4. The Data

4.1 Satellite data

The 6.7µm (water vapor) and 10.7µm (IR window) satellite imagery used in the study are from the International Satellite Cloud Climatology Project (ISCCP) data set. Over the period of the data used in this study, data were derived from two different satellites: Meteosat-3 (July 1, 1993 to January 31, 1995) and GOES-8 (February 1, 1995 to August 31, 1999). There is a 15-month gap in the ISCCP data set between March 1996 and May 1997. The first month (February, 1995) of data derived from the GOES-8 satellite when it was coming online could not be used. Differences were observed in various parts of the data set. Meteosat-3 has its own navigation procedure, radiance and brightness temperature calibration and the north-south resolution is slightly less than the GOES-8 data. The earlier part of the GOES data (February 1995 - February 1996) has a different navigation procedure than the latter part (June 1997 - September, 1999) since different agencies processed the data for ISCCP. The data were purchased from the National Climatic Data Center (NCDC) by CTIO and University of Tokyo for use in an earlier study (Erasmus and van Staden, 2001).

Full earth scans are scheduled every three hours. However, cancellation of one or more images per day occurs periodically due to satellite housekeeping procedures, satellite maneuvers, eclipse events and switches to rapid scan mode during the Northern Hemisphere summer. The data for the study area were extracted from the full earth scans and compiled in a separate database. Sample images are shown in Figure 11.

Figure 11.
Sample ISCCP satellite images sectors of the study area (18^oN to 40^oN and 96^oW to 124^oW) on March 20, 1998 at 0845UT. From left to right: visible channel (0.55µm), infra-red window channel (10.7µm) and water vapor channel (6.7µm).

Quality control, calibration and documentation of the ISCCP data are generally good. Documentation was found to be unsatisfactory for data obtained from the Meteosat-3 satellite when it was used as a fill-in satellite at 75^oW after the demise of GOES-7 and before GOES-8 was brought online. For these data, radiance and brightness temperature calibration information is accurate and available (Rossow, et al., 1995; Brest et al., 1997). However, a suitable calibration of the upper tropospheric humidity (UTH), a derived water vapor parameter, was not carried out. Since the satellite was on loan from EUMETSAT to NOAA during this period, EUMETSAT did not consider the UTH calibration to be their responsibility. For NOAA, their focus at the time was on GOES-8. Consequently no calibration was done for the conversion of Meteosat-3 water vapor brightness temperatures to UTH.

In an earlier study (Erasmus and van Staden, 2001) efforts were made, unsuccessfully, to obtain UTH calibration information for Meteosat-3. It was decided to obtain a period of overlapping satellite data for Meteosat-3 and GOES-8 so that an inter-calibration could be performed. (An accurate UTH calibration is available for GOES-8 data.) Repeated problems were encountered in attempts to obtain such an overlapping data set. In view of these developments a calibration of UTH for Meteosat-3 was undertaken using the daily Denver rawinsonde data for 1994. The calibration produced through this effort has enabled a seamless transition from the Meteosat-3 data to the GOES-8 data. The successful merging of the two data sets is demonstrated in section 6.1.

The format of the ISCCP data (Campbell, et. al, 1997) is a mixture of McIdas (www. ssec.wisc.edu/software/mcidas.html) format and documentation data transmitted directly from the satellite. The basic structure of the data set is a header containing sector specifications, navigation constants and calibration coefficients. This is followed by scan lines of data from the multi-spectral imager interlaced by pixel. Each scan line is preceded by an 80 byte header which includes the time of the scan.

The first part of the header provides information on the image sector data to follow such as the limits of the scan area, time of scan, channels included, spatial resolution and byte positions for the start of each data section. The next section of the header contains the parameters required for input to the software used to navigate the image areas. A program which converts pixel location to latitude‑longitude position with an accuracy of 4km is provided by the National Environmental Satellite Data Information Service (NESDIS). The calibration section of the header provides the data needed to convert the radiance counts to true radiances. Meteosat and GOES perform real-time calibrations of infra-red detectors on-board the satellite using sensor readings from dark space and reference blackbodies. Calibration coefficients thus derived are used to compute radiance values from the raw counts. Further information on the computation of radiance values and derived parameters is given in section 5.

Following the header are the data for the sector (in our case full-disk) arranged according to observation channel, viz. visible, infra-red window channel (10.7µm) and water vapor channel (6.7µm). The data are classified as B1 (highest spatial resolution) by ISCCP. Raw GOES-8 data are 1 km x 1 km resolution in the visible, 4 km x 4 km in the infra-red window channel and 4 km x 8 km (effectively 8 km x 8 km) in the water vapor channel. For ISCCP, the raw data are sampled so that the effective pixel resolution for all channels is 9.1 km x 8.0 km at Nadir.

4.2 Rawinsonde data

In order to determine the presence of cloud in the IR window imagery and to compute an absolute humidity from the satellite-observed relative humidity (UTH), a measurement of the temperature profile above the ground is required. This measurement is obtained from rawinsonde data. At several locations within the study area, balloons carrying instrument packages are released between two (00UT and 12UT) and four (additionally 06UT and 18UT) times per day. These data were obtained on CD from the NCDC. The primary stations (29) are listed in Table 6 and their locations shown in Figure 12. Primary stations have at least two soundings per day. Fifteen other stations with intermittent or less frequent data were also used in the analysis. While coverage over Mexico is noticeably poorer than over the USA, station density is sufficient for the purposes of the proposed analysis. In addition, it should be noted that there are few island-based rawinsonde stations in the ocean areas and all of these are not primary stations. This does have an effect on the reliability of the analysis in these areas. Details on how these data are used in the methodology for cloud detection and absolute humidity computation is provided in section 5.

Figure 12. Locations of the primary rawinsonde stations within the study area.

Table 6. List of the primary (two or more soundings per day) rawinsonde stations used in the analysis (refer to Figure 12 for site locations by number)

No.	Station	Latitude	Longitude
1	Albuquerque	35.05	-122.22
2	Amarillo	35.23	-101.7
3	Oakland	37.75	-122.22
4	Del Rio	29.37	-100.92
5	Denver	39.77	-104.88
6	Dodge City	37.77	-99.97
7	Flagstaff	35.23	-111.82
8	Fort Worth	32.8	-97.3
9	Grand Junction	39.12	-108.53
10	Midland	31.93	-102.2
11	Mirimar	32.87	-117.15
12	Reno	39.57	-119.8
13	Salt Lake	40.77	-111.97
14	Tucson	32.12	-110.93
15	Vandenberg AFB	34.75	-120.57
16	Yuma	32.87	-114.33
17	Mazatlan	23.18	-106.42
18	La Paz	24.07	-110.33
19	Guadalajara	20.68	-103.33
20	Edwards AFB	34.9	-117.92
21	Manzinillo	19.07	-104.33
22	Vera Cruz	19.17	-96.12
23	Bakersfield	35.43	-119.03
24	Brownville	25.9	-97.43
25	Corpus Christi	27.8	-97.5
26	Desert Rock	36.62	-116.02
27	Guaymas	27.95	-110.8
28	Oklahoma City	35.23	-97.47
29	Santa Teressa	31.9	-106.7

4.3 Topography data

In the area analysis (mapping) of cloud cover, the height of the terrain is required in order to estimate surface temperatures from the rawinsonde data. Digital terrain heights at 30 arc seconds (~ 1 km) resolution were obtained from the United States Geological Survey (http://edcdaac.usgs.gov/gtopo30/gtopo30.html). Since the pixel size in the satellite imagery is approximately 10 km x 10km, several (~ 100) terrain points lie within the area corresponding to one satellite image pixel. Since the focus in this study is clearly to characterize conditions over the highest terrain (locally), the terrain heights used in the area analysis were determined for each location in the terrain data domain by setting the terrain height equal to the maximum height of the 36 closest terrain points (a 5 km x 5 km square). Figure 13 shows the terrain as determined in this manner. Some erroneous topography is generated as is evident in some locations along the coast where the 500m contour crosses the coast line but this is inconsequential. More importantly the higher terrain, including some peaks, is well reproduced. The actual topography as used in the area analysis is of higher resolution than is shown in Figure 13 since the plotting routine uses a grid based on the largest spacing between pixels (found in the northwest corner) in the satellite image.

Figure 13. Topography of the study area (contours in m). (Note: The actual terrain height resolution as used in the analysis is significantly better than what is displayed in this figure)

4.4 Definitions of seasons and day/night divisions

Area and site analysis was performed for different seasons and periods of the day. Seasons are defined on a climatological basis as follows:

Winter - December, January, February (DJF)

Spring - March, April, May (MAM)

Summer - June, July, August (JJA)

Fall - September, October, November (SON)

Day/night divisions are based on true solar time or local mean time. The computational method is similar to that of Sarazin (1991) which is based on the Guide to Meteorological Instruments and Methods of Observation, Annex 9D, World Meteorological Organization (1983). The elevation angle of the sun (h_o) is given by the equation:

sin h_o = sin δ * sin φ + cos δ * cos φ * cos t (4.1)

where δ is the declination of the sun for a given day of the year, φ is latitude and t is the solar angular time counted from midday.

δ is given by:

δ = 0.006918 – 0.399912cosθ + 0.070257sinθ +

0.006758cos2θ + 0.000908sin2θ (4.2)

where θ is the annual solar angular time given by:

θ = 2πd_n/365 (4.3)

and d_n is day of the year.

At sunrise and sunset h_o = 0, thus for any given day of the year, one can solve for t in equation 4.1. At the equinoxes, t is exactly π/2 radians, which corresponds to 6 hours in time. Thus, for any given day of the year and latitude the equivalent time in hours before and after midday is given by t * 6 * 2/π.

Local apparent time (LAT) is then given by

LAT = GMT + LC + Eq, (4.4)

Where GMT is Greenwhich Mean Time, LC is a longitude correction of 4 minutes for every degree and Eq, the equation of time, is a correction to obtain apparent (true) solar time from mean solar time.

Eq = 0.0172 + 0.4281cosθ – 7.3515sinθ – 3.3495cos2θ – 9.3619sin2θ (4.5)

The solar time clock is based on pixel location. Therefore, day/night divisions reflect true local day/night divisions. For the purposes of the analysis that follows, “day” is the period from one hour after true (local) sunrise time to one hour before true sunset time. “Night” is the period starting one hour after true sunset time to one hour before true sunrise time. Further divisions into day1, day2, night1 and night2 are done by dividing the applicable period exactly in half.

5. Methodology

In this study, measurements of water vapor and cloud are derived from meteorological satellite observations by passive remote sensing at different wavelengths. The satellite measures the monochromatic emittance of the earth and atmosphere at 10.7µm in the infra-red window and at 6.7µm, a water vapor absorption band. Depending on the wavelength of the emissions being measured by the satellite, different quantities can be derived. Figure 14 shows the weighting functions for different infra-red channels. In the IR window channel, emissions reach the satellite largely unattenuated by the atmosphere so that radiance values measured are due to emission from the surface. However, clouds absorb and emit essentially as blackbodies at infra-red wavelengths. The result is that when clouds are present in the atmosphere, they behave as an elevated emitting “surface” so that radiation reaching the satellite is from the cloud top.

Water vapor in the atmosphere is absorbent at most infra-red wavelengths. The absorptivity for a given wavelength determines the layer in the atmosphere in which out-going terrestrial radiation will be absorbed and re-emitted by resident water vapor. Figure 14 indicates that satellite observations at 6.7µm are sensitive to water vapor emissions from the layer between 600mb and 300mb. (There are only small amounts of water vapor above 300mb. See Figure 15) Emission from this layer depends on the amount of water vapor in the layer and temperature and is typically calibrated in terms of the relative humidity. An independent upper-air temperature measurement is needed to derive an absolute humidity from the relative humidity. This is accomplished by using observed temperature versus height data from rawinsondes or numerical models.

Figure 14. Weighting functions for selected infra-red observing channels (from Rao et al., 1990)

5.1 Conversion of radiance to brightness temperature

In the real-time (raw) data stream for GOES-8, radiance counts are 10‑bits in length for the imager channels. In order to maintain compatibility with older data sets such as GOES-7 and Meteosat-3, these have been scaled into 8-bit counts for ISCCP and the scale factors are listed in the header section of the data file. The infra-red channel calibration consists of a bias scaling factor and a first order gain scaling factor. True radiance values are obtained using the equation:

R = (X ‑ b)/m, (5.1)

where R is radiance (mW/[m².sr.cm^‑1]) and X is the count value. The coefficients b and m are the scaling bias and the scaling gain, respectively. For the IR window channel, in order to get an accurate temperature of the emitting surface, R must be adjusted to account for absorption by water vapor between the surface and the satellite. In dry areas, particularly for high altitude locations, this correction is negligible. R*, the adjusted radiance, depends on the precipitable water vapor (PWV) and is given by R* = R/J where:

J = -0.0163(PWV)+ 1.0119 (5.2).

The brightness (or effective) temperature is then obtained by inverting the Planck function as follows:

T_eff = (c₂*nu)/ln(1 + [c₁*nu³]/R*) (5.3)

where T_eff is effective temperature (K), "ln" stands for natural logarithm and nu (cm^-1) is the central wave number of the channel. The coefficients c₁ and c₂ are the two radiation constants and have values of c₁ = 1.191066x10^‑5 (mW.m^-2.sr^-1.cm⁴) and c₂ = 1.438833 (cm.K). To convert effective temperature to actual temperature T(K), the following formula is used:

T = b*T_eff + a (5.4)

The constants a (K) and b depend on the observation channel. These are bias and gain adjustments that account for variations in the inverse Planck function across the spectral passband of the channel. The differences between the values of T and T_eff increase with decreasing temperature. They are usually of the order of 0.1 K and hence negligible for most calculations.

5.2 Conversion of 6.7µm brightness temperature to UTH

The Upper Tropospheric Humidity (UTH) is a measure of the relative humidity of a layer extending from 600 mb to 300 mb. For GOES data, Soden and Bretherton (1993, 1996) have derived a semi-empirical relationship between UTH and 6.7µm channel brightness temperature in clear areas. It is important to note, therefore, that the results presented below for water vapor are applicable under clear sky conditions.

The basic form of the relationship is:

UTH = [exp(a + b*T) * Cos q] / p0 (5.5),

where q is the satellite viewing zenith angle, a and b are the least squares fit slope and intercept of the regression line as defined by the empirical relationship and p0 is a normalized pressure variable.

p0 = p(T=240K)/ 300, (5.6)

where p (in mb) is the pressure level where the temperature (T) is 240K. The values for a and b are seasonally dependent and are obtained from a table listing their values for each month of the year. The factor p0 accounts for the lifting (lowering) of the weighting function peak (Figure 14) in warm (cold) airmasses. Where the satellite viewing zenith angle exceeds about 75^o the UTH computation becomes increasingly uncertain. In the area analysis (section 6) the far northwest corner of the study area is unmapped for this reason.

5.3 Computation of precipitable water vapor

The precipitable water vapor (PWV) is a quantity indicating the absolute humidity in the atmosphere above some predetermined altitude such as the surface or a constant pressure level. PWV is derived from the satellite-based UTH measurement. Since the UTH is a measure of the relative humidity in the layer between 300mb and 600mb, for pressure levels between 300mb and 600mb the relative humidity is set equal to the UTH. Then the corresponding mixing ratio (x), the mass of water vapor per mass of air (Kg/Kg), at each level (10mb increments are used) can be computed as follows:

x = UTH . x_s (5.7).

x_s, the saturation mixing ratio, is the maximum water vapor carrying capacity of the air at a given temperature and pressure. It is computed using the rawinsonde temperature and pressure measurement.

The next step in the computation of PWV is deriving the mixing ratio values for pressure levels below 300mb and above 600mb. Figure 15 shows the average mixing ratio profiles for four months in the year 1993 as observed by the Denver rawinsonde. The profiles exhibit good linearity with pressure (height) above 600mb. Similar moisture profiles are observed at dry locations in the subtropics above the inversion layer. It is also clear that the contribution to total PWV from levels above 300mb is very small. To obtain the unknown mixing ratio values, the computed values for 300mb and 600mb were respectively scaled to lower and higher pressure levels. This was done using the daily rawinsonde sounding for the closest station and time.

Once the mixing ratio profile is obtained, then,

_p

PWV = (1/g) ò x.dp (5.8)

^o

where dp is the incremental pressure change with height in Pascals and g is the gravity acceleration constant. The units for PWV are then kg.m^-2 or mm of water.

Figure 15. Average water vapor mixing ratio versus pressure (height) profiles for four months in 1993 as determined from the Denver rawinsonde.

In a related study (Erasmus and van Staden, 2001) it was found that, in northern Chile, cold surfaces at high altitude may have an impact on the computation of PWV. The effect is limited to sites with an altitude above the 600mb (~4400m) pressure level under very dry conditions at night. These locations are affected because, at 6.7µm, the satellite senses emissions from the layer between 600mb and 300mb. Therefore, if the surface extends above the 600mb level, emission from the surface may be measured. This only occurs under very dry conditions (PWV <~ 1 mm) when there is not enough water vapor in the air to completely absorb and re-emit radiation from the surface.

In the area being surveyed in this study few, if any, of the locations under consideration are affected. For the area mapping of precipitable water vapor, ground effects are inconsequential since only values below 1mm PWV are affected and these are all included in the first PWV bin (0-1mm). In the site analysis, at sites with a surface altitude above 4000m a check was made for the presence of ground affects and none were found to exist.

To demonstrate the validity of the satellite PWV measurements, observations of PWV made from the ground at Mt. Graham were compared to those from the satellite for the same period. 225 GHz radiometer data were obtained from the Submillimeter Telescope Observatory (SMTO) (maisel.as.arizona.edu:8080/) for the period June 1997 to September 1999. The data are observations of atmospheric opacity every half hour (for 24 hours). Precise conversion from opacity to PWV requires the use of an atmospheric model and upper-air meteorological data. At SMTO a conversion factor of 19 is being used for on-site applications (Dumke, 2002) so this value was adopted for the purposes of this comparison. The comparison was based on observations in the period June 1997 to May 1998.

The SMTO data includes observations made when cloud is present. To facilitate comparison with the satellite observations that are made strictly under clear conditions, an attempt was made to remove cloudy records by placing an upper limit on radiometer PWV values. It is not possible to know exactly what the value of PWV will be when clouds are present since this depends on air temperature and altitude of the clouds. Based on experience forecasting PWV at La Silla Observatory, the highest PWV value observed in the absence of cloud is about 17mm (www.eso.org/genfac/pubs/astclim/ forecast/meteo/ERASMUS/las_fapp.txt). Adjusting this limit to the higher Mt Graham site altitude the corresponding value would be 13mm. This is an upper limit, so clouds may nevertheless be present when the PWV is lower than 13mm.

Figure 16 is a plot of the monthly average PWV from the satellite and radiometer (ground). In the summer months, it is evident that the 13mm cut-off does not exclude all cloudy situations. By considering radiometer PWV values less than 7mm only, the summer-time discrepancy disappears and the balance of the year remains in good agreement with the satellite. The annual figures for the primary statistics are shown in Table 7.

Figure 16. Mean monthly PWV (mm) at Mt Graham for the period June 1997 to May 1998 as determined from satellite and ground-based radiometer (Submillimeter Telescope Observatory ) observations.

Table 7. Primary statistics for PWV (mm) at Mt Graham for the year June 1997 to May 1998 from satellite and ground-based radiometer (Submillimeter Telescope Observatory) observations.

	Satellite	Ground
		PWV<13mm	PWV<7mm
10^th Percentile	1.15	1.15	1.07
1^st Quartile	1.86	1.76	1.55
Median	2.60	3.18	2.52
3^rd Quartile	5.99	6.01	3.91

The comparison clearly shows that the satellite and ground-based radiometer PWV measurements for Mt Graham are in good agreement. Erasmus and van Staden (2001) found similarly good agreement at Paranal and Chajnantor.

5.4 Cloud detection and classification

The presence of cirrus (high altitude) clouds and their thickness is inferred from the 6.7µm imagery. Since these clouds are found at an altitude (9-12km) higher than the water vapor emission layer, IR radiation from water vapor below the 300mb level is absorbed and re-emitted at colder temperatures by the cloud particles. Since the relationship between UTH and water vapor brightness temperature defined in section 5.2 is only valid under clear conditions, the presence of cirrus cloud particles causes UTH values to rise to the point that they are no longer valid. When UTH values rise to around 50%, cirrus cloud particles start forming by condensation and deposition (the cloud particles may not be visible at this stage or have any effect on optical transparency). As UTH values rise further, the cloud particles grow in size and number and the cirrus cloud gets thicker. When UTH values rise above 50%, therefore, the UTH becomes an indicator of the presence and transparency of cirrus clouds. A first attempt at determining the threshold UTH values for the transition from clear to transparent and transparent to opaque conditions was made by visually comparing cirrus cloud in water vapor channel and IR window channel images (Erasmus and Peterson, 1996). Based on this comparison using Meteosat-3 data, threshold values of 72% and 150% were set. Subsequently, using better calibrated GOES-8 data, Erasmus and Sarazin (2000, 2001) have started to define these thresholds more accurately. They used atmospheric transparency measurements made on the ground at optical wavelengths and compared these to a transparency index based on the satellite UTH measurement. While this work is still in progress, Erasmus and Sarazin (2000, 2001) have shown that the satellite transparency index does effectively discriminate between photometric and non-photomeric observing conditions as measured by the Line Of Sight Sky Absorption Monitor (LOSSAM) at La Silla Observatory. The UTH threshold values have subsequently been revised as follows:

Clear: UTH £50%

Opaque: UTH ³100%

Transparent: 50%<UTH<100%

The 10.7µm channel data are used to detect cloud in the middle and upper troposphere. In principle the procedure for cloud detection is straightforward. Pixel temperatures (T_ir) computed from the 10.7µm satellite data need to be referenced against an independent temperature measurement. Typically, temperature drops with height in the atmosphere, so if T_ir is colder (by some margin) than the surface temperature (for example) at a given pixel location, the presence of cloud above the surface is indicated. In practice, however, there are some obstacles to the task of unambiguous cloud detection.

Firstly, there is the need for an independent reference temperature measurement with which the satellite IR channel temperature (T_ir) can be compared. The most suitable reference data available in the study area are from rawinsonde soundings. Balloons carrying instrument packages measuring temperature, pressure and humidity are released twice a day (00UT and 12UT) from selected meteorological stations. Wind data are derived by tracking the position of the balloon using a radio theodolite. These stations are typically 400-500km apart. Even so, since horizontal temperature gradients are typically small compared to vertical gradients, it is generally possible to derive a reasonable estimate of the surface pressure and air temperature from a nearby rawinsonde station.

As a first step towards determining the cloud detection temperature threshold (T_r), the surface pressure (P_s) and corresponding surface temperature (T_s) for a given location may be estimated using the sounding data and the terrain height. Given the altitude of the surface and the geopotential heights of the pressure levels, P_s and T_s can be estimated by interpolation from the rawinsonde data. However, the actual surface temperature may be warmer or colder than T_s since there is usually additional cooling (night) or warming (day) of the air by contact with the ground. If the estimated surface temperature is cooler than the actual surface temperature (day-time) cloud detection is not compromised. If cloud is present (even a thin layer near the surface) during the daytime, the cloud top temperature (T_ir) will be colder than the estimated surface temperature. So if T_r = T_s, cloud is correctly determined to be present. However, if the actual temperature is colder than the estimated surface temperature (T_s) and T_ir < T_r = T_s, then two conditions are possible - cloud may be present or the ground is cold and is incorrectly being interpreted as cloud. In order to avoid this problem a T_r must be used that is lower than T_s when the actual surface temperature is colder than T_s. At the same time the difference between T_r and T_s must be minimized so that cloud, if it is near the ground, does not go undetected.

In order to optimize the value of T_r, cloudiness observed at different times of the day (four day/night periods) and seasons of the year was analyzed at five sites in the study area: San Pedro Martir, Mt Graham, Co. La Negra, Boundary Peak and Kitt Peak. These sites represent the range of altitudes, latitudes and inland extents of existing and potential sites within the study area. It is reasonable to expect that high altitude, high latitude inland sites will exhibit the largest problem with detection of ground in the winter since this setting maximizes nocturnal ground cooling. On the other hand, at sites near the coast, at lower altitudes and at those with well vegetated surfaces the ground cooling effect would be less.

For these five sites, T_r was initially based on P_s as computed from the nearest rawinsonde sounding and the actual site altitude. This value for T_r obviously leads to ground detection at night for the reasons discussed above. Given these conditions, the pressure level (altitude) on which T_r is based was reduced (increased) in a step-wise manner using increments of 10mb (~100m). It was found that, at the sites where ground detection is less of a problem, ground detection is absent when the pressure level on which T_r is based was 120mb above the surface. Ground detection was determined by examining the cloud counts for the individual pixels making up the 9-pixel area (see below) representing the site. Evidence for ground detection is readily apparent as an aberrant count in pixel locations corresponding to the highest local terrain. The pressure compensation of 120mb is clearly a maximum that corresponds to the greatest ground cooling towards the end of long winter nights. At other times of the night and during other seasons of the year, the required pressure compensation would be less. This was taken into account in the algorithm dealing with the ground detection problem.

It was found that ground detection is eliminated at all sites when the pressure altitude reaches 200mb above the surface. The main reason for differences between the sites appears to be the proximity of the rawinsonde station to the site. In the area and site analysis a generally applicable method for dealing with the ground detection problem was sought. For this reason, any differences between sites was represented as an offset pressure adjustment between zero and 80mb and the remaining 120mb was modeled as a layer of variable thickness in terms of the night length.

A solar time clock was used to compute the local apparent time of the satellite image (t_si), sunrise (t_sr), and sunset (t_ss). From this information the length of the night (t_nl), was computed. A reference time of one hour after sunrise (t_sr + 1) was determined to be the time when ground effects are no longer evident from the night before. The number of hours between the reference time and the satellite image time (t_sr + 1 - t_si) was computed. It may take some hours for the air to be cooled by the ground after sunset but cooling of the surface itself commences directly after sunset. In summer, residual heat slows the onset of ground cooling while in winter the opposite is true. Accordingly a night-time cooling period (t_nc) is computed in proportion to night length as follows:

t_nc = t_nl + [t_nl -12]/2 (5.9)

Cooling is assumed to start t_nc hours before t_sr + 1 and is increased to a maximum at t_sr + 1. If the satellite image time is less than t_nc hours before (t_sr + 1), the amount of cooling that has occurred at the time of the satellite image time is translated into a pressure compensation (P_sc) that must be subtracted from P_s to find the pressure level on which T_r is based, as follows:

P_sc = 36 ln [(t_nc) - (t_sr + 1 - t_si)] +20 (in mb) (5.10)

This relationship is graphed in Figure 17. A logarithmic function is used since this relationship describes the manner in which temperature drops at night after sunset. A pressure correction is used rather than a temperature correction because the temperature profile above the surface is known from the rawinsonde data. In this way, available knowledge on how the temperature drops with height above the altitude of the site is used in determining T_r. This is preferable to simply subtracting a constant temperature offset from T_s. If the satellite image time is not in the time window when ground cooling is occurring, then P_sc = 0.

As noted above, in the site analysis, any additional pressure adjustment required to avoid ground detection at a particular site is accomplished by means of a customized offset between zero and 80mb. In the area analysis, where digital terrain heights are used, a universal offset of 100mb was applied. This value takes into account that digital terrain heights are typically about 500m lower than the actual terrain heights. However, since the difference between actual terrain heights and digital terrain heights varies considerably depending on the shape of the local terrain the possibility of ground detection remains. Nevertheless the effect is minimal. Since ground detection affects only one or two pixels in the 9-pixel area used to determine sky cover (see below), maps showing the “Usable” fraction may be considered free of ground detection problems. Over low terrain the 800mb pressure level (~2000m) is used to define T_r in the area analysis. This ensures that the ground is not being detected while lower level cloud (e.g. coastal cloud) that may extend above sites of interest is included.

Figure 17. Graph of the relationship used to determine pressure level compensation (mb) at night.

The procedure for cloud detection in the analysis that follows uses observations made at both 6.7µm and 10.7µm. First, the 6.7µm imagery is used to determine the existence of transparent or opaque cirrus at high altitude. If a pixel is determined to have opaque cirrus then the final cloud cover classification for that pixel location is “opaque” since the corresponding pixel in the 10.7µm image would also give an opaque signature. However, if a pixel is either clear or transparent from the 6.7µm image analysis, the corresponding pixel in the 10.7µm image is examined. If cloud is detected in that pixel then the pixel location is classified as opaque. If not, then pixel locations classified respectively as clear or transparent remain clear or transparent.

The sky cover classifications described in the previous paragraph are the extent of those possible for individual pixels. The clear fraction, based on the classification described above, may be considered as an upper limit for the fraction of time that observing conditions are photometric. This is the case because:

(i) Sub-pixel scale cloud elements that are sufficiently small and/or sparse may lead to a pixel with such cloud elements being classified “clear”

(ii) A larger cloud element located partly in two or more pixels may result in the individual pixels being classified as clear if a sufficiently large fraction of the pixels are cloud free.

(iii) Pixels with UTH values near the Clear-Transparent threshold may not be purely photometric

A more accurate determination of clear (hence photometric) and partly cloudy (spectroscopic) conditions can be made using a cluster of pixels to represent the site instead of an individual pixel. As shown schematically in Figure 18, a 9-pixel area may be used to represent the astronomical “sky” at the site. At the level of the Tropopause (about 12km), for an observer on the ground viewing the sky, this 9-pixel area would correspond to the sky within approximately 60^o of zenith.

The number of pixels within the area for each cloud cover category can be counted and that count used to provide a more accurate measure of observing conditions. For example, if cloud elements are in the area, even if most are sub-pixel scale, it is likely that at least one of the 9 pixels will have either a transparent or opaque signature. Thus, if all nine pixels in the site area are simultaneously clear one can be fairly confident that observing conditions are indeed photometric. For the 9-pixel area the following classification scheme of cloud cover and observing conditions was used:

Clear (Photometric): All 9 pixels are clear

Transitional (Spectroscopic): 6-8 pixels are clear (1-3 pixels are transparent or opaque)

Opaque (Unsuitable for astronomy): 5 or fewer pixels are clear

2	3	4
9	*Site 1	5
8	7	6

Figure 18. Schematic diagram showing the 9-pixel site area in plan view (left) and cross-section (right). At left, each square represents a 10km x 10km pixel in the satellite image (North is towards the top of the page). The numbers shown in the figure are used to reference the pixel locations. At right, assuming a site altitude of 4km, at Tropopause level (approximately 12km), the “sky” encompassed by the 9-pixels corresponds approximately to an area of observation within 62^o of zenith.

In order to verify the accuracy of the satellite measurement of observing quality, a comparison was made with records of observing conditions at San Pedro Martir Observatory (SPMO) for a one year period (June 1997 to May 1998). Since 1982 a record of observing conditions has been kept for SPMO (Tapia, 1992). Using periods of “half-nights”, conditions were classified as Photometric (less than 15% cloud cover or no more than 30 minutes of cloud cover in a 5 hour period) or Spectroscopic (more than 15% but less than 65% cloud cover). These definitions are fairly similar to the satellite-based categories defined above. Figure 19 is a plot of the monthly values. In some months, for the ground-based observations, less than half of the nights were sampled. For the satellite, observations are made every night, typically three times per night. The annual figures for both photometric and spectroscopic fractions are shown in Table 8.

Figure 19. Photometric fraction by month at San Pedro Martir Observatory for the period June 1997 to May 1998 as determined from satellite and ground-based observations.

Table 8. Photometric and spectroscopic fractions for San Pedro Martir Observatory for the year June 1997 to May 1998 from satellite and ground-based observations.

	% Photometric	% Spectroscopic	% Useable
Satellite	69.8	11.8	81.6
Ground	67.5	15.6	83.1

It is clear from this comparison that there is good agreement between satellite-based and ground-based measurements of observing conditions for San Pedro Martir Observatory. Differences in the fractions obtained for each observing method are consistent with differences in the definitions of what constitutes photometric or spectroscopic conditions. Similar levels of agreement were found at Paranal Observatory (Erasmus and van Staden, 2001).