Weather Forecasting

Forecasters compress the information from a weather station by means of an internationally agreed code, which allows data to be sent rapidly by cable or radio, and shared with other weather bureaux. The code is a series of five-figure numbers in a standard sequence agreed in 1982. The information can subsequently be displayed in a standard fashion (Figure 15.2) on the corresponding point on a map. Such a map, with figures from many places, is called a synoptic chart, providing a snapshot of the weather at the time of measurement. A synoptic chart reveals what weather systems affect the region. For instance, the data in Figure 15.3 indicate a cold front along a line across which there is a sudden drop in temperature from east to west by about 8 K, a rise in dewpoint by about 6 K and a backing of the wind from north-

Synoptic Chart Symbols
Figure 15.2 Coded information for a report from Christchurch (New Zealand) as displayed on a synoptic chart. The central circle is plotted at the location of Christchurch on the map. Cloud symbols are discussed in Figure 8.11 and wind symbols in Figure 14.4.

A weather forecast is a statement of what seems probable, not a prediction of what is certain. It can be done in several ways, as follows. Whatever the method, the aim is to do better than either tossing a coin (which gives a 'random forecast') or simply guessing, which depends on the oddities of human prejudice and experience.

Folklore

Useful guidance is sometimes given by the experience distilled into folklore. An example is a traditional method of forecasting in Peru, for determining when conditions are propitious for planting crops. The method shows remarkable success. It is based on the brilliance of stars (i.e. the air's moisture content) and the occurrence of lightning, the taste of rain, etc. A similarly complicated method is used in Nigeria, based on the behaviour of chameleons, hawks, doves and grasshoppers, the leafing and fruiting of certain trees and selected calender and astronomical events.

Unfortunately, many weather sayings are worthless. For instance, a belief that can be traced back twenty-five centuries in Europe, that the coming year's weather copies that of the twelve days after Christmas. One reason for folklore being disappointing is its use in places remote from its origin. For instance, a saying about a red sunset promising fine weather tomorrow, common in Britain and fairly reliable there, is less useful in southern continents. The reason is that red skies in Britain result from Rayleigh

Synoptic Chart Global Warming

Figure 15.3 A synoptic chart of south-east Australia at 6 UTC (i.e. 4 p.m. Eastern Summer Time) on 23 August 1991. It shows only the wind, temperature, dewpoint, pressure ('04' means 1,004 hPa, '98' means 998 hPa), cloudiness (oktas) and precipitation, according to Figure 15.2. The part on the right shows only the temperature and dewpoint for six points near the cold front.

Figure 15.3 A synoptic chart of south-east Australia at 6 UTC (i.e. 4 p.m. Eastern Summer Time) on 23 August 1991. It shows only the wind, temperature, dewpoint, pressure ('04' means 1,004 hPa, '98' means 998 hPa), cloudiness (oktas) and precipitation, according to Figure 15.2. The part on the right shows only the temperature and dewpoint for six points near the cold front.

scattering (Section 2.3) caused by numerous ice particles in the upper troposphere ahead of a warm front approaching from the west, whereas such warm fronts are rare at populated latitudes of the southern hemisphere (Section 13-3).

Persistence Forecasting

The easiest method of forecasting is to assume a continuation of the present—the persistence forecast. It is successful where the weather is dominated by processes which last longer than the period of prediction. For instance, it is easy to forecast the rainfall over the next week in a monsoonal area, where rains over several months alternate annually with dry periods of more months; if it is dry now, we are in a dry period, which will probably continue beyond the seven days we are concerned about. Similarly, there appears to be a 60 per cent chance of a relatively dry month ahead in New Zealand if this month's rainfall is less than average. The chance of thunder tomorrow at Nelson in New Zealand is almost eight times greater if there is thunder today. Other examples of persistence are given in Section 10.4.

The accuracy of persistence forecasting in one country is illustrated in Table 15.2, in terms of the 'correlation' between recent and future daily mean temperatures. The shorter the time ahead of forecasting, the stronger the connection, i.e. the more accurate a persistence forecast will be.

Table 15.2 The correlation between the mean of the daily average temperatures over the past 'n' days, and the mean over the coming 'm' days, in Norway; the tabulated values show the correlation coefficient as a percentage

Average over the coming m days

Number of recent days (n) m = I m = 3 m = 7 m = 15 m = 30

Table 15.2 The correlation between the mean of the daily average temperatures over the past 'n' days, and the mean over the coming 'm' days, in Norway; the tabulated values show the correlation coefficient as a percentage

Average over the coming m days

Number of recent days (n) m = I m = 3 m = 7 m = 15 m = 30

n = 1

70

59

51

43

35

n = 3

59

55

49*

44

35

n = 7

51

49

48

46

35

n = 15

43

44

46

47

31

n = 30

35

35

35

31

21

* That is, the correlation between the mean temperatures of the last three days and the next seven days, respectively, is 49 per cent

* That is, the correlation between the mean temperatures of the last three days and the next seven days, respectively, is 49 per cent

Climatological Forecasting

Whereas persistence forecasting is most accurate over short periods (before factors for change have had time to operate), the best estimate of the weather a long time ahead is the average value of past measurements there at that time of day and year—the climatological forecast. Such an estimate evens out the effects of processes which take a shorter time than the period of prediction. This way of averaging-out disturbing processes complements that of ignoring them, which is involved in persistence forecasting, and the average of the persistence and climatological forecasts proves to be notably accurate, as well as simple. In fact, the expense of other methods of forecasting always has to be justified by demonstrating better accuracy than this combined method.

Incidentally, there is no so-called 'Law of Averages', no truth in the idea that a series of above-normal temperatures, for instance, somehow increases the chance of below-normal values in the future in order to maintain the past average. Tossing a series of heads suggests a double-headed coin, rather than the inevitability of tails soon.

Statistical Forecasting

A statistical forecast uses past records of relevant factors at a place to find equations relating them to the weather on the following day, and then uses the equations for forecasting. An example is frost forecasting, described in Note 15.C. However, the risk of frost is very dependent on the locality (Section 3.6), especially in valleys, so relationships worked out in one place do not apply elsewhere. Regional forecasts of this kind are useful only for radiation frosts (Section 3.6). Another example of statistical forecasting is the prediction of rainfall from values of 5001,000 hPa thickness (Note 12.E).

Approximate 24-hour forecasts have also been based on sea-level pressure (indicating the degree of uplift, i.e. of cloud formation), the change of pressure (i.e. the approach or departure of a front), the wind direction (which determines the advection of heat and moisture), and the cloudiness, i.e. the amount of solar heating.

A related statistical technique involves a contingency table of past observations, relating the frequency of occurrence of certain conditions at a place to earlier measurements at the same place or elsewhere. For instance, there is a strong tendency for heavy rain in northern Victoria (at about 35°S) in the period September- October if air pressures at Darwin (at 12°S) were low during the previous July-August. Likewise, the prediction of the season's number of tropical cyclones around Australia (Section 13.5) may be based on a prediction of the ENSO cycle (as there tend to be more cyclones during a La Niña, Figure 13.15), the Quasi-Biennial Oscillation (more cyclones when the lower stratospheric winds are easterly, Section 12.3), and the SST around Australia (more cyclones when the SST is above-normal). Since these three factors are all either predictable or varying slowly during a season, tropical-cyclone frequency is fairly predictable.

Statistical relationships between conditions at widely separated places are known as teleconnections (Section 10.7). They can be either simultaneous or lagged, in the latter case they can be used for forecasting. For instance, it is relatively wet in Indonesia and New Guinea during the latter half of most years in which there has been a La Niña episode off Peru (Figure 10.17). In addition to the ENSO cycle, there are other, weaker connections between conditions at different latitudes, e.g. central Chile tends to be cooler and wetter when westerly winds strengthen over the south-eastern Pacific ocean. Also, relationships between conditions at different longitudes (such as the eastwards migration of weather systems, Section 13.3) lead to a tendency for Adelaide's weather to be experienced 12-24 hours later in Sydney, a thousand kilometres to the east.

Statistical methods are much used in longrange forecasting. One problem with statistical forecasting is that it applies only to the place where the data were gathered. Even there, relationships may change, so they need regular updating.

Analogue Forecasting

A further method of forecasting over two or three days involves comparing today's synoptic chart with thousands of charts drawn in the past to find those most similar, and then assuming that the consequences will be the same. The synoptic charts used may be for the surface or for 300 hPa height, or, preferably, both.

Unfortunately, exact matches are not possible, and the sequels to the nearest approximations to today's chart turn out to differ from each other, so that there is no clear indication of what now to expect. The sequels differ because changes of the atmosphere are essentially chaotic (Note 15.D). So analogue forecasting has been largely abandoned.

Periodicity Method

The daily rhythm of warm days and cooler nights, and the annual cycle of rainfall in most places, leads us to look for other regularities of weather. Several were discussed in Section 10.7 in connection with the occurrence of droughts. The Madden-Julian Oscillation was mentioned in Section 12.1. If any were to prove reliable, it would allow prediction. For instance, if there were a 26-week repetition of some feature of weather and if twenty weeks have elapsed since the previous occasion, one can expect another in six weeks' time.

Sometimes there may be several rhythms in combination, creating occasional outstanding maxima and minima. Indeed, detection of four periodicities in parallel within the records of rainfalls in New Zealand since 1900, and then extrapolation into the future, allowed successful prediction in 1980 of the dry period from 1982-85.

It has often been suggested that the weather varies in accord with the eleven-year fluctuation of the annual number of sunspots (Note 15.E). The QBO has some influence on tropical cyclone frequency and annual rainfall at various places (Section 10.7) and there may be some effect of the phase of the Moon (Note 15.F). But none of these (except perhaps the QBO) is sufficiently regular or pronounced to be useful in weather forecasting. A graph of rainfalls looks remarkably like a graph of random numbers; similar apparent but unreal regularities occur occasionally in both.

Dynamical Forecasting

Next we consider the method of forecasting currently used by meteorological services around the world, based on calculations of the changes that will occur in each part of the whole atmosphere, starting from as complete a statement as possible of present conditions. This consists of the information available on a synoptic chart of recent surface measurements (Figure 15.3) and on charts of conditions aloft, at the standard levels of 850, 700, 500, 300 and 200 hPa. Deriving these charts is known as the analysis. Dynamical forecasting then involves using the analysis to derive a prognosis, i.e. charts of the situation to be expected at some specified time in the future.

Until the 1970s, the prognosis was based on empirical rules for modifying the current synoptic chart, and on human judgement. A key feature was the identification of the positions of airmass boundaries, i.e. the fronts. It was then possible to use the Bergen model (Section 13.3) to estimate subsequent frontal development and movement, followed by inferences of the resulting wind directions and atmospheric uplift, which determine temperatures, cloudiness and rainfall. Such forecasts were reasonable up to about 24 hours ahead, but serious errors were common.

Numerical Weather Prediction

Nowadays, high-speed supercomputers are used instead to calculate changes to the synoptic chart. As a result, analysis of the weather has become objective, and the prognosis is based on equations which predict the changes of temperature, humidity, velocity, etc. at each point of an imaginary three-dimensional lattice (Figure 15.4). The lattice may consist of perhaps nine layers (representing nine levels of the atmosphere), and a rectangular grid of points in each layer for places separated by 500 km, for instance. Then a simplified set of equations called the primitive equations (Note 15.G) is used to describe the basic laws of fluid motion and to calculate changes of conditions. This method of forecasting is called Numerical Weather Prediction (NWP) (Note 15.H), providing fresh prognoses each twelve hours, for instance, to show conditions up to five days ahead.

It has to be assumed in NWP that conditions are uniform around each grid point (Figure 15.5), a regrettable simplification necessitated by the limitations of even the largest compters. With point separation (i.e. a 'resolution') of 500 km, a model is unable to allow for the very different climate conditions on opposite sides of the southern Andes, for instance. More importantly, such a 'coarse-mesh' model cannot detect the mountain range itself, though it affects the weather for thousands of kilometres downstream (Note 12.K). And, most importantly, it cannot allow for atmospheric processes smaller than the grid size, such as thunderstorms. To cope with these problems, it is becoming increasingly common for a global model of widely spaced points to be supplemented by an embedded 'fine-mesh model' for a region, of points only 60 km apart at eighteen levels of the atmosphere, say, describing the region's atmosphere in more detail, to obtain more refined prognoses there.

The advantage of NWP is that it avoids errors of human judgement in deriving the prognosis, and can be steadily improved by enlarging the amount and reliability of input data, by new understanding of the physics of atmospheric change, and by faster, larger computers. The speed of computer systems used in NWP has increased tenfold every three years for the last thirty. As a result, errors of four-day forecasts in 1995 were no more than those for 24-hour forecasts in 1980.

Nowcasting

Regional forecasts for up to 24 hours ahead are now possible, using a computer model with a

Computers Used Weather Forecast

Figure 15.4 Part of a model used for Numerical Weather Prediction, representing a lattice of regularly spaced points which sample the troposphere to 15 km, say. It should be regarded as continuing sideways to cover the whole globe. This is an eight-layer model, but some models have more layers for greater accuracy, if a faster computer is available. The horizontal dimension of a grid box here is about 500 km, but some models have a closer spacing of grid points over the region of particular interest to the forecasters.

Figure 15.4 Part of a model used for Numerical Weather Prediction, representing a lattice of regularly spaced points which sample the troposphere to 15 km, say. It should be regarded as continuing sideways to cover the whole globe. This is an eight-layer model, but some models have more layers for greater accuracy, if a faster computer is available. The horizontal dimension of a grid box here is about 500 km, but some models have a closer spacing of grid points over the region of particular interest to the forecasters.

Figure 15.5 Schematic difference between (a) surface conditions in the real world, and (b) the equivalent in a computer model, showing the spatially stepwise description adopted in Numerical Weather Prediction.

local resolution of only 20 km, for instance. Such models can predict the onset of a sea breeze or the time that a cold front passes by, or a squall line (Section 9.5). The accuracy of such 'nowcasts' is limited mainly by the availability of frequent, closely spaced measurements for updating the model. This problem is being tackled by increasing use of data from satellites, aircraft and ground-based radars.

Short and Medium-range Forecasts

The dynamical NWP method is used for 'shortrange forecasts' of a day or two and also for medium-range forecasts of 3-6 days, but there remains an essential role for weather forecasters. They have first to compare the prognoses from the models of different organisations (e.g. from the European Centre for Medium Range Weather Forecasts, at Reading in southern England, and from the Australian Regional model in Melbourne), in the light of past success in forecasting local movements of small and large highs and lows at this time of year. Having chosen a prognosis, the forecaster must interpret it in terms of the local weather, which is on a smaller spatial scale, in view of local experience of sea breezes, geography, current satellite pictures of clouds and so on. This interpretation often involves reckoning the positions of fronts; NWP models simulate well the evolution of frontal disturbances (Section 13.3), but are unable to pinpoint where the fronts are, because of their limited resolution. The whole procedure leads to estimates of the likelihood, amount, and type of rain, and daily extreme temperatures. Finally, the forecaster determines the need for warnings of tropical cyclones, thunderstorms, strong winds, bushfire risk, floods, hazard to exposed animals in cold and wet conditions, and so on.

Medium-range NWP models are similar to those for short-range forecasting, but they are global because fast-travelling disturbances, such as short waves in the jet stream, can circle the Earth in six days. The range of short and medium-range forecasts, especially in midlatitudes, is limited by the lifetime of frontal disturbances being 3-7 days (Section 13.3). It is difficult to predict the condition of a disturbance not yet created.

Longer-range Forecasts

Extended-range forecasts deal with conditions 6-10 days ahead. They are produced by the same NWP models that yield medium-range forecasts, but involve more uncertainty, usually consisting merely of a statement about the rainfall and temperature being above, about or below normal. Similar descriptive forecasts are made for times of 10-30 days (a long-range forecast) or 1-4 months (a seasonal outlook). These result from a combination of the persistence, climatological, statistical, analogue or periodicity methods described above. Also, use is made of a dynamical NWP model which allows for oceanic processes, which are too slow to be important in short-range weather forecasting.

Meteorological bureaux now regularly provide seasonal outlooks, with an accuracy notably enhanced by our increased understanding of the relevance of the Southern Oscillation, indicated by the sea-surface temperatures, the strength of the Trade winds, the location of areas of deep convection across the tropical Pacific ocean, and the depth of the thermocline (Notes 11.C and 12.N).

Accuracy

There are several measures of forecasting skill (Note 15.I) used to monitor the success of the agencies concerned. The forecast accuracy depends on (a) the feature of concern (such as the rainfall, daily maximum temperature, wind speed, the location of a tropical cyclone, or the occurrence of a storm, etc.), (b) the length of the lead time (the time between the forecast statement and the expected event), (c) the season of the year, (d) the location and (e) the forecasting method used. We will consider these in turn.

(a) In general, an unusual or a localised event, such as a tropical cyclone or a thunderstorm, is harder to foretell than the ordinary or the extensive, like a high-pressure system. In the case of occasional tropical cyclones, for example, it is inherently difficult to detect them in the early stages, but once a TC is mature the location of its eye and the strength of its circulation can be estimated by satellite. This information is manually entered into NWP models, in order to forecast the TC's future course. This deliberate injection of specific local information is called 'bogussing'. When a TC poses a threat to populated areas, planes are flown into the eye of the storm to obtain more information for bogussing.

Rainfall is the most difficult to forecast because it is patchy in time and space; the 'skill' in three-day forecasts in one American study published in 1981 was 45 per cent for daily maximum temperatures but only 18 per cent for the incidence of rainfall. A common yardstick in assessing the accuracy of prognostic charts is a comparison of estimate against measurement of the height of the 500 hPa level in the atmosphere, or else the pressure at sea-level.

(b) Obviously, the accuracy of forecasting falls off as the lead time increases. There is a doubling of error for each two or three days of numerical forecasting, and it outgrows the error of climatological forecasts after 1015 days. The average error in predicting the daily maximum temperature at Melbourne is 1.7 K for a lead time of 24 hours, 2.4 K for 48 hours, 2.9 K for 72 hours and 3.1 K for four days, compared with 2.9 K for a climatology-plus-persistence forecast.

(c) Forecasting is easier in any place with a highly seasonal climate, as in a Mediterranean climate (Chapter 16) or in the north of Australia (except during the transition from the Wet to the Dry).

(d) It is easier to forecast the development of a disturbance where there is a sharp contrast between adjacent air masses. For this reason, forecasting in midlatitudes is more accurate than in the tropics, where steep temperature gradients are rare. Also, there is less difficulty in predicting conditions over a large plain than those amongst the irregularities of mountains or a coastline.

At the coast, errors are less in forecasting the minimum than the maximum temperature, because the latter is affected by the occurrence or not of a sea breeze (Section 14.2), whilst the minimum is stabilised by the ocean nearby. Inland, the possibility of cold air flowing onto a low-lying weather station at night makes forecasting the minimum the more difficult (Figure 15.6).

(e) A test in 1989, of six methods of forecasting thunderstorms within nine hours in Colorado, showed accuracies no better than that of persistence or climatological forecasting.

There have been dramatic improvements in longrange forecasting during the last decade or two, due to our increased understanding of ENSO (Section 12.7). In December 1982, for instance, the New Zealand authorities were able to predict correctly an unusually cool summer, an 80 per cent chance of drought in the following January-March, and abnormal rains on the west coast of the South Island. Seasonal outlooks of the rainfall in early spring for Australian farmers are now correct 70 per cent of the time.

Of course, accuracy is not the only criterion of successful forecasting. Timeliness, lead time and manner of presentation are also important, and all have improved in the last twenty years.

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