Engineering topics

Hathaway, David H.

Publications and source records attributed to Hathaway, David H..

At least 73 records · Page 4

NASA NTRS2000

Status of Cycle 23 Forecasts

Forecasts for the amplitude of cycle 23 that were reported prior to the start of, the cycle covered a full range of, values from very small to very large. A forecast reached by the consensus of a panel of forecasters convened at the time of minimum in 1996 [Joselyn et al., 1997] suggested that this cycle would be much larger than average with the smoothed International Sunspot Number reaching a maximum of 160 +/- 30 in the middle of the year 2000. A recent survey of solar cycle prediction techniques [Hathaway et al., 1999] found that the two most reliable techniques for forecasting the cycle prior to its start give similar predictions for this cycle's maximum -- 154 +/- 26 and 153 +/- 33. Curve-fitting and regression techniques can be used with some confidence now that cycle 23 is well underway. These techniques indicate a more modest sunspot cycle with a maximum of 112 + 10 -- only slightly larger than average. The current (May 2000) prediction using the combined predictions from both precursors and curve-fitting gives a cycle amplitude of about 135 +/- 20. This is within the errors given by the consensus and the precursor technique predictions but very close to their lower bounds. Inspection of the characteristics of cycle 23 thus far indicates that in some respects this cycle is an outlier but in other respects it is quite normal.

Hathaway, David H.↗

NASA NTRS1999

A Synthesis of Solar Cycle Prediction Techniques

A number of techniques currently in use for predicting solar activity on a solar cycle timescale are tested with historical data. Some techniques, e.g., regression and curve fitting, work well as solar activity approaches maximum and provide a month-by-month description of future activity, while others, e.g., geomagnetic precursors, work well near solar minimum but only provide an estimate of the amplitude of the cycle. A synthesis of different techniques is shown to provide a more accurate and useful forecast of solar cycle activity levels. A combination of two uncorrelated geomagnetic precursor techniques provides a more accurate prediction for the amplitude of a solar activity cycle at a time well before activity minimum. This combined precursor method gives a smoothed sunspot number maximum of 154 plus or minus 21 at the 95% level of confidence for the next cycle maximum. A mathematical function dependent on the time of cycle initiation and the cycle amplitude is used to describe the level of solar activity month by month for the next cycle. As the time of cycle maximum approaches a better estimate of the cycle activity is obtained by including the fit between previous activity levels and this function. This Combined Solar Cycle Activity Forecast gives, as of January 1999, a smoothed sunspot maximum of 146 plus or minus 20 at the 95% level of confidence for the next cycle maximum.

Hathaway, David H.↗

NASA NTRS1999

Comment on "The Predicted Size of Cycle 23 Based on the Inferred three-cycle Quasiperiodicity of the Planetary Index Ap"

Recently, Ahluwalia reviewed the solar and geomagnetic data for the last 6 decades and remarked that these data "indicate the existence of a three-solar-activity-cycle quasiperiodicity in them." Furthermore, on the basis of this inferred quasiperiodicity, he asserted that cycle 23 represents the initial cycle in a new three-cycle string, implying that it "will be more modest (a la cycle 17) with an annual mean sunspot number count of 119.3 +/- 30 at the maximum", a prediction that is considerably below the consensus prediction of 160 +/- 30 by Joselin et al. and of similar predictions by others based on a variety of predictive techniques. Several major sticking points of Ahluwalia's presentation, however, must be readdressed, and these issues form the basis of this comment. First, Ahluwalia appears to have based his analysis on a data set of Ap index values that is erroneous. For example, he depicts for the interval of 1932-1997 the variation of the Ap index in terms of annual averages, contrasting them against annual averages of sunspot number (SSN), and he lists for cycles 17-23 the minimum and maximum value of each, as well as the years in which they occur and a quantity which he calls "Amplitude" (defined as the numeric difference between the maximum and minimum values). In particular, he identifies the minimum Ap index (i.e., the minimum value of the Ap index in the vicinity of sunspot cycle minimum, which usually occurs in the year following sunspot minimum and which will be called hereafter, simply, Ap min) and the year in which it occur for cycles 17 - 23 respectively.

Wilson, Robert M.↗

NASA NTRS1999

A Survey and Synthesis of Solar Cycle Prediction Techniques

A number of techniques for predicting solar activity on a solar cycle time scale are identified, described, and tested with historical data. Some techniques, e.g. regression and curve-fitting, work well as solar activity approaches maximum and provide a complete description of future activity, while others, e.g. geomagnetic precursors, work well near solar minimum but only provide an estimate of the amplitude of the cycle. A synthesis of different techniques is shown to provide a more accurate and useful forecast of solar cycle activity levels. A combination of two uncorrelated geomagnetic precursor techniques provides the most accurate prediction for the amplitude of a solar activity cycle at a time well before activity minimum. This Combined Precursor Method gives a smoothed sunspot number maximum of 154+/-21 at the 95% level of confidence for the next cycle maximum. A mathematical function dependent upon the time of cycle initiation and the cycle amplitude then describes the level of solar activity for the next complete cycle. As the time of cycle maximum approaches a better estimate of the cycle activity is obtained by including the fit between previous activity levels and this function. This Combined Solar Cycle Activity Forecast gives, as of January 1999, a smoothed sunspot maximum of 146+/-20 at the 95% level of confidence for the next cycle maximum. The success of the geomagnetic precursors in predicting future solar activity suggests that solar magnetic phenomena at latitudes above the sunspot activity belts are linked to solar activity which occurs many years later in the lower latitudes.

Hathaway, David H.↗

NASA NTRS1999

Large-Scale Coronal Heating from the Solar Magnetic Network

In Fe 12 images from SOHO/EIT, the quiet solar corona shows structure on scales ranging from sub-supergranular (i.e., bright points and coronal network) to multi- supergranular. In Falconer et al 1998 (Ap.J., 501, 386) we suppressed the large-scale background and found that the network-scale features are predominantly rooted in the magnetic network lanes at the boundaries of the supergranules. The emission of the coronal network and bright points contribute only about 5% of the entire quiet solar coronal Fe MI emission. Here we investigate the large-scale corona, the supergranular and larger-scale structure that we had previously treated as a background, and that emits 95% of the total Fe XII emission. We compare the dim and bright halves of the large- scale corona and find that the bright half is 1.5 times brighter than the dim half, has an order of magnitude greater area of bright point coverage, has three times brighter coronal network, and has about 1.5 times more magnetic flux than the dim half These results suggest that the brightness of the large-scale corona is more closely related to the large- scale total magnetic flux than to bright point activity. We conclude that in the quiet sun: (1) Magnetic flux is modulated (concentrated/diluted) on size scales larger than supergranules. (2) The large-scale enhanced magnetic flux gives an enhanced, more active, magnetic network and an increased incidence of network bright point formation. (3) The heating of the large-scale corona is dominated by more widespread, but weaker, network activity than that which heats the bright points. This work was funded by the Solar Physics Branch of NASA's office of Space Science through the SR&T Program and the SEC Guest Investigator Program.

Falconer, David A.↗

NASA NTRS1999

The Photospheric Convection Spectrum

Spectra of the photospheric cellular flows are determined from Solar and Heliospheric Observatory/Michelson Doppler Imager (SOHO/MDI) observations. Spherical harmonic decompositions are obtained from the full-disc observations. Fourier decompositions are obtained from the high-resolution observations. The p-mode oscillation signals and instrumental artifacts are reduced by temporal filtering of the Doppler data. The resulting spectra give power (kinetic energy) per wavenumber for effective spherical harmonic degrees from 1 to about 3000. The spectra show distinct peaks representing granules and supergranules but no distinct features at wavenumbers representative of mesogranules or giant cells.

Hathaway, David H.↗

NASA NTRS1998

On the Correlation Between Maximum Amplitude and Smoothed Monthly Mean Sunspot Number during the Rise of the Cycle (from t = 0-48 months Past Sunspot Minimum)

During the rise from sunspot minimum to maximum, the observed value of smoothed monthly mean sunspot number at maximum RM is found to correlate with increasing strength against the current value of smoothed monthly mean sunspot number R(t), where t is the elapsed time in months from minimum. On the basis of the modern era sunspot cycles (i.e., cycles 10-22), the inferred linear correlation is found to be statistically important (i.e., at the 95-percent level of confidence) from about 11 mo past minimum and statistically very important (i.e.. at the 99-percent level of confidence) from about 15 mo past minimum; ignoring cycle 19, the largest cycle of the modern era, the inferred linear correlation is found to be statistically important from cycle onset. On the basis of R(t), estimates of RM can be gauged usually to within about +/- 30 percent during the first 2 yr and to within about +/- 20 percent (or better) after the first 2 yr of a cycle's onset. For cycle 23, because controversy exists regarding the placement of its minimum (i.e., its onset), being either May 1996 or perhaps August 1996 (or shortly thereafter), estimates of its RM are divergent, being lower (more like a mean size cycle) when using the earlier epoch of minimum and higher (above average in size) when using the later-occurring minimum. For smoothed monthly mean sunspot number through October 1997 (t = 17 or 14 mo, respectively), having a provisional value of 32.0. the earlier minimum date projects an RM of 110.3 +/- 33.1, while the later minimum date projects one of 137.2 +/- 41.2. The projection is slowly decreasing in size using the earlier onset date, while it is slowly increasing in size using the later onset date.

Wilson, Robert M.↗

NASA NTRS1998

A Search for Giant Convection Cells on the Sun

Giant convection cells (slow, long-lived cellular flows in the Sun's convection zone with typical diameters greater than about 100,000 km) have been the subject of many searches over the last 30 years. If such flows exist, they should play a key role in structuring the Sun's large scale magnetic field and in driving the large scale axisymmetric flows: the differential rotation and meridional circulation. Detailed observations of the flows in these cells may also allow us to better predict future magnetic field configurations and the solar activity associated with them. Line-of-sight velocity data from the Michelson Doppler Interferometer on the ESA/NASA Solar and Heliospheric Observatory provides us with new opportunities to search for giant cells. This data is free of any atmospheric distortion and has been obtained continuously without any day/night gaps for more than two months at a time. These two-month datasets are important because giant cells are expected to have lifetimes somewhat longer that the Sun's 27 day rotation period. Any reappearance of a flow pattern after 27 days would be an important confirmation of the existence of these cells. The approach taken in this search is to separate the giant cell velocity signal from the other, stronger velocity signals by using a spherical harmonic representation of the spatial structures and a fourier decomposition of the temporal behavior. Any giant cell signal should be characterized by low spatial wavenumbers with temporal frequencies appropriate to the solar rotation of these patterns.

Hathaway, David H.↗

NASA NTRS1998

Mesogranulation as A Distinct Scale of Convection in the Sun

We present evidence for the existence of mesogranulation as a scale of convection distinct from granulation and supergranulation through analysis of full-disk Doppler velocity images of the Sun collected by the Michelson Doppler Imager (MDI) aboard the NASA/ESA Solar and Heliospheric Observatory (SOHO). Our analysis procedures isolate nearly steady flows in the solar photosphere and yield power spectra of convection for spherical harmonic degrees up to I = 1000. Each spectrum exhibits an obvious supergranulation peak at I approximately 130 and a broad secondary peak at I approximately 600 with a distinct break in the spectrum between these peaks at I approximately 300. We believe that this secondary peak is a signature of mesogranulation with typical cell diameters of about 7 Mm. Our standard analysis procedure is to first remove the p-mode oscillation signal by averaging individual Dopplergrams over 17-minute intervals. Next, by fitting to standard functional forms we remove Doppler signals due to the motion of the spacecraft, the convective blueshift, solar rotation including differential rotation, and the meridional circulation in order to produce Dopplergrams dominated by convective motions. By mapping these processed images onto heliographic coordinates and projecting onto spherical harmonics, we produce a power spectrum of solar convection for each 17-minute period. We construct synthetic images and pass them through the same analysis procedure in order to determine the actual solar convection spectrum that reproduces the analyzed results. We find that a small but increasing percentage of high-degree convective power is lost in the analysis as we approach the limit of resolution of the detector but'that the broad, mesogranulation peak at I approximately 600 must be included in the convection spectrum of the synthetic images.

Bachmann, Kurt T.↗

NASA NTRS1998

The Solar Dynamo

The solar dynamo is the process by which the Sun's magnetic field is generated through the interaction of the field with convection and rotation. In this, it is kin to planetary dynamos and other stellar dynamos. Although the precise mechanism by which the Sun generates its field remains poorly understood despite decades of theoretical and observational work, recent advances suggest that solutions to this solar dynamo problem may be forthcoming. Two basic processes are involved in dynamo activity. When the fluid stresses dominate the magnetic stresses (high plasma beta = 8(pi)rho/B(sup 2)), shear flows can stretch magnetic field lines in the direction of the shear (the "alpha effect") and helical flows can lift and twist field lines into orthogonal planes (the "alpha effect"). These two processes can be active anywhere in the solar convection zone but with different results depending upon their relative strengths and signs. Little is known about how and where these processes occur. Other processes, such as magnetic diffusion and the effects of the fine scale structure of the solar magnetic field, pose additional problems.

Hathaway, David H.↗

NASA NTRS1998

Analysis and Modeling of Coronal Holes Observed by CORONAS-1: Morphology and Magnetic Field Configuration - 1

Two low-latitude coronal holes observed by CORONAS-1 in April and June 1994 are analyzed together with magnetic field measurements obtained from Wilcox and Kitt Peak Solar Observatories. To estimate the comparable temperature of these two coronal holes, the YOHKOH observations are also utilized. Using this information, we have constructed three-dimensional magnetic field lines to illustrate the geometrical configuration of these coronal holes. The calculated synoptic maps are used to determine the existence of closed and open field regions of the hole. Finally, we have correlated the characteristics of two coronal holes with observed solar wind speed. We found that the brighter coronal hole has high speed solar wind, and the dimmer coronal hole has low speed solar wind.

Obridko, Vladmir↗

NASA NTRS1998

Comment on the Predicted Size of Cycle 23 Based on the Inferred Three-Cycle Quasi-Periodicity of the Planetary Index Ap

Recently, Ahluwalia [1998] reviewed the solar and geomagnetic data for the last 6 decades and remarked that these data "indicate the existence of a three-solar-activity-cycle quasi-periodicity in them." Futhermore, on the basis of this inferred quasi-periodicity, he asserted that cycle 23 represents the initial cycle in a new 3-cycle string, implying that it "will be more modest (a la cycle 17) with an annual mean sunspot number count of 119.3 +/- 30 at the maximum," a prediction that is considerably below the consensus prediction of 160 +/- 30 by Joselyn et al. [1997] and of similar predictions by others based on a variety of predictive techniques. Several major sticking points of Ahluwalia's presentation, however, must be redressed, and these issues form the basis of this comment. In particular, it is shown that Ahluwalia used inappropriate values of the Ap index in his analysis, that the inferred 3-cycle relationship which Ahluwalia claims for both Ap and SSN does not exist for the previous 6-cycle interval (prior to cycle 17) for SSN, that his inferred fit is only of marginal statistical significance (having r = 0.81), and that two alternative precursor fits (both with r = 0.96 or greater) exist which strongly suggest that R max for cycle 23 will be much larger than forecast by Ahluwalia (namely, about 168-187). Thus, caution must be exercised in accepting Ahluwalia's findings.

Hathaway, David H.↗

NASA NTRS1998

Estimating the Size and Timing of Maximum Amplitude for Cycle 23 from Its Early Cycle Behavior

On the basis of the lowest observed smoothed monthly mean sunspot number, cycle 23 appears to have conventionally begun in May 1996, in conjunction with the first appearance of a new cycle, high-latitude spot-group. Such behavior, however, is considered rather unusual, since, previously (based upon the data- available cycles 12-22), the first appearance of a new cycle, high-latitude spot- group has always preceded conventional onset by at least 3 months. Furthermore, accepting May 1996 as the official start for cycle 23 poses a dilemma regarding its projected size and timing of maximum amplitude. Specifically, from the max-min and amplitude-period relationships we infer that cycle 23 should be above average in size and a fast riser, with maximum amplitude occurring before May 2000 (being in agreement with projections for cycle 23 based on precursor information), yet from its initial languid rate of rise (during the first 6 months of the cycle) we infer that it should be below average in size and a slow riser, with maximum amplitude occurring after May 2000. The dilemma vanishes, however, when we use a slightly later-occurring onset. For example, using August 1996, a date associated with a local secondary minimum prior to the rapid rise that began shortly thereafter (in early 1997), we infer that cycle 23's rate of rise is above that for the mean of cycles 1-22, the mean of cycles 10-22 (the modern era cycles), the mean of the modern era'fast risers,' and the largest of the modern era 'slow risers' (i.e., cycle 20), thereby, suggesting that cycle 23 will be both fast-rising and above average in size, peaking before August 2000. Additionally, presuming cycle 23 to be a well- behaved fast-rising cycle (regardless of whichever onset date is used), we also infer that its maximum amplitude likely will measure about 144.0 q+/- 28.8 (from the general behavior found for the bulk of modern era fast risers; i.e., 5 of 7 have had their maximum amplitude to lie within 20% of the mean curve for modern era fast risers). It is apparent, then, that sunspot number growth during 1998 will prove crucial for correctly establishing the size and shape of cycle 23.

Wilson, Robert M.↗

NASA NTRS1997

Gauging the Nearness and Size of Cycle Minimum

By definition, the conventional onset for the start of a sunspot cycle is the time when smoothed sunspot number (i.e., the 12-month moving average) has decreased to its minimum value (called minimum amplitude) prior to the rise to its maximum value (called maximum amplitude) for the given sunspot cycle. On the basis (if the modern era sunspot cycles 10-22 and on the presumption that cycle 22 is a short-period cycle having a cycle length of 120 to 126 months (the observed range of short-period modern era cycles), conventional onset for cycle 23 should not occur until sometime between September 1996 and March 1997, certainly between June 1996 and June 1997, based on the 95-percent confidence level deduced from the mean and standard deviation of period for the sample of six short-pei-iod modern era cycles. Also, because the first occurrence of a new cycle, high-latitude (greater than or equal to 25 degrees) spot has always preceded conventional onset of the new cycle by at least 3 months (for the data-available interval of cycles 12-22), conventional onset for cycle 23 is not expected until about August 1996 or later, based on the first occurrence of a new cycle 23, high-latitude spot during the decline of old cycle 22 in May 1996. Although much excitement for an earlier-occurring minimum (about March 1996) for cycle 23 was voiced earlier this year, the present study shows that this exuberance is unfounded. The decline of cycle 22 continues to favor cycle 23 minimum sometime during the latter portion of 1996 to the early portion of 1997.

Wilson, Robert M.↗

NASA NTRS1997

Solar Cycle Predictions Near Sunspot Minimum

Observations of solar magnetic activity and the dynamics of the solar convection zone have produced severe constraints on models of the Sun's magnetic dynamo. These constraints are so severe that, at present, we do not have numerical models that can accept the current conditions and then march forward in time to predict future activity. Given this state of solar dynamo theory we are forced to examine previous behavior to discover patterns and trends that afford us some measure of predictability. Here we examine the behavior of several indicators of solar activity near solar minimum that are well correlated with the amplitude of the following solar maximum to predict the level of solar activity over cycle 23. Sunspot numbers, areas, and positions are useful for characterizing solar cycle behavior due to the extent of the data (12 cycles or more). These data exhibit several patterns that relate future activity to past behavior. With the Odd-Even effect the odd numbered cycles have been larger than their even numbered predecessors for each of the last six cycle pairs. With the Amplitude-Period effect short period cycles have been followed by large amplitude cycles and long period cycles have been followed by small amplitude cycles for 10 of the last 13 cycles. With the Maximum-Minimum effect the sunspot number at minimum is directly correlated with the sunspot number at maximum for a given cycle. The geomagnetic indices aa and Ap are also related to solar activity by the connections between disturbances in the solar wind and variations in the Earth's magnetic field. Like the Maximum-Minimum effect for sunspots, the size of the aa and Ap indices at minimum are directly related to the amplitude of the following maximum. The number of geomagnetically disturbed days (days with Ap >= 25) over the course of a cycle is another indicator for the size of the next cycle. The aa and Ap indices can each be separated into a component in phase with the current sunspot cycle and an "extended cycle" component that is directly related to the following cycle. Individually each of these indicators provides some measure of predictive ability for the amplitudes of previous cycles. Taken in combination we find that the predictions are much more accurate. Our multi-variate analysis indicates that a maximum sunspot number of 160 +/- 20 should occur near the end of 1999 for cycle 23.

Hathaway, David H.↗

NASA NTRS1996

Prelude to Cycle 23: The Case for a Fast-Rising, Large Amplitude Cycle

For the common data-available interval of cycles 12 to 22, we show that annual averages of sunspot number for minimum years (R(min)) and maximum years (R(max)) and of the minimum value of the aa geomagnetic index in the vicinity of sunspot minimum (aa(min)) are consistent with the notion that each has embedded within its respective record a long-term, linear, secular increase. Extrapolating each of these fits to cycle 23, we infer that it will have R(min) = 12.7 +/- 5.7, R(max) = 176.7 +/- 61.8, and aa(min) = 21.0 +/- 5.0 (at the 95-percent level of confidence), suggesting that cycle 23 will have R(min) greater than 7.0, R(max) greater than 114.9, and aa(min) greater than 16.0 (at the 97.5-percent level of confidence). Such values imply that cycle 23 will be larger than average in size and, consequently (by the Waidmeier effect), will be a fast riser. We also infer from the R(max) and aa(min) records the existence of an even- odd cycle effect, one in which the odd-following cycle is numerically larger in value than the even-leading cycle. For cycle 23, the even-odd cycle effect suggests that R(max) greater than 157.6 and aa(min) greater than 19.0, values that were recorded for cycle 22, the even-leading cycle of the current even-odd cycle pair (cycles 22 and 23). For 1995, the annual average of the aa index measured about 22, while for sunspot number, it was about 18. Because aa(min) usually lags R(min) by 1 year (true for 8 of 11 cycles) and 1996 seems destined to be the year of R(min) for cycle 23, it may be that aa(min) will occur in 1997, although it could occur in 1996 in conjunction with R(min) (true for 3 of 11 cycles). Because of this ambiguity in determining aa(min), no formal prediction based on the correlation of R(max) against aa(min), having r = 0.90, or of R(max) against the combined effects of R(min) and aa(min)-the bivariate technique-having r = 0.99, is possible until 1997, at the earliest.

Wilson, Robert M.↗

NASA NTRS1996

On Determining the Rise, Size, and Duration Classes of a Sunspot Cycle

The behavior of ascent duration, maximum amplitude, and period for cycles 1 to 21 suggests that they are not mutually independent. Analysis of the resultant three-dimensional contingency table for cycles divided according to rise time (ascent duration), size (maximum amplitude), and duration (period) yields a chi-square statistic (= 18.59) that is larger than the test statistic (= 9.49 for 4 degrees-of-freedom at the 5-percent level of significance), thereby, inferring that the null hypothesis (mutual independence) can be rejected. Analysis of individual 2 by 2 contingency tables (based on Fisher's exact test) for these parameters shows that, while ascent duration is strongly related to maximum amplitude in the negative sense (inverse correlation) - the Waldmeier effect, it also is related (marginally) to period, but in the positive sense (direct correlation). No significant (or marginally significant) correlation is found between period and maximum amplitude. Using cycle 22 as a test case, we show that by the 12th month following conventional onset, cycle 22 appeared highly likely to be a fast-rising, larger-than-average-size cycle. Because of the inferred correlation between ascent duration and period, it also seems likely that it will have a period shorter than average length.

Wilson, Robert M.↗

NASA NTRS1996

On the Importance of Cycle Minimum in Sunspot Cycle Prediction

The characteristics of the minima between sunspot cycles are found to provide important information for predicting the amplitude and timing of the following cycle. For example, the time of the occurrence of sunspot minimum sets the length of the previous cycle, which is correlated by the amplitude-period effect to the amplitude of the next cycle, with cycles of shorter (longer) than average length usually being followed by cycles of larger (smaller) than average size (true for 16 of 21 sunspot cycles). Likewise, the size of the minimum at cycle onset is correlated with the size of the cycle's maximum amplitude, with cycles of larger (smaller) than average size minima usually being associated with larger (smaller) than average size maxima (true for 16 of 22 sunspot cycles). Also, it was found that the size of the previous cycle's minimum and maximum relates to the size of the following cycle's minimum and maximum with an even-odd cycle number dependency. The latter effect suggests that cycle 23 will have a minimum and maximum amplitude probably larger than average in size (in particular, minimum smoothed sunspot number Rm = 12.3 +/- 7.5 and maximum smoothed sunspot number RM = 198.8 +/- 36.5, at the 95-percent level of confidence), further suggesting (by the Waldmeier effect) that it will have a faster than average rise to maximum (fast-rising cycles have ascent durations of about 41 +/- 7 months). Thus, if, as expected, onset for cycle 23 will be December 1996 +/- 3 months, based on smoothed sunspot number, then the length of cycle 22 will be about 123 +/- 3 months, inferring that it is a short-period cycle and that cycle 23 maximum amplitude probably will be larger than average in size (from the amplitude-period effect), having an RM of about 133 +/- 39 (based on the usual +/- 30 percent spread that has been seen between observed and predicted values), with maximum amplitude occurrence likely sometime between July 1999 and October 2000.

Wilson, Robert M.↗