1. INTRODUCTION

The dramatic ruins of Great Houses in Chaco Canyon, New Mexico, have challenged the interpretive skills of generations of archaeologists. Even though they are the largest monumental pre-Columbian structures north of Mexico, they apparently were nearly empty most of the time. The 17 Great Houses in the canyon were likely built by a few permanent residents assisted by pilgrims, or possibly with corvée labor. The largest structure in Chaco Canyon, Pueblo Bonito (Fig. 1) was 4 or 5 stories tall, incorporates some 695 rooms, and must have had great ceremonial importance.

Who were the pilgrims who may have walked for up to two weeks to reach the canyon around Winter Solstice? Who were the residents of the canyon, who somehow acquired the power to invite or force people from outside to build their Great Houses? The power of the place may have been cosmological in the broadest sense, i.e. an attempt to bring people into parallelism with the larger world.

Cardinality is a repetitive theme in the Chacoan cosmos and its architecture (Fig. 2). The major road entering the canyon from the north appears to have been intentionally aligned approximately along the meridian. The major dividing wall in Pueblo Bonito as well as the axis of its Great Kiva are oriented north-south. It may have been highly important that rituals, daily activities, or sleeping were carried out in parallel with the larger cosmos.

The canyon is a very beautiful place, endowed with dramatic sunrises and sunsets. Some Native American traditions view it as a sipapu, the axis mundi in creation mythologies, and the place of emergence for human populations. In the 11th and early 12th centuries there may have been a natural spiritual magnetism drawing pilgrims into the canyon. Religious specialists in the canyon may have promised abundant rain and crops for those who came to participate in festivals. In return, they may have asked for their assistance in construction of the great houses.

Pilgrims may have converged on Chaco Canyon from more than 100 outlying communities, some up to 240 km distant and requiring 10 to 14 day journeys. These events would have required a well organized calendar. Many festivals in the canyon would probably have occurred near December solstice, when agricultural tasks were light and the San Juan River could be crossed. Part of those festivals may have included observation of sunrises and sunsets, demonstrating the predictive power and legitimacy of the leadership. In the early 12th century when the attractive powers of the canyon may have been in decline, Great Houses were placed at locations for observing dramatic solstice sunrises and sunsets (Fig. 3).

Through its study of orientations of structures and the astronomical calendar, archaeoastronomy can provide insight into the cosmology of the Chacoans. However, some published studies have suffered from methodological problems that confuse interpretation. In addition to methodological problems in measuring orientations of walls and axes of symmetry, interpretation of results depends on statistical methods (see e.g. Sims, this volume) and ethnographic data. Standards for archaeoastronomy fieldwork and data reduction have been developed; however they are contained in sources that have limited distribution (e.g. Aveni 2001, pp. 124-126; Aveni, 2003; Ruggles, 1996), and have not been consistently applied in published work.

We discuss the benefits of magnetic compasses for preliminary surveys, and the justification and methods for follow-up surveys with theodolite or transit, as well as for photographic confirmation. A particular problem arises if conventional surveyors’ data reduction techniques are applied when surveying walls. We urge use of Standard Deviation to quantify error potential for wall surveys, and demonstrate how use of Standard Error for inherently scattered data can provide deceptive results.

In addition to statistical rigor, archaeoastronomy needs the application of available culturally-pertinent ethnography. We use equinox architectural alignment claims at Chaco as a case study. We performed field work in an effort to validate past equinox alignment claims. We also performed a detailed ethnographic review seeking interest in equinox among the Puebloan people who are generally accepted to be the descendants of Chaco’s builders. We find that the tested equinox claims are not adequately precise to operate visually, and that there is no ethnographic support for them. Rather, the well-documented importance of cardinality in Puebloan cosmology provides a more plausible explanation for Chacoan cardinal east-west building orientations. We conclude that approximate equinox alignments are an unintended consequence of deliberate cardinality, and that equinox claims at Chaco are most likely errors of ethnocentrism.

2. MAGNETIC COMPASSES

The magnetic compass is portable, low cost, and easy to use. Using a magnetic compass to measure azimuths is straightforward in principle. A magnetic bearing is directly read from the instrument, and converted to an azimuth by correcting for the magnetic angle of declination. The best practice is to utilize a sighting compass and record bearings in field notes as they are taken. Conversion of bearings to azimuths should not be done in the field because it introduces multiple potential sources of error. The worst case is to record an erroneously converted azimuth without the original bearing. This results in the loss of useful data, and leads to interpretation errors. Do not adjust the compass for magnetic declination as this introduces an additional experimental error.

To convert a magnetic bearing a current angle of declination should be used, these are web published by the US National Geophysical Data Center (see http://www.ngdc.noaa.gov/geomagmodels/Declination.jsp). The angle of declination should never be taken from a map because movement of the earth’s magnetic pole is significant. For example, during a recent 10-year period the angle of declination has changed by over a degree in northwest New Mexico.

Accuracy of one solar/lunar disk width (~ ½°) is desirable when seeking solar or lunar alignments (Ruggles, 2005, pp. 112-113). Multiple factors limit compass accuracy including annual and diurnal variations in the earth’s magnetic field, and local magnetic anomalies. As a practical matter, errors of 1° to 2° commonly occur with magnetic compasses. It is theoretically possible to improve accuracy by means of averaging and use of corrective methods (see e.g. Rodgers, 1921), but results are inconsistent. We urge that magnetic compasses be utilized for preliminary surveys only.

Compass survey data including the magnetic bearing, date, and location should be recorded onto a sketch of the horizon or architectural feature being measured. Redundant measurement of a prominent topographic feature’s bearing can be used to support error checking during data analysis. It is important to record clinometer measurements of horizon altitude on each bearing to enable comparison to ephemerides.

Predicted astronomical alignments should be subject to visual and photographic confirmation. For complex data sets such as multi-marker horizon lines or low frequency astronomical events (e.g. lunar cycles), follow up theodolite or transit survey is desirable.

3. THEODOLITE SURVEY

Surveys can be conducted using either transit or theodolite. Theodolites offer higher precision and image magnification, which is useful when sighting on distant horizon markers. Quality used theodolites may be purchased at very reasonable cost because they have largely been supplanted by total stations among professional surveyors.

Measuring Wall Azimuths: The theodolite is positioned at a fixed offset distance from one end of the wall (we routinely use 1m), leveled, and zeroed on a backsight (Fig. 4). An easily identified backsight with a sharp profile should be selected. An artificial backsight may be created by placing a finishing nail into a stake behind the theodolite operator at a distance of five meters or more. The theodolite is sighted on the backsight, and zeroed.

The backsight becomes the arbitrary zero point for all angles. It is sketched and labeled on the data reporting form, and should be measured repeatedly to ensure that the theodolite has not been bumped. The theodolite position (latitude and longitude) is also recorded based upon a GPS reading.

Angles are read at 1 m intervals along the wall beginning at the point closest to the theodolite. The Standard Deviation ("SD") of the mean azimuth will quantify the wall’s straightness. A minimum of four measurement points are required to enable calculation of a meaningful SD. A meter scale is used to measure the offset from the wall surface at each point; consistent with the theodolite’s offset at the wall’s end. The scale should be placed on the wall face as close to ground level as possible, and leveled using a bubble level. The angle is recorded for each point. Horizon altitude measurements are taken if there is potential for visual astronomical rise or set alignments. After the horizon altitudes are recorded, the backsight is rechecked and recorded as a validation point.

Sun sights enable backsight-based angles to be converted to azimuths relative to true north. Four sun sights each are taken for azimuth and altitude. Times for recorded sun sights can be obtained from a GPS receiver. We recommend use of solar projection onto a sheet of paper to avoid the risks associated with direct sighting of the sun using a filter. Angles are recorded for the trailing limb of the sun. Alternating between azimuth and altitude enables independent validation of sun sights during data reduction. After the eight sun sights have been recorded, the backsight angle is rechecked.

To measure a wall azimuth for a fallen structure, angles may be taken from points at the top of a berm of material if one is clearly defined (Fig. 5). The case depicted is the outlier Great House called Pierre’s Acropolis, located on Chaco’s famous Great North Road. We found that Unit B’s Southeast wall is accurately aligned with Hosta Butte on the distant horizon on an azimuth of 197.2° (N=6, SD=.6°). This result supports the idea that purely astronomical interpretations of Chacoan architecture are an oversimplification. Sacred topography can have importance in a traditional cosmology. This previously unreported alignment to sacred geography is consistent with the Hosta Butte alignment of the Great South Road discussed by Van Dyke (2008, p. 150), and demonstrates the value of considering alternative hypotheses.

Measuring Horizon Features: Minor variations of the procedure may be needed to measure other features. For example, when measuring horizon points to assess potential calendrical foresights, both the altitude and azimuth angle must be recorded for each point. In addition, each horizon point should be measured and recorded four times in order to provide validation and support calculation of standard error.

4. DATA REDUCTION

Reduction of theodolite measurements yields the mean azimuth(s) of surveyed features, and horizon altitudes on these azimuth(s). These can be compared to ephemerides to forecast astronomical rise or set alignments. We use United States Naval Observatory ("USNO") ephemeris data. USNO limb correction estimates account for both atmospheric refraction and the angular radius of the sun’s disk (USNO, 2009). The mean and error levels are calculated for each set of measurements.

Quantifying Error: Use of standard deviation in reduction of wall data differs from the convention applied by surveyors. A surveyor measuring a boundary is working with an assumed straight line and applies standard error to quantify variation in the measurement process. In contrast, we are seeking to infer astronomical intent based on inherently scattered data from measurements of physical structures. As a result, use of standard error can create an unintentional illusion of precision, and may confuse interpretation.

To illustrate why use of standard deviation is important, we consider the extreme case presented in Fig. 6. If we measure thirty five points along a "C" shaped wall from the center point as shown in the figure at left, we might obtain the set of angles shown on the right. The calculated SD of 52.27° makes it abundantly clear that the wall is far from straight. The SE of 8.96°is more open to misinterpretation.

To make matters worse, because the square root of the sample size (in this case 35) is the denominator of the standard error calculation, if we increase our number of data points the calculated error will diminish towards zero. For example, arbitrarily increasing N to 140 for this data set reduces the calculated standard error from 8.96° to 4.48°, further confusing interpretation.

To summarize, because standard deviation quantifies variance from the mean in a data set, it should be used to calculate the error level for a wall’s average azimuth. This approach avoids arbitrarily reducing stated error for larger samples, and provides insight into how straight the wall actually is. In contrast, when making repetitive measurements of the same point (e.g. a horizon marker) use of standard error is certainly correct, because the data should not be scattered.

Sun Sights: Sun sights are used to find the difference between measured angles, and true azimuths. For each sun sight’s recorded time in UTC, the sun’s azimuth and altitude is obtained. This azimuth or altitude is corrected using USNO’s provided correction for atmospheric refraction and the angular radius of the solar or lunar disk. The radius is the difference between the ephemeris’ positional target (the center of the solar disk) versus the measured trailing limb. Correction must be done with attention to the local time as follows:

After limb corrections are applied, the difference is taken between each resulting value and the ephemeris data. For azimuth, this difference provides the correction factor needed to convert theodolite angles (taken with respect to the backsight) to true azimuths. The altitude sun sights are redundant; however they serve as an error check.

5. PHOTOGRAPHIC CONFIRMATION

Photography is the best way to validate predicted alignments. Bracketed exposures with an unfiltered digital camera are adequate to demonstrate an operating solar or lunar alignment (Fig. 7, left). Unfiltered photographs offer the benefit of more valid recreation of the visual experience. Notwithstanding, filtered images provide a defined disk that supports calibration of photographs to theodolite predictions as an independent check of the survey and data reduction process (Fig. 7, right).

As suggested by professional photographer Patrick René, we use a standard #11 Welder’s Shade and exposure bracketing to obtain clear definition of the solar disk when desired. To identify best exposure settings, experiment ahead of time with your camera using manual exposure settings if possible.

6. ETHNOGRAPHY AND INTERPRETATION: AN EQUINOX CASE STUDY

Two contrasting approaches to archaeoastronomy were labeled as "green" and "brown" by Aveni during the 1980’s. Following the Oxford I conference two volumes were published, divided roughly into European and New World studies. The Green volume of old world archaeoastronomy contained studies that were heavily dependent on statistical analysis of places where little ethnographic data was available. The Brown volume described archaeoastronomy of the new world and benefitted from ethnography, anthropology, and cultural history (Aveni, 2008, p.9; Iwaniszewski, 2001). Modern research in archaeoastronomy combines these two approaches whenever possible, utilizing both ethnographic and historical materials, as well as rigorous statistical methods when dealing with quantitative data (Aveni, 2003).

Unfortunately, work continues to be published that ignores such proven methods. For example, Sofaer (2008, p. 90) presents a table of azimuths for the "Principle Wall or Axis" of Chacoan structures which includes errors stated as "+/- N°". Nowhere in the associated text is the method applied to estimate error described.

Complications do arise when applying ethnography to cultures such as the ancestral Puebloans. We have a significant body of ethnography relating to modern descendants of the people who built at Chaco Canyon. Nonetheless, we cannot identify specific descendant clans with any certainty, and the ethnography post-dates construction by centuries. No culture stagnates for centuries, so the ethnography must be applied cautiously (Young, 2006).

No reference to Puebloan interest in, or pre-contact knowledge of the equinox has been identified through review of astronomical ethnography (Ellis, 1975; McCluskey, 1977; Zeilik, 1985; Zeilik, 1986), or through review of multiple primary and secondary ethnographic sources that contain fragments of cosmological, calendrical or astronomical information (Cushing, 1883; Dozier, 1983; Fewkes, 1891; Fewkes, 1897; Hough, 1915; Lockett, 1933; Mindeleff, 1891; Ortiz, 1972; Parsons, 1994; Sando, 1998; Stirling, 1942). Some researchers have suggested equinox alignments at Chaco Canyon in spite of the fact that they have no ethnographic support. Examples include Sofaer (2008, pp. 50-54; pp. 91-93) who identified equinox associations with locations including Pueblo Bonito, Pueblo Alto, Tsin Kletsin, the three-slab site on Fajada Butte and Hungo Pavi, as well as Farmer (2003) who claims a visual equinox alignment at Pueblo Bonito.

There is no compelling reason for traditional sky watchers to place importance on observation and measurement of the equinox. The modern definition of equinox is the time (or more broadly date) when the sun crosses the celestial equator with a declination of 0°. The celestial equator is itself a theoretical geometric construct. Equinox sunrise and sunset are displaced from the cardinal azimuths when observed on an elevated horizon. Therefore, no precise visual association exists between cardinality and equinox in any place with a variable horizon such as Chaco Canyon.

One way to identify a date near to equinox would be to split the angle between solstice sunrise positions on the horizon. This approach also depends on a flat horizon to give consistent results, and is therefore unsuitable for use at any location with a variable horizon where the elevations of the horizons at summer and winter solstices differ. Dates of such an "equinox" will vary at different locations. An alternative method was proposed by Alexander Thom based on the idea of counting the days between the solstices, and using one half of that count to identify a near-equinox date. This method is rendered inaccurate by the difficulties in fixing solstice dates precisely using visual observations. Day counting will identify dates that vary by five or six days or more from year to year. At the latitude of Chaco Canyon a six day change near the equinox results in a shift of over 3° in the sun’s rise or set azimuth. Two other approaches to approximating the equinox have been identified, including finding the day where sunrise and sunset occur exactly opposite one another (also dependent upon a flat horizon), or precise timing of the length of day and night. A detailed critique of equinox in the context of traditional visual astronomy was provided by Ruggles (1999), who reasonably concluded, "In short, the equinox is a concept unlikely to have any meaning from an earth-based perspective within a non-western world view."

Pueblo Bonito is illustrative of the problems associated with claims for visual equinox alignments. The west section of Pueblo Bonito’s south wall is aligned to within 12’ of cardinal. Sofaer (2008, pp. 88-91) asserts that cardinality and the equinox are equivalent, and identified Pueblo Bonito as being "associated with the cardinal directions (meridian and equinox)". The east section of Pueblo Bonito’s south wall is deflected from cardinal by approximately 4°. Farmer (2003) claims that this deflection was a design feature intended to create a visual alignment at equinox sunset as observed from the "platform" at the wall’s east end.

To test these claimed equinox associations we conducted theodolite surveys of Pueblo Bonito’s south wall during 2009. Results are presented in Table 1. Both surveys were conducted from the center of the wall to minimize measured horizon altitudes, and analyzed using USNO ephemerides. Sofaer’s claimed west section alignment is found to be off by three days, and Farmer’s claimed visual alignment for the east section is off by four. Even the three day difference is significant. The sun’s horizon rise point shifts by over ½° per day at equinox at Chaco’s latitude. A three day shift is over three solar diameters.

Photography on Sept 21, 2009 confirmed that Farmer’s claimed visual equinox alignment does not occur (Fig. 8). Neither section of Pueblo Bonito’s south wall incorporates a working visual equinox alignment.

No statistical case can be made in the absence of a working alignment, and there is no known ethnographic evidence for Puebloan interest in the equinoxes. In contrast, there is abundant ethnographic evidence that cardinality is of central importance in Pueblo cosmology (see e.g. Ortiz, 1972, pp. 14-15, 20-23; Sterling, 1942, pp. 5-6, 8-11, 19, 24). In the case of Pueblo Bonito, it is notable that in addition to the east-west cardinality of the south wall’s west section, the importance of the north-south cardinal azimuth is demonstrated by the accuracy of the central dividing wall.

We conclude that the alignment of the west section of Pueblo Bonito’s south wall is most plausibly linked to intentional cardinality. The method used to achieve accurate cardinality remains open to future research and debate. Considering the local topography and the accuracy achieved, the Chacoans may have used a combination of night sky observations and daytime shadow casting with a gnomon. In any event, the orientation of Pueblo Bonito is not plausibly linked to visual observation of equinox. Equinox is a western concept. Currently available evidence indicates that claims of Chacoan equinox alignments are errors of ethnocentrism.

When archaeoastronomy findings are consistent with ethnographic evidence, the ethnography may be applied to demonstrate potential intent. Irrespective of ethnographic support, rigorous statistical testing of quantitative results is in order. Notwithstanding, if our objective is to understand the role of astronomy in culture (versus simply demonstrating intent) then ethnographic integration is required (Ruggles, 1996).

7. CONCLUSION

The results of our recent archaeoastronomy field work and research at Chaco Canyon, New Mexico illustrate how methodological errors can lead to erroneous interpretation of cultural intent. Use of inappropriate standard error instead of standard deviation may lead to deceptive precision claims for alignments. Visual alignment predictions from compass, theodolite, or transit surveys should be photographically confirmed, or they should be explicitly identified as prospective and unconfirmed. The erroneous equinox claims for Chaco’s Pueblo Bonito illustrate the importance of photographic confirmation, as well as the importance of conducting interpretative analysis in the context of applicable ethnography. Based upon these results, we suggest that the following guidelines for field survey and interpretation are applicable to archaeoastronomy research in other cultural contexts:

 ACKNOWLEDGEMENTS: We gratefully acknowledge support by the following people of our 2009 fieldwork: Gene McCracken, Greggory Rothmeier, Beverly and Bob Beehler, Nancy Malville, John Nickerson, and National Park Service staff including Russ Bodnar, Tracy G. Bodnar, Wendy Bustard, G.B. Cornucopia, Dabney Ford, Roger Moore and Superintendent Barbara West.