DOES THE RATE OF RAINFALL in a storm have a pattern or is it random? Richard W. Stimets of the University of Lowell has devised an experiment with which one can search for such patterns. Analyzing the storms that pass over the eastern end of Massachusetts, he has found that the rainfall in some of them does indeed form certain patterns, indicating that the moisture in clouds is occasionally organized.

What might cause the organization? Storms in North America are normally associated with low-pressure regions that travel approximately eastward. The low-pressure system is a great mass of air made to circulate counterclockwise by the rotation of the earth. A typical storm has two fronts, or boundaries separating air masses of different temperatures and winds. On the leading (eastern) side of the storm system is a warm front. This boundary extends from the center of the system to the east or southeast. On the northern side lies cold air. On the southern side is warm air brought up from the Gulf of Mexico by the counterclockwise circulation of the system. The warm air tends to ride up over the cool air. In the southwestern part of the system is a cold front, which is a boundary that extends from the center of the system and toward the southwest. On the southeastern side is warm air. On the northwestern side is cold air brought down from Canada by the circulation. The cold air tends to slide in under the warm air.

In a warm front warm air rises over cold air along a sloped boundary. As the moist, warm air rises it expands and cools; some of the moisture condenses to form precipitation. A cold front is formed by a mass of cold air intruding on warm air. The warm, unstable air lifted by the intrusion forms clouds and storms. The cold front travels faster than the warm front and eventually overtakes it. The combined front is said to be occluded.

I shall limit my discussion to the storms of younger systems in which the cold front is separated from the warm one. Both fronts can produce rain. Can they also produce atmospheric waves that force the rainfall into a general rhythm? Do they generate distinct concentrations of precipitation separated by some characteristic distance?

To monitor the patterns of rainfall Stimets employs a tipping-bucket rain gauge he obtained from Rainwise, Inc. (P.O. Box 443, Bar Harbor, Me. 04609). A funnel on the top directs water into one of two buckets below. When the bucket is full, it tips, losing its water and bringing the other bucket into position. The capacity of each bucket is equivalent to .01 inch of water spread over the collecting area of the funnel.

Each time a bucket tips it closes a reed switch. The switch shorts a circuit that is connected to a strip-chart recorder. The strip-chart recorder displays each tip of a bucket as a spike One can easily determine the rainfall rate by scanning the chart: the spikes are well separated during light rain but cluster during heavy rain.

The average rate of rainfall can be computed from the chart in two ways One way is to assume that the rate is constant

during the interval between tips. The rate is therefore equal to .01 inch of rain divided by the time between tips.

One might also fit a function to the data by means of interpolation. When the rainfall rate is plotted on a graph, the interpolation yields a smoother curve than the first method does. The graph also displays peaks that are somewhat higher.

Rainfall rates can vary considerably during a storm, ranging from less than .001 inch per hour to more than four inches. What Stimets looked for was evidence of periodicity. He studied data on 30 storms from a rain gauge at Wellesley, Mass. All the storms produced at least .4 inch of rain and lasted for at least four hours. He divided much longer storms into eight-hour segments. He then fitted an interpolation function to the data so that he could compute the average rates per minute.

Next Stimets did a Fourier analysis of the average rates. This analysis reveals any sinusoidal variations in the data even when they are buried in noise. The analysis yielded information about which periods of sinusoidal functions best fit the average rates of rainfall.

A typical result for a single storm is a graph called a power spectrum. It reflects sinusoidal variations in the rainfall. The horizontal axis shows the time periods on which the Fourier analysis was based; the vertical axis shows how often the sinusoidal variations appear in the rainfall [left].

For convenience Stimets applied a scaling factor so that the longer periods are more condensed on the horizontal axis than the shorter periods. The graph peaks at about 160 minutes, indicating that a sinusoidal variation with a period of 160 minutes best fits some of the data. In other words, rainfall intensified approximately every 160 minutes.

The graph for a single storm may be too noisy to interpret. In order to improve the peaks representing periodic variations Stimets combined the data from many storms of the same type. He assumed that a recording station can sample four kinds of low-pressure system: a cold front, a warm front, a land cyclone and a coastal cyclone. On the basis of multiple samples of such storms Stimets has concluded that all but the coastal cyclones may show periodicity in rainfall.

In the first case the station samples the passage of a cold front. If the low-pressure system exists, it lies to the north of Massachusetts, probably in Canada. In the second case the station samples a warm front. The low-pressure center would be west of the station, somewhere near the Great Lakes. In each case Stimets considers the low-pressure center to be far enough away so that there is relatively little movement of air at the station.

The third case involves a storm pattern called a land cyclone. The low-pressure center of the system is so close to the station (within 500 kilometers) that the cyclonic wind circulation may affect the rate of rainfall. The station may sample both warm and cold fronts, usually receiving more rain from the warm front.

A coastal cyclone, the fourth general case, is peculiar to the coastal areas of the northeastern U.S. Its low-pressure center

passes to the south and east of the station. Thus no clearly defined weather front is seen. Sometimes these storms are weak. Sometimes a coastal cyclone intensifies and becomes a "nor'easter," a type of storm that can last for days.

Stimets charted the average power spectrum for eight cold-front storms. The chart shows a large peak at 480 minutes (eight hours); it is the result of dividing the data into eight-hour periods and also reflects the fact that many of the storms lasted for about eight hours. The peak at 135 minutes is more important: it suggests a pattern in the rainfall rate. As the cold fronts passed over the recording station their rainfall rates tended to vary, producing a period of about 135 minutes. A smaller peak that appears at about 48 minutes may also represent a periodic variation.

The power spectrum derived from the data collected during the passage of five warm fronts also reveals a characteristic periodicity. The power distribution again peaks at 480 minutes for reasons associated with the analysis of the data. More interesting are the peaks at 95 and 48 minutes. The data for six land-cyclone storms have a peak at 80 minutes. The data for coastal storms appear to be entirely random.

Stimets notes that even though characteristic periods seem to be associated with storms in three of his four general categories, the organized component of the rainfall is minor. Most of the rainfall rate is random. The maximum organization appears to be associated with cold-front storms: up to 30 percent of their power lies in the long period peaks, which rise out of the noise level.

If indeed there is some organization to the rainfall in certain types of storms, does the spatial organization of the storm cause it? The question is accessible to observation. If the concentration of precipitation within the storm clouds does indeed vary in some periodic way, a ground station would record an intensification of rainfall as the formation responsible for it passed overhead.

Stimets points out that studies with radar and other instruments have indeed identified two basic precipitation-producing structures in storms: rain bands and precipitation cores. Rain bands are precipitation areas that may be hundreds of kilometers long. Distances of SO to 100 kilometers separate rain bands from one another. They move in the approximate direction of the average airflow. Precipitation cores are smaller regions of concentrated precipitation that lie within rain bands.

The period between the passage of one rain band or core and the next is equal to the distance separating the structures divided by the speed at which they move. Stimets says the rain bands forming near cold fronts usually travel at speeds of 30 to 60 kilometers per hour. A spacing of 50 or 100 kilometers between rain bands would produce periods of between 50 and 200 minutes in the rainfall rates recorded at a station. The long-period peak at 135 minutes found in Stimets' data for cold-front storms falls quite neatly into this range. The smaller peak at 48 minutes is near enough to be considered also. He suggests that the long-period peak results from rain bands and that the smaller-period peak is more likely to be associated with the precipitation cores.

The average power spectrum for warm fronts has a peak at 95 minutes. For land cyclones the peak is at 80 minutes. Although both times fall within the range of possible periods for rain bands, Stimets believes they are more likely to be attributable to the precipitation cores.

The second peak in the data for warm fronts is at 48 minutes. It might indicate structure in the front passing over a recording station in about that much time. The peak might also be generated artificially in the analysis of the data. When the data contain narrow signals that are much stronger than the rest of the signals, a Fourier analysis can produce extra peaks that are harmonics of the basic peak. Since the main peak in the power spectrum for a warm front is at 95 minutes, the second harmonic would be expected at half that interval, the second harmonic almost matches the peak at 48 minutes.

Stimets attributes the absence of peaks in the coastal-storm data to the fact that no fronts passed over the stations. It is certainly conceivable that all the organization in a storm derives from a front. The variability of the coastal cyclones might also be responsible for the absence of periodicity. These storms seem more subject to changes in intensity and direction of travel than other storms. As a result any evidence of structure may be smeared.

An improvement in instrumentation may lead to an improvement in the quality of information. Stimets has therefore recently begun to replace the strip-chart recorder in his equipment with a printing calculator to which the circuit shown in Figure 9 has been added. The circuit, which was designed by Cesare C. DeLizza of the University of Lowell, consists of a crystal oscillator and two dividers that produce one pulse per second. Stimets enters an initial count into the calculator and closes the switch labeled S1. Thereafter the oscillator adds a count every second to the calculator.

A dual flip-flop circuit monitors the rain gauge. Whenever the gauge causes a short circuit by tipping, the circuit prints the time displayed on the calculator. The device has reserve battery power so that it can function even when a storm or a careless person turns off the electrical power.

DeLizza's circuit is designed for a Sharp printing calculator. To attach it open the calculator and find where the leads from the "print" and the "+=" keys join the printed circuit board. Also find the common wire between those keys. Solder the "print" lead of DeLizza's circuit to the first of the junctions on the board, the "add 1" lead to the second junction and the "common" lead to the common wire between the keys. The connection represented by the top line in the circuit diagram is to be attached to the positive side (the red wire) of the calculator's adapter socket for alternating current.

The connection represented by the bottom line in the diagram is to be attached to the negative terminal of the calculator battery. Solder a lN4001 diode between the red and white wires in the adapter socket for alternating current, so that the cathode connects with the red wire. The elements labeled TIL-111 are optically coupled phototransistors.

The element labeled X1 is a crystal that resonates at 3.579545 megahertz. Adjust the capacitor labeled C1 until a measurement of the frequency (made at pin 7 on the MM5369 clock oscillator) shows 3.579545 megahertz. The output of the clock oscillator is 60 hertz. The first 4017 integrated circuit beyond it divides the frequency by 10. The next one divides it by 6. Thus the pulse rate communicated to the rest of the circuit is one hertz (one pulse per second).

The printing calculator gives a better resolution of variations in rainfall than the strip-chart recorder. Indeed, Stimets can now monitor individual clouds that take from five to seven minutes to pass. Preliminary results on the power spectrum of cold-front storms suggest that such a cloud may show up as a small peak.

Stimets is also working on installing a network of rain gauges to include many schools in the Boston area so that storms and the rain bands associated with them can be monitored over a much greater area.

In the past decade several research groups have discovered periodic structures in the storms associated with both warm and cold fronts. Peter V. Hobbs and his associates at the University of Washington have studied the large- and small-scale organization of middle-latitude cyclones. They employ an elaborate observation network composed of radar systems, instrumented airplanes and balloons that they coordinate with a system of ground stations.

Hobbs and his group studied in detail a cold front that passed through the observation network on November 17, 1976, moving east southeast. The precipitation near the front was concentrated in rain bands that were parallel or approximately parallel to the front. The bands showed three different arrangements.

One arrangement extended over 50 kilometers of the warm sector ahead of the front. It consisted of two or three bands traveling faster than the cold front, the rear band being just ahead of the front at ground level. Another arrangement, behind the cold front, consisted of four bands that were each several tens of kilometers wide and traveled faster than the front. The third arrangement was a single rain band only four kilometers wide that stayed above the cold front.

The high points of this narrow band were at altitudes of from 1.5 to 4.5 kilometers. The other rain bands were higher: their peaks lay at altitudes of five and six kilometers. During the observation one of the wide bands behind the cold front overtook the front and passed it, apparently moving over the narrow rain band that travels with the front.

The rain bands in the warm sector and those behind the cold front produced concentrated precipitation from irregularly shaped cores. The narrow rain band along the front also had cores, but in that band they were elliptical and roughly aligned, suggesting that convection currents were more organized in these cores than they were elsewhere.

The rain bands and cores behind the cold front moved at roughly 100 kilometers per hour, identical with the wind speed that prevailed at altitudes of three to six kilometers. Evidently the wind steered the bands. The winds also steered the bands in the warm sector. The band above the ground location of the cold front moved at the speed of the front (about 65 kilometers per hour) rather than at the speed of the winds.

Air at the front of a rain band in the warm sector ascended rapidly and then flowed to the rear of the band. By tracing this movement, Hobbs and his group discerned a complicated system by which rain was produced. The top of the band functioned as a "seeder zone" of ice particles. Once the particles nucleated they grew by the deposition of water vapor. Eventually they fell into a "feeder zone," where they grew further by sticking together, forming rime or receiving more water vapor. Below the feeder zone the temperature increased enough to melt the ice, producing rain.

The vertical structure of a wide rain band behind the cold front was similar except that it lacked the large-scale convection displayed by the warm sector preceding the front. As before, the particles initiated in the seeder zone grew and fell until they melted and became rain.

The seeder zones of both sets of rain bands contained regions of updrafts and downdrafts called generating cells. Ice particles apparently grew in the updraft portions until they were large enough to fall out of the cell; they may also have traveled laterally.

Apparently the horizontal arrangement of these generating cells parallel to the front produces the organization that leads to the formation of rain bands and presumably to the variations in rainfall detected by Stimets. Along a perpendicular line the cells align in a roughly periodic fashion. Hence rain bands and the variation in rainfall rates may be the result of the arrangement of generating cells in the seeder zones.

Can you detect rain bands without instruments? Imagine the variation in the rainfall when a cold-front storm of the kind described by Hobbs and his colleagues passes you. The first rain you detect is in the warm sector ahead of the front. The rainfall rate increases whenever a rain band in that front group passes you.

When the cold front reaches you, the rain-band traveling with it delivers another heavy deluge. Whenever one of the wide rain bands behind the front passes, you again receive heavy rain. Eventually the last rain band of the storm system passes and the rainfall begins to let up.

Actually the rate of rainfall would not be that clearly organized. Superimposed on the general pattern of rainfall are smaller-scale variations due to the precipitation cores formed by the generating cells. The rainfall is also modified by winds through which the particles fall. At ground level in any given storm you might not always notice any general organization of the precipitation.

Can the results produced by Stimets be explained in terms of the cold-front storm investigated by Hobbs and his associates? Since Stimets worked with storms on the opposite side of America, such a comparison may not be fair.

Still, I wondered if the rainfall studied by Hobbs showed a characteristic variation over time.

I considered the rain bands traveling behind the cold front. Suppose they were uniformly spaced with a period of 30 kilometers. Traveling at about 100 kilometers per hour, they would yield a periodic variation in rainfall with a characteristic time of about 33 minutes.

The precipitation cores within the bands were more closely spaced than the bands. Since the cores were irregularly shaped, assigning them a characteristic spacing is difficult. Suppose it was about 10 kilometers. In that case the cores would yield variations in rainfall with a characteristic time of about six minutes.

Both my results suggest faster variations than one would infer from Stimets' data. Cold-front storms are highly variable, however, and my comparison may not be valid. Perhaps the rain bands studied by Hobbs and the other investigators moved faster than the ones studied by Stimets. One result of the higher speed would be to force greater variations in the rainfall.

Hobbs and his former student Paul H. Herzegh have reported much smaller structures, resembling rain bands, that are near a warm front. Radar observations revealed wavelike bands that formed near a stationary warm front running east and west. They were parallel to the front, about eight kilometers wide and spaced about 12 kilometers apart.

Hobbs and Herzegh found that the bands originated from generating cells in a seeder zone. The cells were laid out along a line perpendicular to the front. The updraft portions of the cells favored the formation of ice particles Thus the roughly periodic arrangement of generating cells dictated the formation of the rain bands.

You might like to construct a rain gauge similar to Stimets'. Do the storm systems passing through your area display rain bands that can be recorded by your gauge? Do they display characteristic times of the kind detected by Stimets? A network of gauges deployed over a few hundred kilometers might enable you to track the rain bands. Both Stimets and I would be interested in your results. Questions about details of Stimetst work can be addressed to him at the Department of Physics, University of Lowell, Lowell, Mass. 01854.

Bibliography

THE MESOSCALE AND MICROSCALE STRUCTURE AND ORGANIZATION OF CLOUDS AND PRECIPITATION IN MIDLATITUDE CYCLONES, 1: A CASE STUDY OF A COLD FRONT. Peter V. Hobbs, Thomas J. Matejka, Paul H. Herzegh, John D. Locatelli and Robert A. Houze, Jr., in Journal of the Atmospheric Sciences, Vol. 37, No. 3, pages 568-596; March, 1980.

THE MESOSCALE AND MICROSCALE STRUCTURE AND ORGANIZATION OF CLOUDS AND PRECIPITATION IN MID-LATITUDE CYCLONES, 2: WARM FRONTAL CLOUDS. Paul H. Herzegh and Peter V. Hobbs in Journal of the Atmospheric Sciences, Vol. 37, No. 3, pages 597-611; March, 1980.

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