and change with less expensive lower-resolution remotely sensed data. These complex sampling designs are not considered here, but they could be considered if recommended by the Kotka IV participants.

The current analysis is limited to single-stage pre-stratified random sampling. Strata are formed with 1-km data, such as the FRA 2000 global forest cover map, that covers the entire population.

Two types of stratification are evaluated:

1. Optimisation for forest cover from 1-km AVHRR data at one point in time; and

2. Optimisation using changes in 1-km AVHRR data (or 250-m MODIS data) over a 10-year time period.

Two different sizes of sampling units are considered:

3. 150x150-km Large Sampling Unit (LSU) that conforms to an image from Landsat or a similar satellite.

4. 10x10-km Small Sampling Unit (SSU) that conforms to an satellite image with 1-m resolution or a high-altitude (e.g., 1:40,000) aerial photograph.

Strata and sub-strata

The first level of stratification is the ten FRA 2000 Ecological Zones in Figure 2. These strata are used to assure that each Zone has a sufficient sample size for analysis. Each Zone is further divided into sub-strata to minimize variance of an estimate.

Optimal boundaries for each sub-stratum were formed using methods recommended by Cochran (1977:127-131). First, consider sub-strata optimised to estimate change in forest area over 10-years with the 150x150-km Large Sampling Units (LSUs). For each sampling unit, AVHRR data from 10-years apart are used to estimate the change in forest area (km²). (The methods used to simulate multi-date AVHRR data in this analysis are given above). AVHRR estimates have significant bias caused by misclassification errors (Czaplewski 1992). However, estimates from AVHRR are correlated with estimates from Landsat and Ikonos. Since AVHRR estimates are available for all N sample units in the population, AVHRR data can be used to define the boundaries of sub-strata for all sample units.

Boundaries of sub-strata are determined by sorting all 1,473 LSUs in the hypothetical population by the AVHRR estimate of change in forest area (km²). Then the cumulative of the square root of the AVHRR estimate is formed and divided into L equal intervals (see y axis in Figure 5, in which k=5). The AVHRR values corresponding to those intervals define the sub-strata boundaries. An equal number of samples (n_kh) is assigned to each sub-stratum h. Different numbers of sub-strata were investigated for 2<L<6 (Cochran 1977 pp 132-134). The efficiency for L=5 was almost identical to L=6 (except for n<75); and L=5 is used for all evaluations in this analysis. Figure 5 illustrates use of the same method for the 284,760 10x10-km SSUs in the hypothetical population. Finally, the same procedure was independently applied to AVHRR data from one point in time to optimise estimates of forest area at that time, although these are not illustrated in Figure 5.

Figure 5: Stratification based on Neyman allocation for 150x150-km and 10-10-km Sample Units

Estimators

One of the unique luxuries with this type of hypothetical population is that all relevant statistics are known from the database. Therefore, the performance of alternatives statistical designs and simulated sample sizes can be determined exactly with the true totals (Y_k) and variances (S_k²) for each ecological zone k. With a real population, those statistics are unknown, and they must be estimated from a single sample (i.e., y_k and s_k²).

Using notation from Cochran (1977), the estimate for stratum k (ecological zone) is the sum of sub-strata (h) estimates:

The estimate across all ecological zones is:

The estimates for the rate of change is computed with a Taylor series approximation (Cochran 1977).

Results

A primary purpose of the simulation is to predict the statistical accuracy of future sample estimates for FRA 2010. Accuracy is a function of sample size, and sample size affects costs.

Figure 6 summarizes the results for Europe and CIS. The standard error with the 150x150-km LSUs approaches zero as n approaches 1473 because of the finite population correction factor. As expected, the sub-strata boundaries optimized for forest area (using AVHRR estimates at time 0) produces more precise estimates for forest area as determined with Landsat and Ikonos data. Likewise, sub-strata boundaries optimized for changes in forest area (using AVHRR estimates at time 0 and time 10) produces more precise estimates for changes in forest area as determined with Landsat and Ikonos data.

Figure 6: Standard errors expected for Europe and CIS combined

The rate of change in forest area (expressed as a proportion of forest area), is the ratio of two estimates: forest area (km²) at time 0, and change in forest area (km²) between times 0 and 10. Empirical results show that sub-strata optimized for change in forest area also are most efficient for estimates of rates of change (Figure 6).

Estimates for woodland are also relevant to FRA 2010. However, the sub-strata analyzed here ignore woodland statistics during optimization. Empirical results in Figure 6 show little difference among stratification alternatives in estimating woodland area at time 0. However, the stratification optimized for change in forest area is also more efficient for estimating changes in woodland area because of the positive correlation among between forest and woodland changes. This correlation is imposed by the change model used to build the hypothetical population (Table 19), and the value of these simulation results to FRA 2010 depends directly on the realism of the hypothetical population.

One surprising result is the greater efficiency with the 10x10-km sampling units (solid lines in Figure 6) relative to the 150x150-km sampling units (dashed lines in Figure 6). Larger sampling units typically have less among-unit variance than smaller sampling units, and this pattern is true with the hypothetical population. Therefore, the larger sample units usually have higher statistical efficiency when costs are not considered. This expectation does not hold true in Figure 6. The analysis was thoroughly checked for errors, and none were found. The explanation for these counter-intuitive results appears to be the methods used to optimize sub-strata for variance reduction (Figure 5). The small sampling units can be grouped into more homogeneous sub-strata compared to the large sampling units.

Figure 7 presents similar results for one of the ten ecological zones: Boreal Coniferous Forest. This Zone has the highest rate of change among all ecological zones in the hypothetical population. The sample size n in Figure 7 represents the entire sample size for Europe and CIS, and only a portion of these n samples is allocated to the Boreal Coniferous Forest zone.

Figure 7: Standard errors expected for the Boreal Coniferous Ecological Zone

Results for the large 150x150-km sampling units in Figure 6 and Figure 7 assume that each is measured with Landsat data, not the more accurate 1-m Ikonos data. However, there is a bias in the estimates from these large sampling units caused by misclassification. Figure 8 compares the magnitude of this bias relative to the standard error. For analyses of the entire Europe and CIS region, the bias in estimated forest area at time 0 is significant except for very small sample sizes (n<75). The significance of this bias is somewhat less when analyzing a single ecological zone, but becomes significant in this example with a total sample size of n>300. The bias is insignificant for estimates of changes between time 0 and time 10 for Europe and CIS, largely because the net change at this scale is only 0.16%. The bias is very notable for the Boreal Coniferous Forest zone, which has the largest loss of forest (-5.34%) among all ecological zones in this hypothetical population. The conclusion is that bias caused by misclassifications with Landsat data, relative to 1-m Ikonos data, can be large enough to be a concern for FRA 2010.

Figure 8: Expected standard errors relative to bias in Landsat estimates

Discussion

These simulations serve as a preliminary “proof-of-concept” showing one technique available to help plan for FRA 2010. Different statistical designs and degrees of complexity are possible. Results from the Kotka IV meeting will help direct these future analyses if the recommendation is to expand the remote sensing survey beyond that used for the tropics by FRA 1990 and FRA 2000.

The sample of 10x10-km Ikonos images performed unexpectedly well. However, this option would be very difficult to implement in practise. The assumption is that change detection uses two dates of imagery for the same sample unit, separated by approximately 10 years, and sub-strata are formed based on change detection with AVHRR or MODIS at the end of this time period. This will allow efficient selection of Ikonos scenes at time 10, but it is very unlikely that an Ikonos image for the same scene at time 0 is available in any archive.

It is very possible that Landsat could produce full global coverage of land cover classification in the near future. Future simulations could consider this asset. However, this product might exist for only one point in time, and sampling for change detection could remain relevant. Regardless, the FRA 2010 might assume that Landsat classifications for continental and even global coverages will be produced by other institutions. Perhaps a unique niche for FRA 2010 among these international programs could be collection of high-resolution data from Ikonos imagery or field samples.

The value of this simulation depends directly upon the realism of the assumptions used to construct the population. If this type of work continues, then improvements should be considered. For example, the calibration models are the same for all Ecological Zones, but they would be more realistic if they were modified for each Zone. Also, the change model uses many ad hoc assumptions that could be improved.

Literature cited

Cochran, W.G. 1977. Sampling techniques. Third Edition. John Wiley & Sons, New York. 428pp.

Czaplewski, R.L. 1992. Misclassification bias in areal estimates. Photogrammetric Engineering and Remote Sensing. 58(2):189-192.

FAO. 1996. Forest resources assessment 1990: Survey of tropical forest cover and study of change processes. FAO Forestry Paper No. 130. Rome. 152pp.

FAO. 2001. Global forest resources assessment 2000. Main Report. FAO Forestry Paper No. 140. Rome. 479pp.

Zhu, Z. & Walter, E. 2001. Global forest cover mapping. FAO. FRA Working Paper No. 50 Rome. 29pp.

FAO. 2000. Forest resources of Europe, CIS, North America, Japan and New Zealand. Geneva Timber and Forest Study Papers No. 17. Geneva, 445pp.

Loveland, T.R., Zhu, Z., et al. 1999. An analysis of the IGBP Global Land-Cover Characterization Process. Photogrammetric Engineering and Remote Sensing, 65(9):1021-1032.

Moody, A. & Woodcock, C.E.. 1994. Scale-dependent errors in the estimation of land-cover proportions: implications for global land-cover datasets. Photogrammetric Engineering and Remote Sensing, 60(5):585-594.

Scepan, J. 1999. Thematic validation of high-resolution global land-cover data sets. Photogrammetric Engineering and Remote Sensing, 65(9):1051-1060.

² Europe has a total land area of 565,930,000-ha; 31% is forestland and 7% is other wooded land (FAO 2000). CIS has a total area 2,213,036,000-ha; 40% is forestland and 4% is other wooded land. Europe covers 21% of the hypothetical population, while CIS covers 79%.

³ This hypothetical population is approximately the same size and general composition as the global tropics, which was studied by FRA with a sample of 117 Landsat scenes (FAO 2001).

⁴ The global accuracy assessment did not consider the water class.

⁵ For proposes of this simulation, the water class in the global map is assumed to contain no Landsat pixels that are water bodies because accuracy assessment data are not available.

⁶ http://www.earthsat.com/resources/feature_project.html