on the expected performance of a solar oscillation network

ON T H E E X P E C T E D P E R F O R M A N C E OF A S O L A R

O S C I L L A T I O N N E T W O R K

F R A N K H I L L

National Solar Observatory, National Optical Astronomy Observatories*. P.O. Box26732, Tucson, AZ 85726-6732, U.S.A.

and

G O R D O N N E W K I R K , J r .

High Altitude Observatoo', National Center for Au~ospheric Research**, P.O. Box 3000, Boulder, CO 80307, U.S.A.

(Received 5 June; in revised form 7 November, 1984)

Abstract. We have estimated the performance of several hypothetical ground-based networks intended to provide continuous observations of solar oscillations for one year. These networks were composed of from 2 to 6 stations distributed both in longitude and between the northern and southern hemispheres. Weather patterns at each site were simulated using a 4 parameter climate model and the results analyzed to yield the duty cycle of the representative networks.

The results indicate that a 2 station network might achieve a 60).o annual mean duty cycle, 3 stations might provide 75~ 4 stations might yield 822.o, and 6 stations might give a 93% annual mean duty cycle. Comparison of an existing 6 station network with our model of the same network suggests that the modelling procedure is realistic provided that the estimates of the climate parameters are accurate.

To illustrate the influence of such networks on observations of solar oscillations, we have created a synthetic time-line of solar velocities from published data and analyzed the power spectrum of the signal as 'observed' by various networks.

1. Introduction

The analysis of solar oscillations provides an extraordinary opportunity for under- standing the interior structure and dynamics of the Sun. In principle, precise observations of the frequencies of the various modes may be inverted to determine such important characteristics as the run of temperature and density, the profile of angular velocity, and the dominant modes of convection in the sub-photospheric levels. How- ever, two empirical requirements must be met for a successful inversion of solar oscillation data: one must have accurate and precisely measured frequencies and the correct identification of the modes. The first requirement demands that the observations cover a long span of time in order to provide sufficiently high frequency resolution in the power spectra. The second requirement implies that the resultant spectrum of the oscillations should not contain spurious 'lines', such as are produced by periodicities in the observing window. It is well known that power spectra computed from observations containing periodic gaps, such as those caused by the diurnal rising and setting

* Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation. ** NCAR is sponsored by the National Science Foundation.

Solar Physics 95 (1985) 201-219. 0038-0938/'85.15 ,�9 1985 by D. Reidel Publishing Compa~o'

202 FRANK HILL AND GORDON NEWKIRK, JR.

wavenumbers per hemisphere of 0, �89 and 1, respectively. In terms of these functions of the Sun, are inevitably contaminated by 'side bands' due to the gap structure. Each real feature in the solar oscillation power spectrum is then flanked by side bands which represent the Fourier transform of the gap structure. The presence of a complex array of side bands superposed on the real spectrum severely confuses an already dense spectrum of solar oscillations and makes correct identification of the modes difficult.

Several approaches are available to overcome, at least partially, the natural limitation of a single, mid-latitude solar observatory in meeting these demands upon the continuity of the data - locate the observatory at either the North or South Pole, fly a satellite observatory in either the proper polar-retrograde orbit or about a Lagrangian point of the Sun-Ear th-Moon system, establish a network of observatories spread out in longitude at mid-latitudes, or mathematically compensate for the missing data. Obser- vations obtained from the South Pole during Austral summer may satisfy the criterion of an uninterrupted series but have a maximum, practical length of about 5 days (e.g. Harvey et aL, 1982; Grec et al., 1983; Stebbins and Wilson, 1983). This is far short of the duraton of about 4 months required to obtain the frequency resolution of 0.1 ~tHz demanded by many investigations. Groups both in Europe and in the United States are actively studying the possibilities of observation of oscillations from space. Mathe- matical restoration of the spectrum by the maximum entropy gap-filling technique (Fahlman and Ulrych, 1982) is extremely attractive but in practice appears to require data with a mean duty cycle of about 60% to be successful. This study evaluates the expected ability of several ground-based networks to provide an as nearly as possible unbroken string of solar oscillations covering one year and its influence on the resultant power spectra. We have not attempted to evaluate the efficacy of any of the restoration techniques to improve the observations still further.

2. Method

In the hope of assessing not only the expected performance of a network but also the reliability of that expectation, we have employed two approaches in our evaluation. In the first approach, the actual records of the minute-by-minute visibility of the sun by a well established network of He flare patrol stations were analyzed for an interval of one year. In the second case, climatological weather patterns at each of six sites of a hypothetical network were approximated by a four-parameter climate model; and the resulting coverage at the individual sites were combined to yield the performance of several possible networks made up of various sub-sets of the six stations. In both cases, we evaluate the performance by calculating the mean duty cycle of the network and an approximate power spectrum of a synthetic series of solar oscillations as would have been observed by the network. Comparison of this 'observed' spectrum with one derived from the uninterrupted series shows clearly the extent of degradation imposed on the spectrum by incomplete observations.

For the analysis of an actual network, we made use of the records maintained by the National Geophysical Data Center, NOAA, Boulder, Colorado of solar flare obser-

ON THE EXPECTED PERFORMANCE OF A SOLAR OSCILLATION NETWORK

TABLE I

Parameters of the flare patrol stations based on climatological data

203

Station Symbol Lat. Long. p Jan. r Jan. # Jul. r Jul.

Ramey, Puerto Rico RA 18N 66W 0.60 5d 0.63 !d Holloman, New Mexico HO 33N 106W 0.60 5d 0.80 5d Palehua, Hawaii PA 21N 158W 0.50 5d 0.60 ld Purple Mt., China PM 32N 119E 0.40 5d 0.40 ld Culgoora. Australia CU 30S 149E 0.60 ld 0.75 5d Bucharest, Romania BU 44N 26E 0.30 5d 0.80 ld

vatories coooperating in the International Data Interchange originally established during

the International Geophysical Year. The network, consisting of six sites distributed

more or less evenly in longitude (Table I), consisted of three of the U.S. Air Force

S O O N (Solar Optical Observatory Network) sites at Palehua, Hawaii; Ramey, Puerto

Rico; and Hol loman, N e w Mexico, plus the three stations at Bucharest Observatory,

Romania, Purple Mountain Observatory, China, and Culgoora, Australia. The minute-

by-minute coverage of this network is depicted for one year in Figure 1, in which black

corresponds to periods of no observations. To calculate the power spectrum of these

records one need only translate them into a window function consisting of the value 1

12

0

12

0

12

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9 0 180 2 7 0 5 6 0

D A Y O F Y E A R

Fig. I. Performance of the actual Bare patro] network composed of 6 stations (Ramey, Holloman, Palehua, Purple Mt., Culgoora, Bucharest) for the year: December 198l through November 1982. Black represents

times of no observations.

204 F1L&NK HILL AND GORDON NEWK1RK, JR.

for periods when the Sun was visible and 0 for all other times. Since we express the window function with a temporal resolution of 2 min and a total length of 262 144 (2 ~3)

points corresponding to 524288 min (364.09 days), the power spectra have a frequency resolution of 31 .7nHz (3.17 • 1 0 - S s ~) and a Nyquist frequency of 8 .33mHz (8.33 • 10 3 s - i). Of course, the mean duty cycle of a network is simply the sum of

the window function divided by the total length of the observing period.

In addition to examining this actual network, we devised approximate models of the weather patterns at six additional observatory sites. Table II, chosen to provide both

a broad distribution in longitude and an even division between northern and southern hemispheres to decrease the influence of widespread cloudiness during the winter

months. Detailed records of cloudiness for all these stations are not easily available; and

we made use of published climatological data on mean insolation (Landsberg et al., 1965) to characterize each of the sites.

The visibifity of the Sun at each station is characterized by two parameters: p, the

mean seasonal probability of clear sky, and r, the mean interval in days between cloudy days. We assume that the entire year can be represented by two 'seasons' typified by

the climatological data for January and July. The values of p are estimated from world maps while those of r were established to mimic the influence of large-scale weather patterns and/or the diurnal cycle at each station. Only two values of z appear in Tables

I and II. z = ld simulates the diurnal buildup of clouds around local noon, which characterizes many stations in the summer while T = 5d simulates the passage of

large-scale cyclonic systems, which dominate winter weather. Although no doubt the

parameters for the individual stations can be 'tuned' to bring about a better simulation,

we consider the current values as adequate for a first approximation of the performance of a representative network.

TABLE II

Parameters of the hypothetical network based on climatoloNcal data

Station Symbol Lat. Long. p Jan. z Jan. p Jul. z Jul.

Izafia, Canary Isl. IZ 28N 16W 0.65 5d 0.85 ld Las Campanas, Chile LC 29S 70W 0.70 5d 0.50 5d Haleakala, Hawaii HA 20N 156W 0.60 5d 0.70 ld Culgoora, Australia CU 30S 149E 0.60 ld 0.75 5d Udaipur, India UD 24N 73E 0.90 5d 0.50 ld Sutherland, S. Africa SU 32S 20E 0.80 ld 0.75 5d

These parameters are used to construct a time-fine of solar visibility for each station for one year using the following model. Since we assume that it is either clear or cloudy, each clear period is followed by a cloudy period. Because many clear and cloudy periods occur in a six-month season, we can assume that the number of clear and cloudy periods are equal. The expected total duration of clear time, during a period T is pT and each clear period lasts an average length z. Thus we expect an average of pT/z clear periods

ON THE EXPECTED PERFORMANCE OF A SOLAR OSCILLATION NETWORK 205

during the time T. The expected total length of cloudy weather during the same period is (1 - p)T and, since the number of clear and cloudy periods is equal, the average length of a cloudy period is (1 - p)@. Of course significant departures from these average durations of clear and cloudy periods are to be expected. According to Evans (1969), a reasonable approximation to the observed duration of cloudy weather is provided by the gamma probability distribution, which has the form

4t - - e 2,/~ ( 1 ) ~2

Expression (1) simply gives the probability of an uninterrupted string of cloudiness t-minutes long and forms the basis for the construction of a synthetic time-line using a Monte Carlo model in which, starting with the first minute of the year, we build up a realization of the entire year using the average length of a clear or cloudy interval at that minute and the gamma distribution to determine the length of each interval. As with all Monte Carlo simulations of random processes, one must generate several simulations to assess the statistical stability of the model. As an additional refinement, we adopt two approximations to the seasonal variations of p and ~. In the first, January values were applied to the months of October to March and July values to April to September ('step function'). In the second, the values for the intervening months were linearly interpolated between the January and July values ('linear function').

To create the final time-line for each station, the simulations were broken up into appropriate day-night cycles generated by the ephemeris equations for the rising and setting of the Sun at the latitude and longitude of the site with the additional constraint that observations cannot begin until one hour after sunrise and must cease one hour before sunset. Of course, all timelines of the individual sites must be translated into Universal Time in order to create time lines for networks composed of combinations of stations. In order to estimate the accuracy of the modelling procedure, we also calculated the performance of the Flare Patrol Network using the parameters in Table I.

3 . R e s u l t s

The statistics of the resulting annual mean duty cycles for the six individual stations of the hypothetical network appear in Table III. A total of 10 realizations of the window function were calculated for both the linear and step functions. Table III provides the mean and standard deviation of the duty cycles for both functions and for the average of the two. The expected duty cycle, defined as the probability of clear weather averaged over the year multiplied by the calculated fraction of daylight hours, appears in the last column. As can be seen, the step function generally yields a higher duty cycle than the linear function and the linear function gives a result that is nearly equal to the expected duty cycle. However, the sample is rather small, and the difference between the expected duty cycle and that yielded by the step function is probably not significant.

We have examined the performance of a total of 10 different networks (Table IV),


T A B L E III

S ta t i s t ica l p rope r t i e s o f ind iv idua l site du ty cycles

S t a t ion S tep L inea r C o m b i n e d

ave. st.d. ave. st .d. ave. st.d. exp.

IZ

L C

M A

C U

U D

S U

0.330 0.008 0.313 0.006 0.321 0.007 0.313

0.255 0 .017 0.250 0 .010 0.253 0.014 0.249

0.289 0.012 0.271 0.014 0.280 0.013 0.271

0.293 0.005 0.280 0.011 0.286 0.008 0.280

0.304 0.007 0.286 0.010 0.295 0.009 0.292

0.340 0.007 0 .324 0 .010 0.332 0.009 0.321

T A B L E IV

H y p o t h e t i c a l n e t w o r k s

N e t w o r k No. S t a t i ons L o n ~ t u d i n a l

s e p a r a t i o n

21 H A 176 ~

S U

22 I Z 165 ~

C U

23 H A 140 ~

I Z

24 L C 143 ~

U D

31 IZ 140 ~

H A 131 ~

U D

32 H A 131 ~

U D 143 ~

L C

33 C U 129 ~

S U 90 ~

L C

41 H A 86 ~

L C 90 ~

S U 129 ~

C U

42 IZ 89 ~

U D 76 ~

C U 55 ~

H A

6 IZ 54 ~

LC 86 ~

H A 55 ~

C U 76 ~

U D 53 ~

S U

ON THE EXPECTED PERFORMANCE OF A SOLAR OSCILLATION NETV~r 207

produced from various combinations of these six hypothetical network sites. It is

obvious that, in any individual network, it is desirable that the stations be as evenly

spaced in longitude as possible. An evolutionary approach wherein one starts with two

stations and then adds stations to the existing network would be represented by

networks 23, 31, 42, and 6. Table V presents a statistical summary of the performance

TABLE V

Statistical properties of network duty cycles

Network Step Linear Combined

ave. st.d. ave. st.d. ave. st.d.

21 0.629 0.014 0.595 0.020 0.612 0.017 22 0.621 0.008 0.593 0.014 0.607 0.011 23 0.595 0.014 0.565 0.014 0.580 0.014 24 0.549 0.018 0.528 0.014 0.539 0.016 31 0.779 0.013 0.744 0.016 0.762 0.015 32 0.742 0.014 0.710 0.016 0.726 0.015 33 0.743 0.015 0.725 0.013 0.734 0.014 41 0.844 0.009 0.825 0.012 0.835 0.011 42 0.853 0.007 0.823 0.003 0.841 0.008

6 0.942 0.003 0.928 0.005 0.935 0.004

of the networks in a manner similar to that present in Table III. The expected duty cycle

cannot be simply calculated for a network of several stations. Figure 2 illustrates the

dependence of annual mean duty cycle on the number of stations N in the network taken

from the statistical properties summarized in Table V.

It is of some interest to compare this empirical dependence of duty cycle upon number

of stations with a simple probabilistic model which assumes that all stations have the

same probability of clear weather and that an uninterrupted 24-hour string of obser-

vations will be produced if at least m of n stations, which are distributed evenly in

longitude, is clear. Such a crude model ignores the consequences of all the cloudy

stations falling on one side of the Earth and any spatial coherence in weather patterns

which may exist. The probability that at least m of N independent stations are clear is

where

N

Dmx = Z ~ , (2) j = m

y ( 1 - p?~-JN! 8j= j!(N -j)!

We may identify the probability D,,,N with the mean duty cycle. One might expect that m = 2 would yield a very optimistic and m = 3 a conservative approximation to the conditions required to provide an uninterrupted run. Figure 2 shows clearly the rise in


1.0

0.9

0.8

0.7

0.6

D 0.5

0 . 4 m

0 . 5 -

0 . 2 -

0.1 -

1 I I I

f /

m = 2 / / e /

/ / /~ /

/ / / /

e / / �9 ,/ / / /

/ /

/ /

/ - /

/ /

/ / m = 5

X

Variat ion of Duty Cycle with Number of Stations

�9 Hypothetical Networks (Table 4) x Flare Patrol Network (Table 6)

0 I I I I I I 0 I 2 :5 4 5 6 7 N

Fig. 2. A plot of the dependence of the combined duty cycle, D, on the number of stations, N, in the sample hypothetical networks (circles). The cross represents the mean annual duty cycle for the Flare Patrol Network for the year December 1981-November 1982. The curves represent the expected duty cycle approximated by Equation (2) for m = 2 and 3 and p = 0.71, the mean of the stations in the hypothetical

network.

mean duty cycle of both the hypothetical networks and the model described by Equation (2) with increasing number of stations.

The influence of a duty cycle less than unity and its window function upon the spectrum of solar oscillations is most easily appreciated by modulating a synthetic time series of oscillations by the window function of each network. To this end we produce an artificial solar velocity signal by summing a set of sinusoids containing observed solar frequencies and amplitudes. The modes incorporated in this model are the low degree 5" modes as published by Grec et al. (1983) and Scherrer et al. (1983). It contains a total of 98 modes with l values from 0 to 5, n values from 12 to 35, frequencies from 1886.5 to 5074.5 ~tHz, and amplitudes from 2.6 to 24.5 cm s - 1. Since the signal is used simply to demonstrate the effects of the windows, we did not apply any correction for the different spatial sensitivity of the two data sets. We then generate a one year time-line of the velocity and multiply it by the window functions of each network. The modulus of the Fourier transform of the resulting time-line is the power spectrum 'observed' by


3000

I I I

,1.. 1 l[,. ....... 3100 3200 3300 3400

. Llll

3500

Fig. 3. A portion of the synthetic spectrum of solar oscillations from 3000 to 3500 laHz as would be observed with a duty cycle of 100}o for a period of one year. The ordinate represents the square root of power on a linear scale with the strongest feature at 3370 laHz establishing the scale. The same represen- tation of this portion of the spectrum showing 24 modes is used in all subsequent figures of this type.

each network; and the deleterious effects of gaps in the data can be ascertained by comparison with the spectrum produced by a 100}o duty cycle. We present several examples of this process.

A portion of the artificial spectrum as would be obtained after one year of observation with a 100~o duty cycle appears in Figure 3. The frequency region displayed covers 3000 to 3500 gHz, with 24 modes present. A very low level of featureless noise produced by the one-year window function and numerical truncation in the sine-wave generation is visible. All subsequent figures of power spectra show this same fi'equency band with the scale in the square root of power set by the observed amplitude of the 3370 gHz mode. Figure 4 shows the same region as it would be distorted by a typical observing year at Sacramento Peak Observatory. The overwhelming confusion generated by the ]/day sidelobes is clearly evident.

The spectrum as would be observed by the Flare Patrol Network (Table I) appears in Figure 5. While most of the high amplitude modes are clearly visible, a residual diurnal cycle overwhelms the low amplitude components. This residual day/night cycle is clearly visible in the time-line of the network as a lack of observations at about 8-12 hr UT throughout the year (Figure 1). This time period is covered only by the station at Bucharest, whose individual time-line shows that the site provided minimal coverages of about 2 hr per week. The overall duty cycle of this network is 65 ~ o.

The spectra 'observed' by the hypothetical networks (Table IV) are illustrated in Figures 6 through 9. Each figure displays the spectrum resulting from a single realization


[LILLLilL ,LJJ, L

I I

I I

3000 3 I00 3200 3300 3400 3500

Fig. 4. A portion of the synthetic spectrum of solar oscillations as would be observed during a typical year at Sacramento Peak Observatory. The overwhelming confusion generated by the 1/day sidelobes and

harmonics is clearly evident.

I I I

3000 3100 3200 3300 3400 3500

Fig. 5. A portion of the synthetic spectrum of solar oscillations as would have been observed by the Flare Patrol Network from Dec. 1981 to Nov. 1982. The diurnal sidelobes are present with enough power to mask

some of the lower amplitude solar features.

O N T H E E X P E C T E D P E R F O R M A N C E O F A S O L A R O S C I L L A T I O N N E T W O R K 21 l

I I I

3000 31 O0

Fig. 6a.

3200 3300

,d, 3 4 0 0

Network 21, longitude separation = 176 ~

I I I

3000 3100

Fig. 6b.

5200 3300 3 4 0 0

Network 24, separation = 143 ~

3500

j 3500

Fig. 6a-d. Portions of the synthetic spectra of solar oscillations as would be observed by the 4 different 2-station networks considered. The day/night sidelobes begin to dominate the lower amplitude solar modes

as the longitude separation between the two stations gets further from 180 ~ .


J~

3000

,,H.,[,,,.I,L,IJ .,l,,,, ,, ., 3100 3200 3300

Fig. 6c. Network 23, separation = 140 ~

III, 3400

L.[,LII 3500

3000

I I [

3100

Fig. 6d.

3200 3300 3 4 0 0

Network 24, separation = 143 ~

3500


t I I

_, 1], ,,L, ....... 3200 3300 3000 3100 3400

Fig. 7a. Network 31.

,~ I.IL

3500

ilL J, .... 3000 3 I00 3 2 0 0 3 5 0 0 3 4 0 0 3 5 0 0

Fig. 7b. Network 32.

Fig. 7a-c. Portions of the synthetic spectra of solar oscillations as would be observed by the 3 different 3-station networks considered. The diurnal sidelobes are still evident, but with less amplitude than in the

2-station networks.


vrp

JI.L,.L. L,L,,. 3000 3 I00

I I

320"0 3300 3400 3500

Fig. 7c. N e t w o r k 33.

of each network. Figure 6 shows the spectra observed by the four combinations of two-stations (Networks 21-24). It is obvious that networks 21 and 22 (Figures 6a and b) are the cleanest with less evidence of diurnal cycle contamination than networks 23 and 24. This difference is due to the combination of a higher mean duty cycle (Table V) and a separation that is much closer to 180 degrees for the first pair of networks than for the second. Figure 7 gives the spectra observed by the three-station networks (31-33). Comparison with Figure 3 reveals some evidence of residual, diurnal sidelobes, but with amplitudes greatly reduced from those apparent in the two-station networks. Figure 8 shows the spectra from the two four-station networks (41 and 42) with still smaller sidelobes; and Figure 9 shows the spectrum form the full 6 station network. As might be expected from the mean duty cycle of 93 ~ for this latter network, the spectrum is practically indistinguishable from the original spectrum shown in Figure 3. However, an elevated level of background noise could still make the identification of modes of low amplitude exceedingly difficult.

Since the visual comparison of these complex spectra is difficult, we have quantified their differences by comparing the number of spurious peaks above two thresholds in Figures 4 through 9. Each spectrum contains all 24 peaks which appeared in that segment of the original spectrum shown in Figure 3. In addition, spurious peaks due to the diurnal gaps appear. The fraction of spurious peaks, Fs, is then (N-24)/N, where N is the total number of peaks in the spectrum. The two thresholds chosen were 5 ~o and

ON THE EXPECTED PERFOR/vlANCE OF A SOLAR OSCILLATION NETWORK 215

3 0 0 0

I I I

3 I00 3200 3300

1

3 4 0 0

i i1-*- I

3500

Fig. 8a. Network 41.

I I

[lilt .... t .... J ...... ill L, 3 0 0 0 3100 3 2 0 0 3 3 0 0

Fig. 8b. Network 42.

I I

L J ] .~

3 4 0 0 ~l -

5500

Fig. 8a-b. Portions of the synthetic spectra of solar oscillations as would be observed by the 2 different 4-station networks considered. It is still possible to see the diurnal sidelobes centered on the larger amplitude

solar modes.


I I I

l,.[ll _l ...... 5000 5100 :5200 5 5 0 0

it. ~t.I �9

:5400 3500

Fig. 9. A portion of the synthetic spectrum of solar oscillations as would be observed by the hypothetical 6-station network. This figure is almost identical to the power spectrum obtained with a 100~.o duty cycle,

as displayed in Figure 3.

10 ~ of the height o f the 3370 g H z mode . The results appear in Tab le VI, which shows

that above a 1 0 ~ th resho ld all the ' real ' peaks are u n a b m i g u o u s l y recovered free of

spur ious peaks by mo d e l ne tworks with 3 or more s ta t ions. W h e n the th reshold is

d r o p p e d to 5 ~o, however , n o n e of the ne tworks are able to comple te ly e l iminate spur ious

peaks a l though in a 6-s ta t ion n e t wo rk only 4~o o f the peaks are spurious.

TABLE VI

Fraction of spurious peaks

Network 10 }'o 5 ~ o

N Fs N Fs

Diurnal (1) 72 0.67 118 0.80 Flare patrol (6) 50 0.52 84 0.71 21 (2) 43 0.44 89 0.73 22 (2) 36 0.33 85 0.72 23 (2) 53 0.55 96 0.75 24 (2) 54 0.56 98 0.76 31 (3) 24 0.00 32 0.25 32 (3) 24 0.00 34 0.29 33 (3) 24 0.00 38 0.37 41 (4) 24 0.00 26 0.08 42 (4) 24 0.00 28 0.14

6 (6) 24 0.00 25 0.04

( ) indicates number of stations.

O N T H E E X P E C T E D P E R F O R M A N C E O F A S O L A R O S C I L L A T I O N N E ' I ~ r O R K

TABLE VII

Parameters of the flare patrol stations based on 1982 records

217

Station Symbol Lat. Long. p Jan. ~ Jan. p Jul. r Jul.

Ramey, Puerto Rico RA 18N 66W 0.39 0.07d 0.36 0.07d Holloman, New Mexico HO 33N 106W 0.50 0.08d 0.59 0.09d Palehua, Hawaii PA 21N 158W 0.21 0.05d 0.32 0.04d Purple rot., China PM 32N 119E 0.24 0.04d 0.09 0.02d Culgoora, Australia LM 22S 114E 0.67 0.06d 0.79 0.06d Bucharest, Romania BU 44N 26E 0.04 0.05d 0.05 0.06d

4. Discussion and Conclusions

The model used to generate the window functions for the networks is approximate and

yields surprisingly high duty cycles and freedom from diurnal side-lobes for the more populous networks. This apparent disparity is emphasized by comparison of the

hypothetical six station network with the existing six station Flare Patrol Network. The

hypothetical one has a mean duty cycle of 93 ~/o compared with 65 ~o for the Flare Patrol Network. One can identify several factors which can be expected to introduce such a bias:

(1) The climatologically based model for insolation is unrealistically optimistic. Since the climatological data on insolation was derived from standard meteorological data consisting of four reports per day, short term interruptions in solar visibility may not

be adequately covered. In addition, our model specifically ignores the presence of spatial correlation in weather patterns, which become important with closely spaced stations.

(2) The performance of the hypothetical network does not include instrumental downtime.

(3) The subset of stations chosen from the Flare Patrol Network is not optimally sited. Its most serious deficiency apparent in Figure 1 is the day-night cycle caused by

the absence of observations from roughly 08 : 00 to 12 : 00 UT, hours covered only by Bucharest.

To explore further the difference between the hypothetical and the Flare Patrol Network, we analyzed the actual time lines of Sun visibility for each individual station in the Flare Patrol network during 1982. The data were analyzed to provide p and r for

January and July. The results are tabulated in Table VII which shows that, except for Culgoora, the measured values of p are substantially lower than the estimated values given in Table I. In particular, Bucharest has values that are an order of magnitude lower than the estimates - a difference which is undoubtedly caused by non-meteorological factors. In addition, the values of z are on the order of 0.1 day, or a few hours, rather than the 1 or 5 days we have used for the model. While these smaller values do not affect the overall duty cycle, which depends primarily on p, an additional simulation shows


that they do slightly affect the synthetic power spectra. Using a value of 0.05 day for T, a number of very low amplitude peaks are added to the spectra produced by the networks. The amplitude of these peaks, however, is on the order of only 2 3 to 3}o of the amplitude of the 3370 gHz peak. Thus, their presence oes not alter Table VI and would not degrade the performance of a network provided that an amplitude threshold of 5 ~o or greater was used to distinguish real from spurious peaks.

When the values for p and r given in Table VII are used as input to the model, the resulting theoretical duty cycle for the combined 6 station Flare Patrol network is 62% in excellent agreement with the observed 65 ~o. Thus, we feel that the modelling procedure is realistic, provided that the input data is accurate.

It appears that the climatologically based models predict performance characteristics which are somewhat optimistic when compared to that of an actual network. Small scale insolation maps generally provide inadequate estimates for p, especially for certain sites such as the Canary Islands where high mountain sites are typically above the lower lying cloud level. In order to assess realistically the performance of any proposed network, actual records on the visibility of the Sun throughout the year must be obtained for each of the candidate sites. This may be done by analyzing existing observatory records (when they exist), or by setting up pyroheliometers. Although the latter approach yields a homogeneous record, experience (Brandt et aL, 1979) indicates that the presence of thin cirrus, which may be deleterious to solar oscillation observations is inadequately recorded by simple pyroheliometers.

Our study suggests that even a two station network may produce data that is largely free of the I/day sidelobes if the sites are close to 180 degrees apart in longitude in carefully chosen locations. Of course, a two station network is particularly vulnerable to adverse weather.

In conclusion, this study suggests that a six station network would potentially provide observations of solar oscillations which would be nearly indistinguishable from uninterrupted coverage, and that even a two station network with carefully chosen sites might be adequate for studies that could tolerate the presence of some sidelobe structure. However, the performance of a hypothetical network depends on the accuracy of the input parameters to the climate model. Clearly, data on the visibility of the Sun for all stations of a proposed network covering an adequate period of time (~ 3 yr) are required to make a realistic assessment of performance.

Acknowledgements

We wish to acknowledge helpful discussions with the other members of the National Solar Observatory Oscillations Network Group: Tuck Stebbins, John Leibacher, Jack Harvey, Tom Duvall, Dave Hathaway, and Ray Smartt; and with Dick Dunn and Jack Zirker; and with Roy Jenne, National Center for Atmospheric Research. We are grateful to John McKinnon and Daniel Wilkinson of the National Geophysical Data Center, National Oceanographic and Atmospheric Administration, Boulder for supplying data


on the o p e r a t i o n o f the F la re Pa t ro l N e t w o r k and to T i m o t h y B r o w n , H igh Al t i tude

Obse rva to ry , for a cr i t ical r ev iew of the pape r before submiss ion .

References

Brandt, P. N. and WShl, H.: 1979, JOSO Annual Report, No. 10. Evans, D. S.: 1969, Astron Astrophys. 3, 247. Fahlman, G. G. and Ulrych, T. J.: 1982, Monthly Notices Roy. Astron., Soc. 199, 53. Grec, G., Fossat, E., and Pomerantz, M. A.: 1983, Solar Phys. 82, 55. Harvey, J., Pomerantz, M. A., and Duvall, T.: 1982, Sky Telesc. 64, 521. Landsberg, H. E., Lippmann, H., Poffen, K., and Troll, C.: 1965, World Maps of Climatology, 2nd Edition,

Springer-Verlag, New York. Scherrer, P. H., Wilcox, J. M., Christensen-Dalsgaard, J., and Gough, D. O.: 1983, Solar Phys. 82, 75. Stebbins, R. and Wilson, C.: 1983, Solar Phys. 82, 43.

on the expected performance of a solar oscillation network

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