Previously there had been little effort to measure terrace abandonment anywhere. Several rough estimates appear in the literature, ranging up to 80 percent for some regions (e.g., Wright 1963, 13, for northern Chile). The Peruvian ecologist Luis Masson recently estimated that there are about one million ha of terraces in Peru, of which 75 percent are abandoned (Masson 1986, 208). He has since reduced this figure to ca. 500,000 to 600,000 ha with at least 50 percent abandoned, which is more realistic (Masson, pers. com., 1988). The problem is that there are a substantial number of terraces on the eastern slopes of the Andes, mostly buried under dense forest and not mappable from air photos. However, even the lower estimate of abandoned terraces is a considerable area for a poor country that seems to have a shortage of agricultural land. The largest concentrations of terraces in the Andes are in southern Peru, extending into Bolivia and northern Chile and Argentina. They are less common in central Peru and are sparse in the north and into Ecuador and Colombia (see maps in Donkin 1979). The Oficina Nacional de Evaluación de Recursos Naturales (ONERN n.d.) has begun mapping terrraces (bench terraces only) in Peru. Preliminary maps have been completed for the southern departments of Arequipa, Puno, Tacna, and Moquegua, with a total of 74,570 ha of cultivated and abandoned terraces, of which 30,770 ha are in Arequipa.

The cultivated sector of the Colca Valley is mainly between Tuti at 3,790 m and Cabanaconde at 3,287 m, a distance of about 60 km (Figure 1). The Colca River is incised into broad fluvial flats on which most of the 12 present villages are located. Agricultural terraces occur on these flats (pampas), on the slopes below, and on the slopes above to as high as 4,000 m. The climate is semiarid, with only about 400 mm annual precipitation, so that irrigation is essential. Soils are mostly mollisols of relatively high fertility. The main crops today are maize and quinoa and the introduced crops of barley, broadbeans, and alfalfa. The 1981 population was about 21,500, which is about half the estimated population for A.D. 1520. For more detail on physical conditions, see Sandor (1987); for history see Cook (1982); and for discussions of the Colca terrraces see Denevan (1987); Guillet (1987a, 1987b, and 1987c); and Treacy (1987a, 1987b). Our field research has been focused on the communities of Coporaque, Achoma, and Cabanaconde (Figure 1).

AIR PHOTOGRAPHY
Overlapping vertical air photos are available for the Colca Valley for 1931, 1955, and 1974. The 1974 photos, at a scale of 1:17,000, were taken for the Majes irrigation project. They are quite suitable for mapping terracing and for differentiating cultivated from abandoned terraces, and the date is reasonably close to the project date (1984). Thus, they were used for mapping the Colca terraces, the results of which are presented here. The 1 :55,000 scale of the 1955 photography (Plan del Sur Project) makes identification of abandoned terraces very diffficult. We also photographed the valley in 1986 (35 mm Kodachrome slides), but the results are not good enough for accurate mapping.

The 1931 photos, at a scale of 1:13,000 and of excellent quality, were taken by the Shippee-Johnson Expedition (Shippee 1932). They are available at the American Museum of Natural History and at the Servicio Aerofotográfico Nacional in Lima. It would be useful to know to what degree cultivation of terraces has expanded or contracted since 1931. We only have the three photos covering the village of Coporaque, and for that community there has clearly been an increase (ca. 30 ha) of cultivation (Denevan and Hartwig 1986, Figure 11).

Terraces were mapped for ten districts between Chivay and Cabanaconde. The districts of Tuti and Tapay were not included because of the lack of complete photo coverage for them. Five of the 10 resulting maps are included here (Figures 2-6). Since the districts overlap, most of the terraced areas are covered (see Denevan and Hartwig 1986, for the other maps). Summary data for the ten districts for the different categories of cultivated and abandoned land are given in Table 1.

TERRACE CATEGORIES
Seven categories of fields were measured and mapped: Upland Cultivated (UC), Upland Abandoned (UA), Terrace Cultivated (TC), Terrace Abandoned (TA), Bottomland Cultivated (BC), and Bottomland Abandoned (BA), plus Not Cultivated (NC).

The Upland fields are rain-fed fields at the higher levels of cultivation (ca. 3,600-3,800 m at Coporaque) on modest to moderate slopes. They can be subdivided into two groups. The first are sloping field terraces (Figure 10), with rustic back walls and perpendicular side walls. The second are stone-bordered (walled) fields, un-terraced (Figure 7). Not all the areas mapped as Upland fields are fully covered by fields. Field checks subsequent to mapping showed that as little as 20 percent of some small sectors were walled or terraced. In other sectors the walls are so deteriorated that mapping from air photos is difficult. Thus, our measurements are too high for some sectors. On the other hand, cadastral mapping (essential for measurement) does not cover all the higher and more remote Upland fields; these fields were mapped but not measured, resulting in overall under measurement. Only 2 percent of all the fields are Upland, so these problems are relatively minor.

We measured 91 percent of the Upland fields as abandoned; 100 percent in Coporaque and Yanque. These are old (pre-Inca) fields, in very poor condition. They were not irrigated and so must have been dependent on rain or controlled runoff. Possibly only portions of these fields were cultivated, and not regularly. They probably were fields of potatoes or quinoa.

The terrace fields are primarily bench terraces (Figure 7), mostly on steep slopes and mostly between the Upland fields and the Bottomland fields. Most are, or were, irrigated by canals. Also included are a few sectors of non-irrigated, segmented (non-continuous) bench terraces, with rustic back walls (Figure 9). These are on higher slopes, are all abandoned, and are older than the irrigated bench terrraces. The irrigated terraces probably evolved from them and replaced them. The degree of abandonment of the bench terraces varies by district from 37 to 81 percent.

The Bottomland fields (Figure 8) are on gently sloping surfaces, mostly on river terraces at lower elevations (ca. 3400 m at Coporaque). They are a mixture of stone or adobe-walled rectangular fields that are not terraced, plus broad "valley floor" terrraces with low stone retaining walls. All are irrigated, and over 90 percent are currently in cultivation. Because walled fields and true terraces are intermingled, these fields are combined as one category.

PROCEDURES
In step one, drafting film overlays were made for the series of 9" x 9" air photos of the Río Colca Valley dated March 30, 1974. The photos are an unrectified panchromatic series at a scale of approximately 1: 17,000. Overlays were cut to fit the photos, and the boundaries of field types were identified through photo examination and inked on the overlays. Photos were not interpreted stereoscopically.

Decisions as to field type were made according to the plot shape, size, and appearance. Long, thin rectangular plots in parallel rows following contours were classified as terraced, since the shape, width, and positions would be dictated by the slope of the terrain and terrace retaining walls. Larger and more irregularly shaped plots were classified as Bottomland, since the flatter slopes would allow larger plots between retaining walls and not require such close conformance to the contours of the terrain. Fields were classified as cultivated if crops could be seen in them or if the plot boundaries were clean, indicating that the retaining walls of the plot were maintained. If boundaries were ragged and the plots appeared weedy, they were classified as abandoned. Long-abandoned fields were located through detection of the white lines of old canals, wall deterioration, and the growth of brush in parallel lines following terrain contours. Areas were classified as not cultivated if no trace of past or present cultivation could be detected.

In step two, the drafting film photo overlays were best-fit and taped together for the whole valley. This required some maneuvering since a combination of the use of unrectified air photos, non-stereoscopic compilation, and vast elevation differences in the terrain resulted in size and shape distortions of field boundaries, plus a variety of scales in the overlays of the photos. The river and roads were used to orient and match contiguous overlays.

In step three, a large sheet (84" x 42") of drafting film was placed over the taped-together photo overlays, and the information was inked on the larger sheet. The result was a map of fields for the valley, though the scale of 1: 17,000 is approximate and no absolute measurements can be made from the map due to the variations in scale and normal distortions inherent in information compiled without stereoscopes from unrectified air photos.

For step four, information was transferred from this large map to a series of tracing paper overlays taped to 1 :5,000 cadastral maps (Ministry of Agriculture, 1979, based on the 1974 photos). These maps have contour lines and indicate cultivated areas, but do not distinguish between fields. The contour lines proved useful for transfering information from the large map to the cadastral overlays, since they could indicate areas of steeper slope which would have been bench terraces.

Unfortunately, the cadastral map coverage is not as extensive as the air photos, particularly in the Upland areas north and south of the river. Many of the outlying abandoned terraced areas away from the river are not included in the cadastral map coverage. Due to a lack of a large-scale base map and the known scale and distortion problems, it would have been useless to convert these areas to 1:5,000 scale, sketch them onto sheets adjoining the cadastral map sheets, and then measure their extent. Consequently, while all the fields have been mapped within the area of photo coverage (Figures 2-6), the measurements in Table 1 are only for the areas covered by the cadastral maps. These maps cover about 99 percent of the cultivated fields but only about 95 percent of the abandoned fields. Thus the proportion of abandoned terraced land associated with each town is actually higher than the measurements from the cadastrals indicate.

In step five, the extent of areas of abandoned and cultivated field types (and not cultivated areas) were measured off the cadastral overlays with a polar planimeter. Each area of a particular field type was given an identifying number and its size was measured and recorded for each town in square inches. These measurements were later totaled for each field type pertaining to the town and connverted to hectares. Measurements were made of lands belonging to the towns of Chivay, Coporaque, Yanque, Ichupampa, Achoma, Maca, Lari, Madrigal, Pinchollo, and Cabanaconde. For example, the town of Pinchollo has seven areas of abandoned terraces, totaling 53 square inches on the 1 :5,000 cadastral maps, representing 85.8 ha.

Lands of different towns (districts) were recorded separately, even though they appeared on the same cadastral sheet and the field type overlapped the town boundaries. The cadastral maps show the boundaries between districts. When all of a town's land on a sheet had been measured, a total was determined and converted to hectares. This figure was added to the total land of all the towns having land on the sheet, and a sheet total was determined. Next the sheet area was determined and compared to the measured total to calculate the planimeter measurement error for the sheet.

In step seven, the results of this procedure were then compiled, providing totals and allowing for comparisons between towns of relative proportions of field types and calculation of relative proportions for the valley as a whole (Table 1).

ACCURACY
Planimeter measurement error was almost always on the plus side and averaged + 1.6 percent. It was impossible to calculate a percentage of errror in transferring information between the different sheets at different scales. It is probably less than 5 percent.

It was also impossible to calculate the error in classifying field types. All classification was done by one person (Laura Hartwig) and great care was taken to be consistent in classification. All classification was done solely from the air photos, though there was later checking against the cadastrals. This was useful for checking cultivated vs. non-cultivated areas, but not for checking classification of the fields into Bottomland, Terrace, and Upland (except indirectly, by looking at contour patterns). A complete ground survey of the Coporaque fields to check the map originally derived from air photos (see Denevan 1987, Figure 14, and Denevan and Hartwig 1986, Figure 4) was carried out by John Treacy, and 10 units out of a total of 67 (or 15 percent) had been clearly classified incorrectly. Most of the errors were for small units, so the actual amount of mapping error was much less than 15 percent, as can be seen by comparing the two sets of data for Coporaque in Table 1. The degree of classification error is probably similar for the other districts. The map here covering Coporaque (Figure 6) contains Treacy's corrections. Table 1 includes both Hartwig's and Treacy's totals for Coporaque.

The mapping for Lari and the Disputed Zone between Lari and Ichupampa has been checked by anthropologist David Guillet (personal communication), and he reports only one significant error. The sector marked "fallow?" in the Disputed Zone on Figures 4 and 5 just above the road should be TA (abandoned terraces).

A check of the measurements for Coporaque is also provided by an independent mapping of those fields from enlarged 1955 photos by Treacy (1987b) who used a technique different from that of Hartwig. Whereas Hartwig obtained 80 ha of Upland fields, 658 ha of Terrace fields, and 661 ha of Bottomland fields, for a total of 1,399 ha of fields, Treacy obtained 85, 590, and 769 ha respectively, for a total of 1,444 ha. The two totals are very close. The totals for the Upland fields are also very close, which is understandable since the Upland fields are readily distinguished from the other field types. The differences between the measurements of Terrace and Bottomland fields likely reflect the fact that visual distinction between the two types is often quite arbitrary. The similar total field areas of 1,399 and 1,444 ha does give confidence that the amount of error, especially due to scale variation, is not great for either calculation process.

Finally, we now have an independent check for the total areas of cultivated and abandoned terraces for most of the entire valley. The recent preliminary measurements by ONERN (n.d.) of just the bench terraces provide a total of 9,500 ha in contrast to 8,962 ha in Table 1. The ONERN figure, however, includes two additional villages, Tuti and Tapay (ca. 400 ha). On the other hand, ONERN used the 1955 air photos (un-enlarged) at the difficult scale of 1:55.000. ONERN calculates that only 24 percent of the Colca bench terraces are abandoned, in contrast to 61 percent in Table 1. The ONERN percentage is much too low and reflects faulty interpretation of abandonment from the 1955 photos. The Upland fields were not mapped and measured where distant from the towns, as these areas are not on the cadastral maps and thus could not be controlled for scale and hence were omitted from our mapping. The figures given are incomplete, and sectors shown as having no Upland fields may actually have some. The total measured is small (315 ha) and if the un-measured fields were added the Upland total would be less than double.

Figure 7. Upper: abandoned, unirrigated walled fields. Upper middle: abandoned, segmented, unirrigated bench terraces. Lower middle: abandoned, formerly irrigated bench terraces. Bottom: cultivated, irrigated bench terraces. From the top to the bottom of the photo, rainfall decreases as the elevation declines from ca. 3,900 m to 3,500 m. Coporaque, 1974; scale ca. 1:4,250.

Figure 8. Irrigated field terraces and walled fields on bottom land (near-level river terrace above the Colca River). The terraces have back walls and usually side walls, whereas the walled fields have walls on all sides. Coporaque, 1974; scale ca. 1:4,250.

Figure 9. Abandoned, segmented (non-continuous), unirrigated bench terraces. Found at wetter, higher elevations and probably older than dryer, lower-elevation irrigated bench terraces. Coporaque. 1974; scale ca. 1:4,250.

Figure 10. Abandoned, unirrigated, sloping field terraces. The field surfaces are naturally inclined rather than artifically flattened as with bench terraces. Front walls trap rain runoff behind them, providing sufficient moisture for crops in those areas. There may or may not be side boundary walls. Found at wetter, higher elevations and probably older than dryer, lower-elevation irrigated bench terraces. Coporaque, 1974; scale ca. 1:4,250.

1. With 61 percent of the bench terraces abandoned, support is given to past speculations that over half of the terraces in many parts of the Andes are abandoned.
2. Overall, 42 percent of all the fields are abandoned, a still very high proportion considering that most of the Bottomland fields are cultivated.
3. The greatest degree of abandonment is of the Upland fields (91 percent), which are not extensive, and the Terrace fields (bench terraces) (61 percent), whereas only 7 percent of the Bottomland fields are abandoned.
4. There is considerable variation from district to district in total area of fields, in the area of Terrace fields versus Bottomland fields, and in the proportion of cultivated to abandoned fields.
5. Coporaque and Pinchollo have the largest areas of uncultivated lands (within the measured sectors), reflecting poorer soils and steep slopes and high elevations. All the districts have uncultivated (and also abandoned) terraces along the Río Colca, a result of steep and rocky slopes.
6. Upland fields are not shown for some of the districts; although most districts do have such fields, they are not on the cadastral maps and so were not measured. Since they are incomplete, cover a small portion of the total field area, are of uncertain function, and if cultivated may only have been cultivated in part, they could be left out of overall totals.
7. There are two boundaries between Lari and Ichupampa indicated on the cadastral maps as the result of a dispute over the boundary. There is a large area of terraces involved (418 ha), of which most is abandoned (97 percent). The lack of clear ownership may in part reflect this abandonment, or vice versa.
8. Yanque has the highest amount of abandoned Terrace land by far (924 ha). This may suggest a proportionally higher population in the past.
9. Ground checks and comparisons with measurement on the 1:55,000 air photos indicate that the degree of error is relatively minor, that interpretation of cultivated versus abandoned terraces on the air photos was mostly accurate, and that the methodology used was satisfactory. On the other hand the differentiation between cultivated and abandoned terraces in the terrace mapping by ONERN (n.d.) using the 1 :55,000 photos is less reliable.

The maps, data, and procedures provided here present a base for further mapping and measurement of the terraces in the Colca Valley as well as elsewhere.

ACKNOWLEDGMENTS
Mapping and measurement of the terraces from air photos was done by Laura Hartwig, University of Wisconsin Cartographic Laboratory, with the asssistance of others in the lab (Onno Brouwer, Director). Hartwig provided most of the information on procedures. John Treacy provided information for the revision of Figure 6 and other suggestions. Funding for the Colca Valley Terrace Abandonment Project was provided by the National Science Foundation, Grant No. BNS-840-6957, and by the National Geographic Society, Grant No. 3100-85, W. M. Denevan, Principal Investigator.

REFERENCES CITED
Cook, N. D. 1982. The people of the Colca Valley: A population study. Dellplain Series, Westview Press, Boulder.

Denevan, W. M., ed. 1986. The cultural ecology, archaeology, and history of terracing and terrrace abandonment in the Colca Valley of southhern Peru. Technical report to the National Science Foundation and National Geographic Society. Madison, WI: Department of Geography, University of Wisconsin.

Denevan, W. M. 1987. Terrace abandonment in the Colca Valley, Peru. In Pre-hispanic agricultural fields in the Andean region, eds. W. M. Denevan, K. Mathewson, and G. Knapp, 1-43. British Archaeological Reports, International Series 359. Oxford.

Denevan, W. M. and L. Hartwig. 1986. Measurement of terrace abandonment in the Colca Valley. In The cultural ecology, archaeology, and history of terracing and terrace abandonment in the Colca Valley of southern Peru, W. M. Denevan ed., 99-115. Technical report to the National Science Foundation and National Geographic Society. Madison, WI: Department of Geography, University of Wisconsin.

Donkin, R. A. 1979. Agricultural terracing in the aboriginal New World. Tucson, AZ: University of Arizona Press.

Guillet, D. 1987a. Contemporary agricultural terrracing in Lari, Colca Valley, Peru. In Prehispanic agricultural fields in the Andean region, eds. W. M. Denevan, K. Mathewson, and G. Knapp, 193-206. British Archaeological Reports, International Series 359. Oxford.

Guillet, D. 1987b. Agricultural intensification and deintensification in Lari, Colca Valley, southern Peru. Research in Economic Anthropology 8:201-224.

Guillet, D. 1987c. Terracing and irrigation in the Peruvian highlands. Current Anthropology 28:409-430.

Masson, L. 1986. Rehabilitación de andenes en la comunidad de San Pedro de Casta, Lima. In Andenes y camellones en el Peru andino: Historia presente y futuro, eds. C. de la Torre and M. Burga, 207-216. Lima: Consejo Nacional de Ciencia y Tecnología.

ONERN (Oficina Nacional de Evaluación de Recursos Naturales). n.d. Terrace mapping project, manuscript (preliminary and incomplete). Lima.

Sandor, J. 1987. Initial investigation of soils in agricultural terraces in the Colca Valley, Peru. In Pre-hispanic agricultural fields in the Andean region, eds. W. M. Denevan, K. Mathewson, and G. Knapp, 163-192. British Archaeological Reports, International Series 359, Oxford.

Shippee, R. 1932. Lost valleys of Peru: Results of the Shippee-Johnson Peruvian expedition. Geographical Review 22: 562-581.

Treacy, J. 1987a. Building and rebuilding agricultural terraces in the Colca Valley of Peru. Yearbook, Conference of Latin Americanist Geographers, 13: 51-57.

Treacy, J. 1987b. An ecological model for estimating prehistoric population at Coporaque, Colca Valley, Peru. In Pre-hispanic agricultural fields in the Andean region , eds. W. M. Denevan, K. Mathewson, and G. Knapp, 147-162. British Archaeological Reports, International Series 359. Oxford.

Wright, A. C. S. 1963. The soil process and the evolution of agriculture in northern Chile. Pacific Viewpoint 4:65-74.