Hilltops protected by Brazil's Forest Code

In this tutorial you map the hilltop permanent protection areas of Brazil's Forest Code, the Áreas de Preservação Permanente de topo de morro. You will read what the law says, see how Terraflux turns its words into an algorithm (summits, saddles, bases, heights, slopes), build the model on a small landscape whose hills were drawn to show each part of the rule, and then run it on real mountains. At the end you will have a map of the protected hilltops and a table of every hill with its base, height and mean slope; you will know why a hill qualifies or not, which inputs and settings change the answer (the plain, the resolution of the elevation model, the way slope is measured), and why the result is a starting point for technical and legal work, not its end.

The rule in the law#

Brazil's law on the protection of native vegetation, the Forest Code (Lei nº 12.651, de 25 de maio de 2012), lists in its article 4 the areas that are Áreas de Preservação Permanente (APP) "em zonas rurais ou urbanas". Its article 3, II, defines an APP as an "área protegida, coberta ou não por vegetação nativa, com a função ambiental de preservar os recursos hídricos, a paisagem, a estabilidade geológica e a biodiversidade, facilitar o fluxo gênico de fauna e flora, proteger o solo e assegurar o bem-estar das populações humanas". Hilltops are its item IX:

IX - no topo de morros, montes, montanhas e serras, com altura mínima de 100 (cem) metros e inclinação média maior que 25º, as áreas delimitadas a partir da curva de nível correspondente a ⅔ (dois terços) da altura mínima da elevação sempre em relação à base, sendo esta definida pelo plano horizontal determinado por planície ou espelho d'água adjacente ou, nos relevos ondulados, pela cota do ponto de sela mais próximo da elevação;

(Lei nº 12.651/2012, art. 4º, IX)

In English: on the tops of hills, mounts, mountains and ranges at least 100 m high and with a mean slope greater than 25°, the areas above the contour line at two thirds of the height of the elevation, always measured from its base; the base is the horizontal plane of the adjacent plain or water body or, in undulating relief, the elevation of the saddle point nearest to the elevation.

The rule has four parts, and each needs a definition before a computer can apply it:

1. An elevation (a hill): a summit and the ground that belongs to it.
2. Its base: the plain or water body around it, or in undulating relief the saddle point (ponto de sela) nearest to it: the lowest point of the ridge that joins it to another elevation, a col.
3. Two criteria: a height above the base of at least 100 m, and a mean slope (inclinação média) greater than 25°.
4. The protected area: the part of the hill above the contour at base + ⅔ of the height.

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The words nearest saddle point are the heart of the rule in hilly country. Peak B in the figure is not 355 m high (its top above the plain): it is a hill of 184 m standing on the shoulder of A, and its base is the col between them. Mountaineers call this height topographic prominence: the height of a summit above the lowest col (its key col) on the way to any higher summit (Kirmse & de Ferranti, 2017). Terraflux reads the law's "nearest saddle point" as the key col, for the reasons given below.

The rule changed in 2012. Under the previous Forest Code (Lei nº 4.771/1965, revoked by Lei 12.651), CONAMA's Resolução nº 303/2002 protected hills from 50 m high with slopes above 30 % (about 17°) "na linha de maior declividade", measured from the lowest depression around them, and also protected ridge lines and groups of nearby hills. The new thresholds protect far fewer hilltops: in a hilly area of the Zona da Mata of Minas Gerais, Guimarães & Moreira (2018) found that the hilltop APPs went from 29 % of the area under the old criteria to none under the new ones. Soares-Filho et al. (2014) and Brancalion et al. (2016) review what the 2012 law changed for conservation and restoration in general.

How Terraflux finds hills and their bases#

surface.hilltop runs landschaft's open implementation of the rule (written from the law, not from another program). It has three steps.

1. Summits and saddles: a falling water level. Imagine the landscape flooded above its highest point, and the water level falling slowly. The first land to appear is the highest summit, an island. As the level falls, other summits appear as islands of their own, and the islands grow. When two islands touch, the cell where they touch is a saddle: from that level down they are one landform. The lower of the two summits ends there: its base is the saddle, its height its prominence. The higher one goes on growing, now with the other's island inside it.

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Terraflux does this on the grid: it sorts the cells from the highest down and joins each to the islands of its eight neighbours already reached (a union-find structure; the history of the joins is a merge tree). Every summit, every saddle and every base is found exactly, in one pass over the cells.

2. The base of each summit. A summit's island ends, and its base is fixed, at the first of these it meets:

• a saddle to the island of a higher summit (base_kind = 0, saddle): the law's "ponto de sela";
• a cell of the plain, if you give a map of plains and water bodies (base_kind = 1, plain): the elevation of that cell, the law's "plano horizontal determinado por planície ou espelho d'água adjacente";
• neither: this is the highest summit of a connected area, which never meets higher ground. Its base is the lowest cell of the area (base_kind = 2, lowest), often the edge of the map, as you will see.

3. Slope, qualification and the protected top. The mean slope of a hill is the mean of the slopes (Horn's method, in degrees, as surface.terrain computes them) of the cells of its island above its base: the law's "inclinação média". With slope = line, it is instead the angle of the straight line from the summit to the hill's foot, the nearest cell at or below the base. A hill qualifies if its height is at least min_height (100 m) and its slope greater than min_slope (25°). Its APP is the set of cells joined to its summit through cells at least \( z_{\text{APP}} \) high: the cells above the threshold contour around that summit.

Where hills nest (B inside A's island), each is judged on its own. If B's top rises above A's threshold but joins A only below it, B is not part of A's APP: it is a separate hill and qualifies or not by itself. Where the protected tops of two qualifying hills overlap, the cell belongs to both, and the hill output names the one with the higher threshold.

When to use it#

• Environmental compliance and the rural environmental registry. Every rural property in Brazil must be registered in the Cadastro Ambiental Rural (CAR, art. 29 of the law) with its APPs. Oliveira & Fernandes Filho (2016), who published an automatic method for hilltop APPs, stress how much mapping them at large scale matters to the CAR. Terraflux maps them for a whole municipality or basin in one run, for checking declared APPs, for licensing studies and for planning restoration.
• Research on the Forest Code. How much land the rule protects, where, and how that changed between the old and the new rule (Guimarães & Moreira, 2018), or under different readings of the law (Oliveira et al., 2019).
• Conservation and restoration planning. Hilltop APPs are part of the network of protected vegetation on properties; with riparian APPs and legal reserves they are inputs to prioritization (see Spatial prioritization) and to scenarios of land change, where they become areas where clearing is not allowed (see Land change simulation).

What it is not:

• Not a legal demarcation. The result depends on the elevation model and on readings of the law. It is a technical starting point that must be checked in the field and by the people responsible for legal work.
• Not the other APPs of article 4. Areas above 1,800 m (item X), steep slopes above 45° (item V), riverbanks, springs, veredas and the others need their own maps.
• Not CONAMA 303/2002 in full, nor Dinamica EGO's CalcHilltop (see below).
• Not a landform classification. For ridges, slopes and valleys everywhere, see geomorphons.

What you need#

• An elevation model in metres. surface.hilltop accepts projected coordinates or longitude and latitude (it then converts the cells' sides to metres at the centre of the map), but projected coordinates are better for the areas in the table; for Brazil, SIRGAS 2000 / UTM (EPSG:31978 to EPSG:31985). The model must describe the ground: radar models such as SRTM include part of the forest canopy, which adds to the heights of forested hills and changes slopes. ANADEM, a terrain model of South America made from Copernicus GLO-30 by removing the vegetation's bias with machine learning and GEDI's lidar heights (Laipelt et al., 2024), and topographic data from IBGE or state surveys are better choices where available.
• A resolution suited to the hills. Coarse cells flatten slopes: a hill steeper than 25° on a 10 m model can fall below it on a 90 m one. Oliveira et al. (2019) found resolutions of about 30 to 75 m adequate in their area, finer data producing too many small saddles and coarser data merging neighbouring hills. Report the resolution you used.
• A map of plains and water bodies (optional but important): any raster on the same grid, non-zero (or 1) on floodplains, lakes, reservoirs, rivers and the sea, 0 or no value elsewhere. Hydrography and water maps (rivers, MapBiomas' water class), floodplain maps, or careful masks of flat lowland made with raster.calc all serve. Without it, every hill's base is a saddle, and the highest summit's base is the lowest cell of the map.
• The files of this tutorial: hills.tif, a synthetic landscape of 4.2 × 6 km in cells of 30 m (SIRGAS 2000 / UTM zone 23S), and plain.tif, its valley floor and river. The valley floor falls from 700 m in the west to 620 m in the east; on it stand five hills drawn to show each part of the rule: a range of two peaks (A and B), a lone steep hill (C), a high but gentle hill (D) and a steep knoll (E).

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Build the model#

Hills and bases#

format = "terraflux/1"

[[nodes]]
id = "dem"
op = "raster.read"
params = { path = "hills.tif" }
note = "Elevation in metres, SIRGAS 2000 / UTM 23S."

[[nodes]]
id = "hilltop"
op = "surface.hilltop"
inputs = { dem = "dem.raster" }
params = { min_height = 100, min_slope = 25, slope = "mean" }
note = "Lei 12.651/2012, art. 4, IX."

The outputs of surface.hilltop:

• app: 1 in the protected tops of the hills that qualify, 0 elsewhere on the model.
• hill: for each protected cell, the hill (a row of hills) whose top holds it; no value elsewhere.
• hills: a table with a row per summit, the highest first: hill (its number), x, y (the summit), top, base, base_kind (0 saddle, 1 plain, 2 lowest), base_x, base_y (the saddle, the plain cell met, or the lowest cell nearest the summit), height, mean_slope and line_slope (degrees), area and area_ha (the hill's region above its base, in map units² and in hectares), qualifies (1 or 0), threshold (\( z_{\text{APP}} \)) and app_cells (the cells of its protected top).

Without a plain, two hills qualify, B and C, but A, the highest, does not: as the highest summit of the map it never meets higher ground, so its base is the lowest cell of the whole map (618 m, at the eastern edge), its height 445 m, and its "mean slope" that of every cell of the map above that level, 5°, mostly valley floor. The rule is applied to the whole landscape as if it were one hill.

Add the plain#

format = "terraflux/1"

[[nodes]]
id = "dem"
op = "raster.read"
params = { path = "hills.tif" }

[[nodes]]
id = "plain"
op = "raster.read"
params = { path = "plain.tif" }
note = "1 on the valley floor and the river, 0 on the hills."

[[nodes]]
id = "hilltop"
op = "surface.hilltop"
inputs = { dem = "dem.raster", plain = "plain.raster" }
params = { min_height = 100, min_slope = 25, slope = "mean" }

Now A's base is the plain at its western foot (691 m, base_kind 1), its height 372 m and its mean slope 30.4°: it qualifies, and its top is protected above 939 m.

Without plain

With plain

Save the results and see them#

format = "terraflux/1"

[[nodes]]
id = "dem"
op = "raster.read"
params = { path = "hills.tif" }

[[nodes]]
id = "plain"
op = "raster.read"
params = { path = "plain.tif" }

[[nodes]]
id = "hilltop"
op = "surface.hilltop"
inputs = { dem = "dem.raster", plain = "plain.raster" }
params = { min_height = 100, min_slope = 25, slope = "mean" }

[[nodes]]
id = "save_app"
op = "raster.write"
inputs = { value = "hilltop.app" }
params = { path = "app.tif" }

[[nodes]]
id = "save_hills"
op = "table.write"
inputs = { table = "hilltop.hills" }
params = { path = "hills.csv" }

[[nodes]]
id = "shade"
op = "raster.terrain"
inputs = { raster = "dem.raster" }
params = { measure = "hillshade" }

[[plots]]
id = "relief"
title = "Relief"
layers = [{ from = "shade.raster" }]

[[plots]]
id = "map"
title = "Hilltop APP"
layers = [{ from = "shade.raster" }, { from = "hilltop.app", opacity = 0.6 }]

terraflux check hilltops.toml
terraflux run hilltops.toml --out output

For a separator that a Brazilian spreadsheet reads, set table.write's separator to ; and decimal to ,.

Read the results#

The synthetic landscape#

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Each hill shows one part of the rule:

• A stands 372 m above the plain at its foot, with a mean slope of 30.4°: it qualifies, and 17.6 ha of its top are protected. Its base is the plain at its western foot (691 m), the highest plain cell it touches, because the valley floor falls eastwards; its eastern foot is about 20 m lower. On sloping floodplains, decide whether that is the reading you want (see the pitfalls).
• B is measured from the saddle that joins it to A (789 m), not from the plain: its height is 184 m, not 355 m. It qualifies on its own, with a protected top of 5.3 ha above 912 m.
• C is a lone steep hill, 166 m high: it qualifies. Its base is listed as a saddle at the level of the plain: it meets the higher ground of A's region (which, falling, has spread over the valley floor) on the plain itself.
• D is 208 m high but its mean slope is only 13.8°: it does not qualify. A high, gentle hill is not protected by the 2012 rule, however large.
• E is steep (30.4°) but only 78 m high: it does not qualify.

Real mountains#

The same model on the Oregon elevation model of the first part, reprojected to UTM zone 10N in cells of 30 m as there (no plain given), finds 292 summits. Most are bumps a few metres high on larger landforms; five stand at least 100 m above their base, and one qualifies: a summit of 1,065 m, 157 m above its saddle, with a mean slope of 25.1°. Its protected top covers 82 cells, 7.4 ha.

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Three things are worth seeing in this table:

• The highest summit fails for a reason that has nothing to do with it. With no plain given, its base is the lowest cell of the map (440 m, in the south-east corner), its height 948 m, and its mean slope (18.1°) is that of the whole map. The result depends on where the map was cut: give the plains and rivers, or read the model with the valley that surrounds the range.
• The hill that qualifies does so by 0.1°. Its mean slope is 25.12°. A different elevation model, a different resolution or a different reading of "inclinação média" may change the decision, as the next section shows.
• It touches the edge of the map. Its base contour reaches the western edge (in the close-up, the dashed line runs off the map). Part of the hill, and maybe a lower saddle, lie outside. Always read a margin around the area of interest wide enough to hold whole hills and their saddles.

How to report#

Give the elevation model (source, date, whether it is a surface or a terrain model), its resolution and projection; the plains and water bodies used as bases and their source; the operator and its settings (min_height, min_slope, slope = mean or line, fraction); and how many summits, how many hills of at least 100 m, how many qualify and the area protected. Give the table of qualifying hills (base kind, base, height, slope, threshold) as an appendix: it lets another analyst check each decision.

Settings that change the answer#

The slope threshold and how slope is measured#

The law fixes the threshold at 25°, but the number of hills that pass it depends on how steep the elevation model makes them. On the Oregon model, lowering min_slope step by step shows how close to the threshold the hills sit:

The jump at 17.5° is the edge effect of the previous section, not a property of the mountains: a reason to always give the plains.

With slope = line (the angle from the summit to its foot), two hills qualify instead of one: the hill of 743 m has a mean slope of 23.2° but a line slope of 25.6°. The two measures differ most on hills whose flanks are uneven (steep near the top, gentle below, or the reverse). Oliveira et al. (2019) found that a mean over the hill's cells generally protected more area than lines from the summit; the law says média without saying of what, so state your choice.

The resolution of the elevation model#

Coarse cells smooth the relief, and slopes fall. Move the slider to see the same mountains at 30, 60, 90 and 120 m:

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PlayCell size (m)

Heights are robust to the resolution (a summit and a saddle are still there at 120 m, a little lower and higher); slopes are not. Victoria (2011), mapping hilltops of the old rule in Campinas (SP) from four elevation models, found that an automatic method made for maps at 1:50,000 did not suit more detailed data, and had to adapt it. Oliveira et al. (2019) proposed lowering the slope threshold for coarse models to compensate, which they say needs more testing. The law has no such correction: use the finest reliable terrain model you have, and report its resolution. Finer is not always better either: on lidar models of 5 and 15 m, Oliveira et al. (2019) found so many saddle points that the relief was cut into hills less than 10 m high. The merge tree copes with that (a small bump has a small height and fails, and the hill it sits on is still measured from its own saddle), but slopes from a very fine model include micro-relief (boulders, gullies, terraces) and are steeper than those of coarser data.

fraction and min_height#

fraction (⅔ by default) moves the threshold contour: 0.5 protects the upper half of each hill. The law fixes it; change it only to test the sensitivity or to apply another rule. min_height (100 m) is the law's; CONAMA 303/2002 used 50 m.

CONAMA 303/2002 and Dinamica EGO's CalcHilltop#

With min_height = 50, min_slope = 16.7 (30 %) and slope = line, surface.hilltop applies the height and slope thresholds of CONAMA 303/2002 to the law's geometry. On the Oregon model, 11 hills qualify instead of 1, and 89.2 ha are protected instead of 7.4 ha:

Lei 12.651/2012

CONAMA thresholds

This is not CONAMA's full rule, and should not be presented as such. CONAMA 303/2002 (art. 2, IV to VI, and art. 3, V and VI) also distinguished morros (50 to 300 m) from montanhas (above 300 m, with no slope criterion), measured the base from "a cota da depressão mais baixa ao seu redor" rather than a saddle, protected the linhas de cumeada (ridge lines) above two thirds of the height of their lowest peak in segments of 1,000 m, and grouped hills whose summits are less than 500 m apart, protecting the whole group above two thirds of the height of its lowest hill. Terraflux implements none of those.

Dinamica EGO, the land change platform of the Federal University of Minas Gerais (Soares-Filho et al., 2002), has a functor for hilltops, CalcHilltop, that follows the older CONAMA rule on an elevation model cut into elevation bands: a hill's base is the band of a local minimum reached downhill, and its slope criterion is the angle from the summit to the nearest cell of the base band that borders other features or the edge of the map. landschaft's authors measured it, with Dinamica EGO 8.13, at 5° on an isolated cone of 21.8° on a plain. Its results therefore differ from both the 2012 law and surface.hilltop, and the two should not be mixed in one study. In landschaft's validation, only the heights of the two were compared (they agree to 0.05 m on cones); surface.hilltop is checked against an independent computation on random elevation models and on cones, ranges and lakes of known geometry.

Common pitfalls#

• No plain. Without a map of plains and water bodies, the highest summit of the map is measured from the map's lowest cell, and its mean slope includes the whole map. Give the plains, or at least check every row of the table with base_kind = 2.
• Sloping plains. The base is the first plain cell a hill's region meets, the highest one at its foot. On a valley floor that falls steeply, the hill's downhill side is lower than its base. If your agency uses another reading (the mean elevation of the foot, the lowest plain cell), compute it from the table's coordinates and say so.
• Edges. Hills cut by the edge of the map are measured incompletely, and their saddles may lie outside. Read the elevation model with a wide margin (several kilometres in mountains), and cut the results afterwards.
• Surface models. SRTM and similar models include part of the canopy: a forested hilltop looks higher and its edges steeper than the ground. Prefer a terrain model (ANADEM, lidar, topographic surveys).
• Resolution. Slopes fall with coarser cells; the decision for hills near 25° depends on it. Report the resolution, and test another if many hills are near the threshold.
• Geographic coordinates. They work, but areas are computed with the cell size at the centre of the map; for large areas or reports of hectares, use a projected CRS.
• Holes. Cells without value break a hill's region apart, and a hole at a saddle or a foot moves the base. Fill small holes first (raster.fill).
• Consolidated areas. The map shows where the law protects hilltops, not what is allowed there: in rural areas occupied before 22 July 2008 (áreas rurais consolidadas, art. 3, IV), article 63 allows some activities to continue on hilltops, and forbids new conversion. Legal consequences are for legal work.

Going further#

• Landforms with geomorphons: ridges, slopes and valleys everywhere, at a scale you choose.
• Terrain from an elevation model: slope and the indices behind the mean slope.
• Terrain hydrology: rivers and floodplains, from which a map of plains can be made.
• Land change simulation and Spatial prioritization: APPs as restrictions and as targets.
• The operators' reference: surface.hilltop, surface.terrain, raster.reproject, raster.calc.

References#

• Brancalion, P. H. S., Garcia, L. C., Loyola, R., Rodrigues, R. R., Pillar, V. D., & Lewinsohn, T. M. (2016). A critical analysis of the Native Vegetation Protection Law of Brazil (2012): updates and ongoing initiatives. Natureza & Conservação, 14, 1–15. https://doi.org/10.1016/j.ncon.2016.03.003
• Brasil. (2012). Lei nº 12.651, de 25 de maio de 2012. Dispõe sobre a proteção da vegetação nativa. Diário Oficial da União, 28 May 2012. https://www.planalto.gov.br/ccivil_03/_ato2011-2014/2012/lei/l12651.htm
• Conselho Nacional do Meio Ambiente (CONAMA). (2002). Resolução nº 303, de 20 de março de 2002. Dispõe sobre parâmetros, definições e limites de Áreas de Preservação Permanente. Diário Oficial da União, 90, 13 May 2002, section 1, p. 68.
• Guimarães, F. S., & Moreira, A. A. M. (2018). As áreas de preservação permanente de topo de morro e a Lei Federal nº 12.651/2012: um estudo de caso na região da Zona da Mata – MG. Caminhos de Geografia, 19(67), 175–187. https://doi.org/10.14393/hygeia196712
• Kirmse, A., & de Ferranti, J. (2017). Calculating the prominence and isolation of every mountain in the world. Progress in Physical Geography: Earth and Environment, 41(6), 788–802. https://doi.org/10.1177/0309133317738163
• Laipelt, L., Comini de Andrade, B., Collischonn, W., de Amorim Teixeira, A., Paiva, R. C. D., & Ruhoff, A. (2024). ANADEM: A digital terrain model for South America. Remote Sensing, 16(13), 2321. https://doi.org/10.3390/rs16132321
• Oliveira, G. C., & Fernandes Filho, E. I. (2016). Automated mapping of permanent preservation areas on hilltops. Cerne, 22(1), 111–120. https://doi.org/10.1590/01047760201622012100
• Oliveira, G. C., Fernandes Filho, E. I., & Francelino, M. R. (2019). Mapping of permanent preservation areas on hilltops: Technical issues. Floresta e Ambiente, 26(4), e20170262. https://doi.org/10.1590/2179-8087.026217
• Soares-Filho, B. S., Cerqueira, G. C., & Pennachin, C. L. (2002). DINAMICA: a stochastic cellular automata model designed to simulate the landscape dynamics in an Amazonian colonization frontier. Ecological Modelling, 154(3), 217–235. https://doi.org/10.1016/S0304-3800(02)00059-5
• Soares-Filho, B., Rajão, R., Macedo, M., Carneiro, A., Costa, W., Coe, M., Rodrigues, H., & Alencar, A. (2014). Cracking Brazil's Forest Code. Science, 344(6182), 363–364. https://doi.org/10.1126/science.1246663
• Victoria, D. C. (2011). Influência da escala em uma metodologia de delimitação automática de áreas de preservação permanente em topo de morro e montanha e adaptação do método para escalas detalhadas. Revista Brasileira de Cartografia, 62(3). https://doi.org/10.14393/rbcv62n3-43684