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Land Degrad. Develop. 11: 273±287 (2000)





Department of Geography and Center for the Study of Institutions, Population and Environmental Change,

Indiana University, Bloomington, Indiana, USA 2Department of Anthropology and Curriculum in Ecology, University of North Carolina at Chapel Hill, North Carolina, USA Received 15 August 1998; Accepted 16 August 1999


We present a model that calculates incident solar radiation falling on terraced and unterraced ®elds in steep slope environments. The results are presented as a function of altitude, latitude, slope aspect, slope angle, and season. The net solar bene®t or cost from slope leveling (terracing) di€ers signi®cantly according to these situational factors. For instance, terracing will confer a net direct solar radiation bene®t of 15 per cent on south-facing 30-degree slopes at the Equator for a typical growing season; it will reduce net annual direct solar receipt by 21 per cent on south-facing 30-degree slopes at 458 N latitude. Modi®ed solar radiation must be considered as potentially important in the historical origins, functioning and abandonment of terracing. It should be a component in agronomic evaluation of modern terrace construction, restoration, or maintenance. Copyright # 2000 John Wiley & Sons, Ltd.

terraces; solar radiation; topography; agriculture



Agricultural Terracing Terracing is an intensive, widespread, and e€ective means by which humans have modi®ed slopes in order to pursue agriculture on otherwise uncultivatable hillslopes, reduce soil erosion, and improve crop productivity.

It is an anthropogenic landscape feature found throughout the tropical and low-latitude temperate regions (Perry, 1916). Studies have located terraces in the New World (Donkin, 1979) and Latin America (Williams, 1990; Treacy and Denevan, 1994), as well as New Mexico (Sandor et al., 1990), Mexico (Smith and Price, 1994), Yemen (Vogel, 1987, 1988; Varisco, 1991), Lebanon (Zurayk, 1994), Nepal (Johnson et al., 1982), China (Xing-guang and Lin, 1991; Veeck et al., 1995), the Mediterranean (Treacy and Denevan, 1994), and Europe (Treacy and Denevan, 1994). Few reliable inventories of the extent of agricultural terracing are available, but selected estimates suggest the impressive scale of the feature: for China, 400 000 km2 (Xing- guang and Lin, 1991: 198); for Peru 500 000 ha (Denevan, 1988).

Terracing can range from unintentional slope leveling due to natural processes of erosion and accumulation against balks or hedgerows to the highly visible and sophisticated public works projects of ancient empires (e.g. Donkin, 1979). The former may have been incidental; the latter obviously follow from sophisticated engineering and draw on large labor and capital inputs. The literature on terracing is small relative to its agroecological importance (Treacy and Denevan, 1994) and it is multidisciplinary, scattered among the disciplines of archaeology, geography, and agronomy.

Despite widespread contemporary use, in most regions terraces originated in antiquity. We have been unable to locate documentation of extensive modern construction of terraces. This historical distance *Corresponding author: Prof. Tom Evans, Department of Geography and Center for the Study of Institutions, Population and Environmental Change, Student Building 120, Indiana University, Bloomington, IN 47405, USA. E-mail: evans@indiana.edu

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inspires a variety of questions: When and how were terraces constructed (or if unintentional, when and how did they develop)? By whom? What agroecological functions were they designed to serve? What functions might they serve as an incidental (unintended) result of their design? How costly are they? What agroecological conditions a€ect their distribution and form? How productive and sustainable are they as an agricultural substrate? Why has much agricultural terracing of the world been at least partially abandoned, and under what conditions would it now be feasible to reclaim or extend agricultural land using terracing?

The last question is one of increasing contemporary importance: although most extant terracing has prehistoric origins (Hilsum, 1987), a future of increasing population and overworked agricultural land, along with a desire to avoid the harmful consequences foreseen as extensive areas of abandoned terraces deteriorate and collapse, has impelled renewed attention to the possibility of restoring and/or constructing new terraces (e.g. de la Torre and Burga, 1986; Johnson et al., 1982; Treacy, 1987, 1989; Vogel, 1987; Zurayk, 1994; Veeck et al., 1995).

Researchers have reported substantial terrace abandonment (50±60 per cent) in Peru1 (Denevan, 1988) and similar estimates have been reported in Chile (Wright, 1963: 73). While Donkin (1979: 35) suggests that the total percentage of terraces abandoned in Central and South America is closer to one-third, this still represents a substantial amount of ®eld surface. Possible causes of abandonment include demographic, social and biophysical factors. Population decrease (disease, out-migration), loss of irrigation management skills, and climate changes have been hypothesized to be responsible for terrace abandonment (Donkin, 1979; Treacy, 1989). Scienti®c researchers and government-funded organizations have supported the reconstruction of abandoned terraces because of their agroecological bene®ts (Treacy, 1989; Zurayk, 1994).

However, terrace reconstruction can require nearly as much labor investment as the initial terrace construction (Treacy and Denevan, 1994: 103). Despite this substantial cost, terrace reconstruction remains a viable means of reducing the fragility of steep-slope environments. Given this context, it is important to understand the agronomic conditions under which terracing is most bene®cial.

We propose that modi®ed solar exposure ± a key component of agricultural productivity ± is among the signi®cant e€ects of terracing. We analyze how latitude, slope angle, slope aspect, altitude and season control the degree to which modi®ed solar insolation may represent a net bene®t or cost as a result of terracing a hillslope. We demonstrate that changes in incident radiation must be considered when seeking answers to questions such as those stated above.

Terrace Functions or Bene®ts Terraces convert non-arable land to arable land on slopes otherwise too steep to cultivate. They also may be used to improve the agricultural potential of slopes that could be cultivated without leveling (Wadsworth and Swetnam, 1998). In either case, scholars have proposed that by default or design terraces achieve a variety of agricultural bene®ts. Terraces may: (1) stabilize slopes to facilitate construction and maintenance of contour irrigation canals (Ortlo€, 1988) or to reduce landslide hazards to agriculture, roads, and settlements (Johnson et al., 1982); (2) reduce runo€ velocity and thereby lessen soil erosion while increasing moisture retention (Spencer and Hale, 1961; Sandor, et al., 1990; Williams, 1990; Smith and Price, 1994: 175;

Vogel, 1987, 1988; Zurayk, 1994); (3) level the planting surface (Smith and Price, 1994: 175); (4) create better or deeper, soils (Spencer and Hale, 1961; Sandor et al., 1990); or, (5) favorably modify microclimate (Treacy, 1989).

Treacy and Denevan categorize such bene®ts as primary, secondary, or epiphenomenal. They argue that cultivators need not have been explicitly aware of these individual functions to none the less appreciate a `sense of overall agronomic advantage that terracing provides' (1994: 95). According to Treacy and Denevan, most observers suggest that moisture management was a widespread primary rationale for the construction of terraces. Soil development may have been primary in some cases. Although erosion control strikes modern 1 Masson (1986) originally reported 75 per cent abandonment in Peru, but this estimate was revised to 50 per cent in Denevan (1988: 28).

Denevan (1988) reported 61 per cent of terraces were abandoned in the Colca Valley of Peru based on aerial photography.

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observers as important, most sources suggest that it was probably a secondary factor in the origin of terracing. Microclimatic modi®cations are most often cited as secondary or epiphenomenal factors.

While terraces may also have served social, political or military functions, most of the geographical and archaeological literature has focused on their more utilitarian agricultural advantages. Actual empirical or experimental study of these functions has been rare. We note also that researchers seldom have considered the costs of terrace cultivation, such as reduction in potential surface area of a leveled ®eld or the maintenance of terrace walls (see Wadsworth and Swetnam, 1998 for an exception). Apart from the work of Earls (1986), solar radiation e€ects, the focus of this paper, have been mentioned in passing in only a few of the sources of which we are aware.

A Solar Radiation Hypothesis By modifying surface orientation and the distribution of shadows, terracing changes the exposure of crops to sunlight relative to that on an unmodi®ed slope. Terracing potentially modi®es the duration, evenness, intensity, and cumulative total solar insolation available to plants. Through direct e€ects on photosynthesis and indirect e€ects on such agronomic variables as soil temperature, soil moisture, and evapotranspiration, we expect this to in¯uence crop productivity. The direction ( positive or negative) and the magnitude of the e€ect of terracing on direct solar radiation will be determined by surface slope, exposure, latitude, altitude, season, time of day, local atmospheric conditions such as daily distributions of cloudiness and re¯ectance from surrounding terrain. With the exception of atmospheric conditions and re¯ectance, these are the variables of our analysis.

We focus on bench, or linear contour terraces (see Treacy and Denevan, 1994: 96±101), a form that typically has the following characteristics: a somewhat inward-sloping, retaining wall of stacked stone, a level surface, a close match to slope contours, cut-and-®ll construction in contiguous, serial rows, and built-in features such as irrigation, steps or niches. The regular geometry of bench terraces facilitates modeling their agroecological features.


Geometric Relationships and Constants The intensity of direct (Brock, 1981: 8) or beam (Kreith and Kreider, 1978: 37) solar radiation per unit area (I, MJ m À2) is a function of (1) the elliptical nature of the Earth's orbit, (2) the solar constant, (3) the solar incidence angle (i), (4) daylength (sunrise±sunset), and (5) solar attenuation through the atmosphere. We discuss each in turn.

A radius vector correction (R), applied to the solar constant to allow for a 3 percent eccentricity in the Earth's orbit. This correction varies between 0.9832 and 1.0167 (Brock, 1981: 4). This correction factor was

estimated using:

1a2 R ˆ 1af1 ‡ ‰0Á033  cos…360da365†Šg The solar constant, the average radiation intensity at the top of the atmosphere, is 1367 W m À2 (Wehrli, 1985).

Solar incidence angle i is the angle between the perpendicular (normal) to a surface and a line parallel to the sun's rays. Solar intensity/unit area is greatest for i equal 0 degrees and least for an i approaching 90 degrees. Five variables control (i) for a planar surface (symbols and de®nitions follow Kreith and Kreider (1978) unless otherwise noted).

(1) Solar hour angle (hs) measures the movement of the sun through the sky from sunrise to sunset. It is determined by 15 degrees times the number of hours before or after the local solar noon, with a

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convention of negative morning and positive afternoon values. Given the time from midnight (T), the solar hour angle may be computed using

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(2) Solar declination (ds) is the latitude where the sun is directly overhead and derives from the tilt of the Earth's axis relative to its orbital plane around the sun; it is the factor responsible for northern and southern hemisphere seasonality. From a northern hemisphere perspective, it varies annually from

23.458 N latitude at the summer solstice to 23.458 S latitude at the winter solstice. Declination is determined relative to Julian days (d), numbered consecutively from 1 January to 31 December (e.g. the

summer solstice is day number 173). Declination may be estimated using the following equation:

ds ˆ 23Á45  sin‰360…284 ‡ d†a365Š

(3) Latitude (L) is measured in degrees, positive north of the Equator and negative south.

(4) Slope aspect, or surface azimuth angle (aw) is the angle on a horizontal plane between due south and the projection onto that plane of a horizontal line tangent to a surface. It is measured in degrees (0 degrees± 360 degrees) beginning from due north.

(5) Slope, or surface tilt angle (b) is the angle between the surface of interest and a horizontal plane. It is measured in degrees, from 0 to 90 degrees.

The ®rst three of these angles (hs, ds, and L) determine the geometry of the solar position in the sky relative to a horizontal plane on the Earth's surface. The second two variables (aw, b) establish the orientation of a planar surface relative to that horizontal. Given values for these variables, incidence angle is established by

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Simpler equations may be used to determine incidence angle for cases restricted to either ¯at south-facing, or non-south-facing surfaces, but the above formulation is able to model all situations (Kreith and Kreider, 1978).

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