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Chapter 1
Prosopis in Brazil

Characteristics of the Semi-Arid Zone of Brazil's Northeast

Benedito Vasconcelos Mendes
Professor at Mossoró's Agricultural Collage-ESAM


The most striking feature of the semi-arid region of Brazil's Northeast, known by the suggestive name of Poligon of Droughts, due to the periodic occurrence of droughts in this polygon-shaped area, is its climate, particularly due to the existence of a rainfall regime which delimits two very distinct seasons: a rainy season lasting 3 to 5 months and called “winter”, which occurs in the first semester of the year; and a longer dry season labelled “summer”, lasting from 7 to 9 months, and which may continue, in the years of drought, for 18 months or more. The rains are generally torrential and irregular both in time and space. The rain's erratic behavior, both in intensity and distribution, causes a periodic occurrence of prolonged droughts. Although the rainfall level is not very low in absolute terms (500 mm per year, on the average), the hydric balance is highly deficient, mainly due to the high evaporation rates. Rainfall is approximately four times less than evaporation. The Polygon of Droughts is externally delimited by the 800 mm isohyeta, and in its lower altitudes precipitation rarely either exceeds 800 mm or falls below 400 mm per year. The highest precipitations correspond to the humid ridges which occur at random in the interior of the dry area, while the smaller ones occur in the town of Cabeceiras, in the State of Paraíba, with a 252-mm annual average. The monthly distribution and the onset of the rainy period vary widely and therefore cannot be determined. The periodic droughts are characterized by lack or bad distribution of rainfall in the “winter” season, entailing insufficient water availability for most agricultural crops and for pasture.

The Polygon of Droughts is one of the hottest semi-arid regions in the world. The average temperature is more or less constant along the year, and relatively uniform throughout the region. Annual temperature averages oscillate between 23° C and 27° C. The daily temperature difference remains constant around 10° C along the latitude bands, as well as in relation to the sea.

Due to its proximity to the Equator, and also due to the scanty cloud cover during the greatest part of the year, the average annual luminosity is very high, with around 2,800 hours of sunlight per year.

One of the climatic factors having great significance for the Polygon of Droughts is its very strong evaporation. Due to the scant and infrequent cloud cover and to low latitude, sunlight bears almost vertically upon the region, a fact which favors high temperatures which, combined with the low atmospheric humidity, cause excessive evaporation. Besides heating up the soil, the strong sunlight acts indirectly through the air displacements which originate hot, dry winds with high average speeds (15 to 20 km/h). The intense evaporation, which reaches an average of 2,000 mm per year, is the greatest factor accounting for the Semi-arid Zone's deficient water balance. The air's relative humidity averages approximately 50%.

Terrain features

The Northeast presents a slightly undulated terrain, ridges raising here and there some 600 m, but only exceptionally exceeding 1,000-m in altitude.

These ridges can be dry or humid, depending on their altitude and position relative to the direction of the winds, upon which the occurrence of orographic rain depends.

During the annual dry period (summer), the humid ridges are veritable oases in relation to the surrounding deciduous and dry caatinga. Rains are abundant and the occurrence of perennial water springs is frequent. With regard to the adjacent areas, the humid rains offer a more pleasant climate, with lower temperatures, greater relative humidity and less insolation, due to a greater abundance of clouds.

The main altitude micro-climates in the Semi-arid Zone are the following: Brejo da Paraíba, located on the Borborema's slope; Cariri Valley, situated on the foot of the Araripe's ridge, in the State of Ceará; the Cearences ridges of Guaramiranga and Ibiapaba; and the Triunfo ridge in the State of Pernambuco.


In general terms, soils are shallow, rocky or sandy, with pH neutral or near 7, poor in organic matter but rich in soluble mineral salts, especially calcium and potassium. The occurrence of extensive salty areas is common; they are formed by the influence of high evaporation rates, by inadequate irrigation practices and by deficient dissolution. This region presents in nearly all of its areas an accelerated process of desertification, due to the great erosion caused by bad soil use, by the indiscriminate deforestation and by the overgrazing of pastures by domestic animals around the watered areas. The presence of a hard crust is common in exposed soils and reduces water seepage, thus favoring water run-off and erosion. This crust is formed by the impact of the rain drops against the bare soil, compacting its particles; this is complemented by the development of a microflora carpet, composed of green-bluish algae and/or lichens.

Water Resources

The rivers are sinnuous, have an intermittent hydrologic regime, a torrential character and remain dry for the most part of the year. Their length is irregular and they exhibit only one annual flow period, lasting 3 to 5 months, and which corresponds to the rainy season. During this period the occurrence of violent flash floods is common, causing significant erosion and flooding of the marginal lands. Another serious problem in the region is the accelerated silting of rivers, dams and lagoons.

Approximately 50% of the Northeastern semi-arid lands are of sedimentary origin, consequently rich in underground water; the other half consists of cristaline soils, which offer low storage potential for underground water. In the cristaline soil area, the subsoil water is scant and of low quality, with larger amounts and better quality only in the alluvial areas near the river banks and in the cracks of the rocks. In spite of its limited amount of underground water, this area is suitable for the construction of dams due to its impermeability. The soils are of good quality, generally rich in aquifers which present abundant good quality water. The sediments consist invariably of limestone or sandstone. In general, the sedimentary zone is not good for the construction of dams, due to its high soil permeability; in the case of areas made up of limestone, the cracks absorb the water which feed the aquifers.

The superficial water resources and the hydrogeologic reserves of the Brazilian semi-arid are limited, being insufficient to irrigate those areas whose topography and fertility make them suitable for irrigation.


The plant cover of the Semi-Arid Region is made up of typical form ions called caatingas (caa = bush; tinga = clear, gray, fragmented). They are formed by a mixture of trees and small bushes, with small deciduous leaves and very drought-resistant. In the caatinga, we can also find some evergreen species, herbs and many succulent plants. During the annual dry period, most arboreal and shrub species shed their leaves and annuals disappear. The caatingas are poor in grasses and rich in legumes. Many species have a good potential for forage, human consumption and industrial use, especially as a source of oils, waxes, resins, tannin, rubber and other products.


The fauna presents little endemism, being poor both in species and in the number of individuals per species. Mammals are small in size, the most abundant being rodents and foxes. The animal species found in larger numbers in the Semi-Arid Region are those which present a greater mobility to migrate during the droughts, returning in the rainy period.

Potential Offered by Prosopis juliflora (Sw) dc in the Brazilian Semi-Arid Region

Benedito Vasconcelos Mendes
Professor at Mossoró Agricultural College-ESAM

Prosopis juliflora is a truly promising tree for Brazil's Polygon of Droughts, on account of its multiple and important potential and actual uses, as well as of its remarkable resistance to drought, heat, and poor soils. This legume tree is native to the Piura desert, Peru, and was introduced in Brazil in 1942. It adapted itself very well to the edaphoclimatic conditions in the Semi-Arid Zone of Brazil's Northeast. It has become one of the most spectacular examples of successful plant introduction in the region.

Its pods offer high nutritional value, high digestibility and excellent palatability for bovines, caprines, ovines, equines, mules, pigs, fowls and other animals, and it may replace corn and wheat flour in their rations. Not only rich in energy, the pods also have a relatively high protein value, with approximately 13% crude protein content. The pulp is sweet, with a high content of saccharose, calcium, phosphorus, iron, vitamin B1 and vitamin B6. Seed protein content ranges from 34 to 39%. The pods may be fed ground or whole to the animals. Ground pods, in the form of flour, make it possible for the animals to use the seeds' protein, for whole seeds are not digested in the animals' intestinal tract. Apart from the high nutritive value of its pods, this xerophyte —which remains green and keeps up production even during intense droughts— also presents the important characteristic of bearing fruit during the driest time of the year, when the stocks of natural fodder drop to critical levels.

Another important characteristic of this fodder tree is its great productivity, averaging around 6,000 kg/year of fruits per hectare, with 10 × 10-m spacing; some plants produce up to 169 kg of pods annually.

Highly productive clones are being produced through vegetative multiplication. Prosopis juliflora vegetative propagation through cuttings, utilizing stakes from the top branches and treatment with indolbutiric acid, presents a sticking index of approximately 70%. Well-stored pods may be conserved for over three years. Although the foliage (leaves and twigs) of many species of the genus Prosopis is well accepted by wildlife and livestock, the green leaves of the species Prosopis juliflora (Sw) dc, cultivated extensively in Brazil's Northeast, are not very palatable, for the cattle eat only the buds. When hayed, however, they are more relished. The hay is rich in nutrients (14% protein content).

The pods were extensively used for human consumption by the indians of Peru, Chile and Argentina, and even today they continue to be used for this purpose in some regions of these countries. They are used for flour, cakes, bread, biscuits, sweets, jelly, syrup, refreshments, brandy, liquor and other products, including algarobina, a beverage highly appreciated in Peru and said to have strengthening and aphrodisiac effects. The Company for Technical Assistance and Rural Extension of the State of Rio Grande do Norte (Brazil), published a recipe book compiled from recipes used by rural housewives, including a number of food items which can be prepared with the fruits of this legume tree, such as flour, cakes, sweets, jelly, syrup, liquor, etc.

Prosopis juliflora wood is hard but nonetheless easy to work with and of excellent quality for carpentry and woodwork. It also has high durability and may be utilized for manufacturing furniture, mosaics, wood flooring, lanes, stakes in general, lathes, sleepers, posts, firewood and excellent-quality coal. Due to its great resistance to termites and to rotting when buried, it is highly recommended for fence stakes.

The fruit skin has high tannin content, and it may be used in tannery. It yields a yellow resin which can be used for manufacturing a glue similar to gum arabic.

P. juliflora, with its ruggedness, precociousness and beauty, is widely used in Brazil's Northeast in the arborization of cities and in gardens, where it is used for hegdes, tree stands and shelterbelts.

The flowers are very melliferous; flowering is abundant and occurs in the driest season of the year, when almost none of the native vegetation has any flowers. Due to this and other characteristics, it is one of the most suitable plants for supporting apiculture in the Semi-Arid Zone.

Recently, it was found that gums of the galactomonas type (carobe gum) may be extracted from this plant. This type of gum, greatly valued in the food industry, is presently obtained in industrial scale from “alfarrobeira” (Ceratonia siliqua) and “guar” (Cyamopsis tetragonoloba).

Another potential use for P. juliflora fruit is the production of ethyl alcohol; 100 kg of pods yield approximately 27 liters of this product.

Prosopis juliflora enriches the soil with nitrogen, assimilating atmospheric nitrogen through symbiotic fixation; its roots enter in symbiosis with bacteria of the genus Rhizobium. This legume removes water and nutrients from the soil's deep layers, and increases the organic matter content in the top layer through the accumulation of litter. It is a superb protector of the soil against wind and water erosion and direct sunlight action, being used for reclaiming saline areas, which are mostly useless for agricultural purposes. This plant may be associated with fodder palm (Opuntia ficus indica) and buffel grass (Cenchrus ciliaris), increasing considerably the fodder production per area unit. Ecologically, an adaptation of the regional fauna to this plant has been observed, for some species of birds already nest in its branches.

Performance of Species of the Genus Prosopis at 24 Months of Age in Petrolina

Paulo César F. Lima
Forester, M. Sc., embrapa/cpatsa Researcher, Petrolina


The medium and long-term afforestation efforts with P. juliflora in the Brazilian Northeast, using P. juliflora seeds produced in the region itself, must take into account potential restrictions due to inbreeding problems, as pointed out by Pires and Kageyama (1985). These authors, in studies conducted on a population in Soledade and included elsewhere in this book, found low heritability and genetic variability coefficients for height and dbh among families, in open-pollinated progeny trials.

The need of enlarging the genetic base and gathering data on the performance of other species of Prosopis in the Brazilian semi-arid region prompted the National Forestry Research Program (pnpf), through the Agriculture and Livestock Research Center for the Semi-Arid Tropic (cpatsa), to introduce other species of this genus into the region. This paper describes the initial performance of P. alba, P. chilensis, P. pallida, P. velutina, P. glandulosa var. torreyana, P. tamarugo and P. juliflora in Petrolina, Pernambuco, 24 months after planting, with the purpose of selecting those species which seem promising for firewood and/or fodder production.

Material and Methods

The trial was established in a “caatinga” property belonging to the Agriculture and Livestock Research Center for the Semi-Arid Tropic (cpatsa), in Petrolina, Pernambuco, at an altitude of 365 m, latitude 09° 09' south, and longitude 40° 22' west. Table 1 shows rainfall and mean temperature recorded at the site during the trial. The rainy season begins in December/January and ends in April/May.

Meteorological Data of the Experimental Site

YearTemperature °C R.H.
No. of Rainy days
198531.619.727.3721,075.6   105  

* Data for January to June.

The soils were classified by Pereira and Souza (1968) as red-yellow latosol. The chemical analysis showed a pH of 5.3, and low availability of phosphorus, calcium and organic matter. Magnesium and potassium content are in the mid-range. Aluminum content is low.

The experimental layout adopted was randomized blocks, with seven treatments and a varying number of replications, as described in Table 2. The plots were square, with 25 plants at 6 m × 6 m spacing. The nine central plants in each plot were considered for the survival, height, dbh, crown diameter and fruit output analyses.

Species, Provenances and Number of Replications

TreatmentSpeciesProvenanceNo. Replications
1P. albaFundo Refresco, Chile4
2P. chilensisSantiago, Chile4
3P. glandulosa var. torreyanaTexas, USA3
4P. julifloraPetrolina, Brazil4
5P. pallidaPiura, Peru4
6P. tamarugoFundo Refresco, Chile4
7P. velutinaTexas, USA3

The seedlings were produced by direct sowing in black polyethylene bags, 8 cm in diameter and 15 cm long. The seeds were inoculated with Rhizobium selected specifically for P. juliflora. At the time of planting, February 1984, a 100-g/plant dosage of 5-14-3 npk was applied. During the first year of establishment, hoeing was carried out on three occasions to prevent weeds from competing with the seedlings. Weeding was performed on three occasions during the second year, and a 1-m-radius space was cleared around each plant.

Results and Discussion

As shown in Table 3, with the sole exception of P. tamarugo, which at 12 months of age presented 100% mortality, all species exhibited survival rates in excess of 75%, 24 months after establishment P. juliflora of local provenance showed 100% survival, differing statistically only from P. alba from Chile.

P. alba exuded a reddish sticky fluid, its leaves started yellowing and then the plants died.

Survival Rates up to 24 Months of Age at Petrolina

P. alba  98 a  96 a 75   b
P. chilensis  98 a  94 a  89 ab
P. glandulosa  94 a  94 a  94 ab
P. juliflora100 a100 a100 a  
P. pallida100 a100 a97 a
P. tamarugo    53   b     0   b
P. velutina100 a100 a100 a 

5% probability level. The values in percentage were transformed into arc sen for the effects of statistical analysis.

As shown in Table 4, P. juliflora was the species with the best height growth, crown diameter and dbh. Its values of 5.38 m and 4.57 cm for crown diameter and dbh, respectively, did not differ statistically from the 4.95 m and 3.42 cm found for the same parameters in P. pallida. The lowest height (1.44 m), crown diameter (1.92 m), and dbh (1.13 cm) were observed in P. glandulosa var. torreyana.

Height, dbh, and Crown Diameter for the Various Species in Petrolina

SpeciesHeight (m)DBH (cm)
24 months
CDiam (m)
24 months
3 months12 months24 months
P. alba0.74ab1.88ab2.87  b2.70  bc3.25  b
P. chilensis0.76ab1.70  b2.56  b1.75    cd2.39  bc
P. glandulosa0.53  b1.11    c1.44    c1.13      d1.92    c
P. juliflora0.95a2.27a4.10a4.57a5.38a
P. pallida0.76ab1.59  bc2.78  b3.42ab4.95a
P. tamarugo0.10    c    
P. velutina0.70ab1.52  bc2.27  bc1.50    cd2.78  bc

Mean values followed by the same letter in the same column do not differ statistically as per Duncan test at 5% probability level.

Pod Output of Various Species of Prosopis at 21 months of age

SpeciesTrees bearing pods
Mean pod output/tree (g)Output range
P. juliflora67428.840 – 2,454.0
P. pallida31232.090 – 2,162.1
P. velutina11    9.64 0 –    147.1

P. juliflora, P. velutina and P. pallida started bearing fruit at 21 months of age, with average outputs, respectively, of 428.84 g; 232.09 g, and 9.64 g of pods per tree, as shown in Table 5 above. The variation from 0.0 to 2 kg in fruit output per tree in P. juliflora was the same as that observed for P. pallida. The percentage of P. juliflora trees bearing fruit (67%) was twice that for P. pallida. Azevedo (1955) found an average output of 2.22 kg of pods/year, in 15 P. juliflora trees in Rio Grande do Norte, with ages ranging from 14 to 24 months.

A scant 11% of P. velutina trees produced fruit, varying from 0.0 to 147 g of pods per tree. Felker found, in 5-year-old populations of this species, outputs ranging from 0.0 to 12.645 kg per tree. No fruit bearing was observed in P. alba, P. chilensis and P. glandulosa until 24 months of age.


P. tamarugo did not adapt to the ecological conditions prevailing in Petrolina, with 100% mortality at 12 months of age. The remaining species showed over 75% survival up to 24 months of age.

The development observed in P. juliflora underlines its potential for the region both for wood and pod production, basing on its height, dbh, crown diameter and fruit bearing observed up to 24 months of age.

P. juliflora, P. pallida and P. velutina started to bear fruit as from their second year.


felker, p., 1983: “Uses of mesquite wood in Argentina and possibilities for genetic selection to provide straight fast growing mesquite,” In: Workshop on the cutting, drying and fabrication of mesquite wood into flooring, handcrafted items and furniture, Kingsville, Texas, 1982 Proceedings… Kingsville, Caesar Kleberg, pp. 33–35.

felker, p., 1982: “Seleção de fenotipos de Prosopis para a produção de vagens e de combustível de madeira,” In: Algaroba, Empresa de Pesquisa Agropecuária do Rio Grande do Norte, Natal-rn, Natal, V. 2, pp. 7–24.

ferlin, g. r., 1978: “Techniques de reboisement dans les zones subdesertique d'Afrique,” 4 p., mimeographed.

gomes, p., 1961: “A algaroba,” Rio de Janeiro, Serviço de Informação Agrícola, 49 p., (sia, 865).

gurumurti, k; raturi, k. and bhandari, h. c. s., 1984: “Biomass production in energy plantation of Prosopis juliflora,” Indian Forester, 110: 879–894.

karlin, u. and diaz, r., 1984: “Potencialidad y manejo de algarrobos en el árido subtropical argentino,” Buenos Aires, secyt, 59 p. illust.

maydell, h. j. von, 1979: “Tree and shrub species for agroforestry system in the Sahelian zone of Africa,” Hamburg, 19 p., paper presented at the Eighth World Forestry Congress, Jakarta, Oct. 1978.

melo, f., 1966: “Agricultura nordestina: Os problemas agropecuários do nordeste seco,” Mundo Agrícola, 15 (170): 39–51.

muthana, k. d., 1985: “Programas de desarrollo de especies Prosopis en India,” in: Estado actual del conocimiento sobre Prosopis tamarugo. International Round Table on Prosopis tamarugo Phil., Arica, Chile, 1984, fao, pp. 191–201.

pereira, j. m. de A. and souza, r. a. de, 1968: “Mapeamento de área de Bebedouro - Petrolina-pe,” Petrolina, sudene, 57 p.

pires, j. e. and kageyama, p. y., 1985: “Caracterização da base genetica de uma populacão de algaroba - Prosopis juliflora (Sw) dc - existente na região de Soledade-pb,” ipef, (30): 29–36.

webb, d. b., 1980: “Guia y clave para selecionar especies en ensayos forestales de regiones tropicales y subtropicales,” London, Overseas Development Administration, 275 p.

Volume, Weight and Product Tables for Prosopis juliflora (Sw) dc at Rio Grande do Norte

Enrique Riegelhaupt
Agronomist, fao Consultant with Project undp/fao/ibdf/bra 82.008
Irandí Barbosa da Silva
Forester, Technician with the Dendroenergy Sub-Group, Project nra 82.008
Francisco Barreto Campello
Forester, Technician with the Dendroenergy Sub-Group, Project nra 82.008
Frans Pareyn
Forester, Associate fao Expert with Project undp/fao/ibdf/bra 82.008


The estimation of the existing volumes of Prosopis juliflora (Sw) dc plantations and spontaneous stands and the assessment of their growth rate are very important for technicians and laymen alike, interested in P. juliflora establishment, management and exploitation. However, to date there is no simple and relatively accurate method for attempting such an estimate. With a view to overcoming this drawback, the Dendroenergy Subgroup of the Brazilian Forestry Institute's Hydro-Forestry Planning Group, headquartered at the Rio Grande do Norte State Office, started a research project whose initial findings are presented in this paper. The authors consider that, although the data base is still limited, the method used is valid, and the functions and tables presented can be improved by incorporating into them a greater number of cases.

Materials and Methods

Characterization of the Populations

The data for the tables were taken from:

  1. A 15-year-old plantation, with a 10 × 10-m original spacing and 84% survival rate at time of data gathering, located alongside the br 226 highway, 85 km from Natal, at the Presidente Juscelino district (6° 10' S. Lat., 35° 40' E. Long.);

  2. An approximately 20-year-old spontaneous population located on the left bank of the Trairí river, Santa Cruz district (6° 20' S. Long.; 35° 55' E. Long.).


Both populations are located within the transitional zone between the State's subhumid and the semi-arid regions. Maximum monthly mean temperatures vary between 29° C and 32° C, and mean monthly minima oscillate between 21° C and 23° C. Mean annual rainfall at Presidente Juscelino was 591.2 mm during the 1963–1971 period, with 428.1 mm (72.4%) concentrated in the period from February to July. At the Santa Cruz district, mean annual rainfall recorded was 662.2 mm, with 550.3 (83.1%) concentrated between February and July. Potential evapotranspiration amounts to around 1,600 mm/year, bringing about a considerable water deficit during 10 or 12 months per year.

Data Gathering

Before felling the trees, circumference at base (cab) and circumference at breast height (cbh) were measured, using a metric measuring tape with 1-cm approximation. Total height (h) was measured with a Suunto clinometer, with 0.5-cm approximation. Then, five trees in each class of basal area were felled, the classes being: i (1–300 cm2); ii (301–600 cm2); iii (601–900 cm2); iv (901–1200 cm2), and v (1201–1500 cm2). The trees were bucked with a chainsaw into four types of pieces:

To estimate sawlog and pole volume, total length and diameter at ¼ and ¾ of length was measured for each piece. For the stakes, total length and diameter at ½ length were measured. Firewood was measured by stacking up the pieces bucked to 1-m length, in order to measure apparent volume. Firewood was then weighed in a 40-kg scale with 0.1-kg approximation. All data were recorded separately for each tree, using a tally sheet designed specifically for the purpose (Annex 1). At time of weighing, 5-cm-thick sections were removed from each piece in 5 trees of each population, to measure moisture content and basic density values in laboratory.

Data processing

To estimate the volume of the products obtained for each tree, a program was written for a ti-66 computer, using the following formulas:

  1. Sawlog volume: (C21 + C22)h/8π) × 10 = Vs (dm3)
  2. Pole volume: same as above = Vp (dm3)
  3. Stake volume: (C½)2 h/4π × 10 = Ve (dm3)
  4. Firewood volume: Dry weight/basic density = Vf (dm3)

To obtain the dry weight, the green weight measured in the field was multiplied by:

To obtain total dry weight for each tree, the volumes of sawlogs, poles, and stakes were multiplied by the corresponding values of basic density, and added to the firewood dry weight. Total volume for each tree was obtained by adding the volumes of sawlogs, poles, stakes, and firewood. This latter value was calculated from the dry weight and basic density (Vf = dw/bd). The coefficients used were:

  SawlogsPoles + StakesFirewood
Basic densitykg/dm3     0.934     0.8840.745
Moisture, Green%31.137.540.8       
Stacking factorm3/mst--0.238

Selection of Variables for Volume Functions

According to Caillez (1980), the variables to be used in a volume function should be:

The most significant variable and the one easiest to measure is diameter, which can be replaced to advantage by circumference. Normally diameter (or circumference) is measured at 1.30 m above ground level. In the case of P. juliflora, the presence of several stems at this height is very common, which requires separate measuring in order to determine total basal area and to obtain therefrom the “equivalent diameter value”. To simplify the practical application of the volume functions, it was decided to test the “circumference at base” (cab), measured at 0.30 m above ground level, as an alternative to “circumference at breast height” (cbh), expressed in cm.

Another variable of great significance is height. In this case, the variable chosen was total height, in light of the difficulties to define the upper end of the stem in the species under study. Height was expressed in m.

Models of Volume Functions Tested

For both samples the following models were tested:

  1. V = a + b (cab)2
  2. In V = a + b (In cab)
  3. V = a + b (cab)2h
  4. V = a + b (cbh)2
  5. In V = a + b In (cbh)
  6. V = a + b (cbh)2h

Table 1 below summarizes the characteristics of the functions tested, for the case of cultivated P. juliflora.

Characteristics of the Volume Functions for Planted P. juliflora

Coeffic. a.-  0.1101- 11.9242-   0.4527-   0.0836- 11.9565-   0.0347
Coeffic. b.   7.198×10-5    2.4648    5.3675×10-6    7.9124×10-5    2.5118    6.0718×10-6
R2   0.9285    0.9663    0.8872    0.9172    0.9529    0.8970
∑ [residues]   1.9198    1.5907    2.0636    1.8866    2.0146    2.0122
S.D. residues   0.1131    0.1074    0.1142    0.1223    0.1391    0.1357
C.v. residues (%) 22.2  21.6  23.0  14.3  27.2  14.8
Mean residue   0.0873    0.0723    0.1188    0.0857    0.0916    0.0915
R / v (%) 14.1  12.9  21.4  16.8  18.0  18.0

As regards the spontaneous P. juliflora population, the characteristics of the functions tested are summarized in Table 2.

Characteristics of the Volume Functions for Spontaneous P. juliflora

Coeffic. a.-   0.0505- 10.4110-   0.0156-   0.0109- 12.5265-   0.0024
Coeffic. b.    7.5856×10-5    2.1461    5.9489×10-6    7.6537×10-5    2.6663    6.4005×10-6
R2    0.9678    0.6803    0.9645    0.8817    0.9677    0.9248
∑ [residues]    1.2892    1.9485    1.1140    2.2488    2.5039    1.7586
S.D. residues    0.0842    0.1339    0.0862    0.1615    0.2032    0.1264
C.v. residues (%)  19.7  36.1  20.2  37.7  45.6  29.7
Mean residue    0.0537    0.0827    0.0464    0.0937    0.1043    0.0733
R / v (%)  12.6  22.3  10.9  21.9  23.4  17.2

Results and Discussion

The analysis of the functions tested for population A (15-year-old cultivated P. juliflora) evidenced distinctly that functions 1 (V = a + b (cab)2) and 2 (In V = a + b In cab) present the lowest residue and the smallest dispersions. The combined variable function (V = a + b (cbh)2 h) estimates tree volumes with significantly higher residues, demonstrating that inclusion of the height variable does not improve these models. When the cbh variable is used, the residue is also greater, therefore being cab the variable to be preferred.

Consequently, the use of function V = -0.1101 + (cab)2 × 7.198 × 10-5 seems advisable, simpler to apply than the logarithmic function. The value of the Percentage Mean Residue for this function, namely 14.1%, indicates that the volume of individual trees so calculated must be taken as a preliminary estimate. However, volume estimate for a population made up by a large number of trees will show good approximation to the real volume of that population.

For the case of population B (spontaneous 2- to 20-year-old P. juliflora), the analysis of the functions shows that the combined variable function [V = a + b (cab)2h] presents the lowest absolute and relative residues, and has a low value for coefficient a Function 1 [V = a + b (cab)2] has slightly greater residues, however modest, and could be preferred in light of its simplicity. In this population, the inclusion of the “total height” (h) variable improves the estimate of individual volumes, indicating good correlation of height with respect to volume. Functions 4, 5, and 6, based on cbh, present higher absolute and relative residue values, indicating once more that cab must be preferred.

Consequently, the following equations are recommended for estimating the volume of spontaneous P. juliflora populations:

V = -0.0505 + 7.5856 × 10-5 (cab)2

V = -0.0156 + 5.9489 × 10-6 (cab)2h

The results were expressed as cubic meters of solid volume with bark for each tree.

Another alternative to assess the quality of volume functions is graphic analysis. Chart 1 presents the regression lines and the real solid volume values for equations 1, 2, and 3 for the cultivated P. juliflora sample, and Charts 2.1, 2.2 and 2.3, the respective residue values (Vr - Ve). From their analysis, it may be concluded that function 1 shows no bias and that the residues increase as an approximately square function with respect to tree diameter. Chart 3 shows the regression lines and the real solid volumes of P. juliflora sampled in the spontaneous population, and Charts 4.1, 4.2, and 4.3, the corresponding values for the residues of functions 1, 2, and 3. In this case, the function which best represents distribution is function 3, and the distribution of its residues shows no bias. Function 1, although it tends to subestimate the volume of smaller trees, is acceptable, unlike function 2 (logarithmic), which shows a distinct bias.

Functions for Dry Weight Estimation

Considering that the best volume estimates were obtained by means of equations of the type V = a + b (cab)2, linear equations were determined for Total Dry Weight as a function of the same variable, with the following parameters:

- For planted P. juliflora:a=-83.4889
- For spontaneous P. juliflora:a=-53.5348

Total dry weight can be estimated by applying the following equations:

Volume Functions for Planted P. juliflora


Planted P. juliflora. Residue Distribution


Planted P. juliflora. Residue Distribution


Planted P. juliflora. Residue Distribution


Spontaneous P. juliflora. Volume Functions


Spontaneous P. juliflora. Residue Distribution


Spontaneous P. juliflora. Residue Distribution


Spontaneous P. juliflora. Residue Distribution


tdw (kg) = -83.5 + 0.058281 (cab)2 (planted P. juliflora)
tdw (kg) = -53.5 + 0.066556 (cab)2 (spontaneous P. juliflora)

Charts 5 and 6 illustrate the respective equations.

Planted P. juliflora Dry Weight


Spontaneous P. juliflora Dry Weight


Tree Form Factors

Form factors for the populations analyzed can be derived from the “b” coefficients of the respective volume functions; in the case of V = a + b (cab)2h, by multiplying the “b” coefficients by the conversion factor 4π × 10-2 = 12.566 × 10-2.

The resulting form factors are: 
For planted P. juliflora:ff = 0.674
For spontaneous P. juliflora:ff = 0.747

Volume, Weight and Product Tables

Accurate estimates of total solid volume are important for forest technicians and researchers alike, and they can be made simpler by using the formulas proposed above. However, these estimates do not furnish data regarding the amount of products which can be obtained from the exploitation of a population, although this type of information is of major interest for management and utilization purposes, apart from being essential for the economic assessment of the plantations.

With a view to providing a useful tool for the above mentioned purposes, a tool that can furnish the data necessary for computing, however approximately, the production that can be obtained from P. juliflora populations, two volume, weight and product tables were prepared, and are presented as Annexes 2 and 3 hereto. With these tables, it is possible to calculate total volume; total sawlog volume and dry weight; amount, volume and dry weight of stakes and poles; and real volume, apparent volume (stacked) and dry weight of firewood for trees with basal circumference between 30 and 135 cm. Volumes are expressed in cubic meters and dry weights in kg.

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