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Toward predictability in agro-climatology

Orman E. Granger

ORMAN E. GRANGER is a climatologist in the Department of Geography, University of California, Berkeley

Over the past few years global climate, traditionally treated as a static environmental element of little but academic importance, has acquired international prominence because of the recent erratic behaviour of weather and the impact it has had on world food and energy reserve, on water resources and international politics. Devastating droughts in the Sahel, in the USSR, and in India, south Asia, north China, Central America, the Caribbean and California; excessive rainfalls and flooding in India, Bangladesh, and the midwestern United States; abnormally warm or cold winters, destructive winds and shortened growing seasons in other parts of the world caused loss of life and economic depression.

These apparently unheralded climatic aberrations sparked an upsurge of reports, papers and general inquiries because previous short runs of mild winters in much of Europe, the southern and midwestern United States and other regions had helped to create an attitude of scepticism about the science of climatology: that is, though it might be interesting, its practical implications for today's world was questionable. This attitude was reinforced by the fact that, with some exceptions, most of the years between 1956 and 1972 were blessed with remarkably favourable climatic conditions for agricultural production, particularly in North America, and for forest products in most of the tropics and mid-latitudes. But variability is an inherent characteristic of climate, and not to be perceived as unexpected, abnormal or anomalous. Further, climate is an important resource not to be taken for granted - a resource whose behaviour is not yet well understood and whose variability is accepted but not yet predictable with a high degree of precision.

TABLE 1. Stations used in calculating areal means of seasonal precipitation

California stations









San Francisco



Santa Cruz






San Luis Obispo



Santa Barbara



Los Angeles



San Diego



Mexican stations




San Blas









Salina Cruz



Many scholars are agreed that the decrease in global temperature evident since 1940 after almost half a century of warming will continue to bring with it increasing variability of climate through the rest of this century and into the next. Some climatologists think that this downward trend in global temperature may be leading to another ice age, if not of the magnitude of the Pleistocene epoch certainly of the magnitude of the "Little Ice Age." In support of their claim they cite the sudden increase in snow and ice cover in the northern hemisphere, circumpolar vortex expansion which blocks the intrusion of humid tropical air into monsoon regions, the higher frequency of droughts in tropical and subtropical areas and decreases in the length of growing seasons to mention a few. Others see the cooling trend and other patterns as a result of extra-terrestrial causes such as sunspots, although it is not yet known exactly how this causal mechanism is linked to climatic fluctuations.

There are also those who see the present climatic fluctuations as having planetary determinants: the frequency of volcanic eruptions, man's input of pollutants and aerosols into the atmosphere, the dramatic increase in CO2 concentration attendant on an indiscriminate burning of fossil fuel and the complete disregard in some regions for ecologically sound land-use policies. Still others hold that climatic fluctuations can be considered as random events: that the climatic future is indeterminate or that the earth-atmosphere-hydrosphere-cryosphere system has inherent in itself, through feedback mechanisms, the ability to move from one well-differentiated state to another through ephemeral states so that deterministic dynamics as now applied may very well be an exercise in futility. In short, we may never be able to predict any one micro-state of the system until we have a complete grasp of the details of all possible micro-states.

We may not know exactly what the climatic future will be, but that does not completely rule out climatic out looks with probabilistic bases. We can legitimately take the position that it is precisely in this operational form that the results of climatic investigations become of utmost importance in policy and management decision making, in averting possible disasters and setting up economic expectations. The risks and ambiguities have to be evaluated in the same way as is done in other situations. Forest management decisions and expectations with respect to forest yields and regeneration are cases in point.

There are innumerable studies demonstrating the strong relationship between productivity and primary climate variables, Drozdov (1971), Jordan (1971), Watson (1963), Chang (1968a, 1965, 1968b), Bazilevich et al. (1968) to list a few, and in all of them the underlying message is that primary productivity is closely related to the variability and fluctuations of climate. Further, it has been demonstrated that climatic variability is most marked in semi-arid and sub-humid regions of the earth and because of the climatic sensitivity of these areas, they may very well be the most effective barometers of large-scale trends.

Figure 1. - Power spectrums of the annual dry season and wet season precipitation series for the period 1921-70 for St. Claire in Trinidad, West Indies, and for the island as a whole.

Figure 2. - Binomially smoothed seasonal precipitation expressed as percentages of the long-term mean for San Diego superimposed on that for Mazatlan lagged by 7 years. Note the time shifts on the abscissae.

Leith (1973) and Leith and Whittaker (1975) have constructed models which predict the net primary productivity of vegetation over land areas from average annual temperature and precipitation. These models have so far performed admirably when their results are compared to those obtained through other approaches. Leith (1976) used the models to predict the possible impact of changes in both temperature and precipitation on net primary productivity in latitudinal belts of 10° from 70°N to 40°S latitudes. The results show that global net primary productivity may change by as much as 5% with simultaneous temperature changes of 1°C accompanied by a 6% change in rainfall. Of this 5%, about 1.6% are due to temperature changes and 3.4% to rainfall changes. Rainfall changes generally have greater impact on global vegetation than temperature changes although there are latitudinal differentiations. Leith cites the 8 % productivity change in the 60-70°N belt as due almost entirely to temperature against the 5% change in the 0-10°N belt, almost all of which was due to precipitation change.

Based on the present state of knowledge with regard to future climatic fluctuations, average annual temperature changes of several degrees and precipitation changes in the order of several tens of percent may be expected (Lamb 1966, Mitchell 1974, Johnsen et al., 1973). The first half of the twentieth century appears to have been a temporary respite from the more "glacial" conditions of the period 1600-1900 and the climatic character of the mid-nineteenth century might provide a better estimate than the 1931-60 or 1941-70 "normal" as to what the next two decades will be.

From their investigation of climatic oscillations between A.D. 1200-2000, using the isotopic composition of glacier ice from the Camp Century ice core as a climatic indicator, Johnsen, Dansgard and Clausen (1970) concluded that if we neglect "accidental events" and the effects of large-scale atmospheric pollution, there is a more than 85% probability that the cooling trend will continue in the next 10-20 years, followed by an increasing tendency reaching a peak between 2010 and 2020. Hubert Lamb and Tadashi Asakura have argued that cooler periods are marked by higher climate variability while Reid Bryson has produced evidence that drought frequency in northwest India in the twentieth century is correlated with cooling in high latitudes. Although the issue of a "cooling trend" is still controversial, it is becoming increasingly apparent that predictive models that enable us to better deal with the uncertainties of climatic variability will be more crucial in the next two decades than they were in the period 1931-60.

On the basis of sun-spot cyclicity, Willett (1976) predicts that over the next 25 years: (a) the temperatures in all latitudes will fall to significantly lower levels than those reached in the mid-1960s (he is uncertain as to whether the fall will start immediately, reaching its lowest level in the 1980s, or start in the 1980s and bottom out in the 1990s); (b) no major prolonged drought will occur in lower middle latitudes, except possibly along the subtropical margins of Mexican border States of the United States; (c) a predominantly dry period during the next two decades in higher middle latitudes, particularly in Canada and northern Europe, and in subtropical latitudes, with a decade of severe drought likely in southern Asia and subtropical Africa. He further predicts that between 2000 and 2030: (a) there will be an abrupt return to markedly warmer weather in middle and higher latitudes during the first decade of the next century, followed by a return to low temperatures, but the warmth of this period will not approach that of the 193160 period in intensity; (b) the warm decade of 2000-2010 will tend to be wetter in higher, middle and subtropical latitudes, but drier in lower middle latitudes; (c) the return to cooler conditions during the 2010-2030 decades should witness also a return to relative wetness in lower middle latitudes and relative dryness in higher middle subtropical latitudes. It must be pointed out that, so far evidence for and understanding of sun-spot/climate relationships have not been sufficiently convincing. However, we are not justified in dismissing the approach completely. If these predictions turn out to be even partially correct, it is evident that there will be large areas of the world that will suffer some adverse effects. Some areas may be harder hit than others and some may even be devastated unless some type of climatic warning system is available on a yearly basis.

Granger (1977) has shown that there have been significant quasi-periodic fluctuations in California precipitation in the past 100 years. There have been periods of marked dryness lasting from 3 to 6 years and correspondingly marked periods of wetness and it is expected that these patterns will continue in the immediate future. From the data series it can be demonstrated that extreme variability is characteristic of periods of decreasing hemispheric temperature. Similar quasi-periodic oscillations showed up in the precipitation series of Trinidad, West Indies, and in the water balance series because of concurrent fluctuations in temperature there (Granger, 1971). These oscillations result in an average of four years of comparatively large moisture deficits, ~40 cm, during the dry season, followed by a year of low deficit, ~7.7 cm (Figure 1). Since 1957, however, there has been a trend toward greater aridity concurrent with a net temperature decrease of, ~1°C.

The studies cited above, together with those of Kraus (1954, 1955, 1958), Trenberth (1976), Longley (1953), Bradley (1976), Krueger and Gray Jr. (1967), Lamb (1966), Hastenrath (1967), Winstenley (1973b), Bunting, Dennett, Elston and Mulford (1976) to list a few, clearly indicate that both temperature and precipitation have fluctuated in the past over large areas of the world and one can infer from these studies that similar fluctuations will occur in the future. Moreover there is strong evidence for parallelism in the behaviour of climatic regimes of different regions, for example, between African and Asian monsoon regimes particularly along their arid margins (Kraus, 1971) and between the Old World and New World summer rainfall regimes (Byrne, Granger and Monteverdi, 1978).

The inescapable conclusion is that the devastating droughts in the Sahel, the USSR, California and other areas of the world in the 1970s have to be accepted as part of the normal climate of these regions and their recurrence should therefore be expected. It should also be realized that the period 1931-60, which is taken almost universally as the standard of comparison, was a period of greater than average rainfall in most areas of the world. If we accept the premise that the impact of climatic aberrations can be minimized if and when their occurrences can be predicted, the challenge reduces to the basic tasks of formulating robust predictive models and of evaluating the extent of social and economic disruption associated with climate perturbations of different levels of magnitude and intensity. Granger, Byrne and Michaelsen (1978), in an attempt to meet the first of these two challenges, devised a model for California from the results of investigations by Byrne, Granger and Monteverdi (1978).

Figure 3. - (A) Power spectra of the seasonal precipitation time series for Mazatlan and San Diego

Figure 3. - (B) cross - spectrum of the same two series

Figure 3. - (C) coherence squared between the two series with Mazatlan as the independent series

Figure 3. - (D) phase shift in lag time between the two series with Mazatlan coming before San Diego.

These latter investigators, in a comparative analysis of recent rainfall trends in the Old World and New World subtropics sparked by the work of Winstanley (1973a, 1973b), uncovered an unexpected 7-year lag effect between summer rainfall in north central Mexico and winter rainfall in southern California. However, the strongest lag correlation was apparent in rainfall series that had been smoothed by 5-year running means and therefore susceptible to the Slutzky-Yule effect. The results for two stations are shown in Figure 2. Granger, Byrne and Michaelsen (1978) explored the lag further both in the frequency and time domains, using cross-spectral analysis which isolates all possible scales of differentiation of the fluctuation of the data series, and lag correlation analyses.

The data set consisted of (a) the seasonal totals of precipitation (May through October for the Mexican stations, and November through April for the California stations) of Mexican and California stations shown in Table 1 for the period 1880-1973; (b) seasonal totals expressed as percentages of their long-term mean to make the values from the two regimes comparable on the same scale; (c) area averages of percentage seasonal precipitation; and (d) weighted moving averages of seasonal percentage precipitation with weights proportional to the binomial coefficients for six terms. The California stations were chosen on the basis of the homogeneity of their precipitation regimes as indicated by inter-station correlation coefficients and coefficients of variation while the choice of Mexican stations was based on Wallen's (1955) classification of Mexican rainfall regimes and corroborated by inter-station correlation analyses.

Spectral estimates with fundamental periods of 2 mD t were obtained for frequency bands 0.0167 cycles per year wide for m = 30 and D t = 1 year. The raw estimates were smoothed by "hanning." The null hypothesis of a white noise continuum was adopted because the first order auto-correlation function was not significantly different from zero nor was there evidence of Markov linear type persistence. The 95% and 5% confidence limits for each spectrum were calculated according to the sampling theory developed by Tukey (1950). The phase and coherence squared were also calculated. The results are shown in Figure 3. Four prominent bands characterize the spectra although only the 2.0-2.1 year band reached a-priori statistical significance. The peaks at 2.1 and 5.5 years add to the already considerable spectral evidence for oscillations in meteorological variables related to precipitation in the central and northern Pacific with similar periods (Wagner, 1971; Angell and Korshover, 1974; White and Clark, 1975; Trojer, 1960; Portig, 1958; and Belarge, 1966).

The cross-spectrum and coherence squared (Figures 3b and 3c) show strong association between the two series at periods of 15-30 years, 12 years, 4.3 years, 2.7 years and 2.1 years. The coherences squared for these periods are all higher than 0.60 and are significantly different from chance occurrences. The time phase spectrum (Figure 3d) shows that the lower frequencies (0.017 to 0.133 cpy) have average phase shift in lag time of ~7 years, while the medium frequencies have lag times between 3 and 4 years. These latter lag times, in sum, produce a beat frequency with a lag of 6.8 years.

These results corroborate the findings of Byrne, Granger and Monteverdi (1978), and lead to the hypothesis that lag effect suggested in the Mazatlan - San Diego analysis may be extrapolated spatially since the selection of stations in both regimes was predicated on homogeneity and high inter-station correlations. Lag correlation coefficients between Mazatlan and San Diego for percentage seasonal precipitation and between the Mexican area means and the California area means for the same variable were therefore calculated. In addition the binomially smoothed series were similarly analysed. The results are shown in Figure 4.

Figure 4. - Lag correlation coefficients against lag time in years between Mazatlan and San Diego for seasonal and weighted seasonal precipitation, and between the Mexican area and California area for areal seasonal and weighted areal precipitation.

Summer precipitation at the selected Mexican stations is negatively correlated at lag zero, but highly positively correlated with winter spring precipitation at the selected California stations seven years later. The correlation coefficients at lag 7 are significant at the 1% confidence limit with tests that take account of the effects of serial correlation and changes in degrees of freedom dye to smoothing (Quenoille, 1952; Bartlett, 1946). The similarity of results in both the frequency and time domains indicates that the 7-year lag is statistically real. However, it is apparently related more strongly to the lower frequency (periods of 7 to 30 years) variances in the two rainfall series.

The 7-year lag effect was incorporated into regression analyses using all but the last eight years of the precipitation series (1880-1973) to produce predictive equations, leaving the period 1966-76 to be used as an independent test. The regression of San Diego seasonal precipitation on corresponding Mazatlan seasonal precipitation seven years before produced an equation with significant correlation coefficient but with a large standard error and small variance explained. This was not unexpected because of the noise in the seasonal precipitation series and the nature of the 7-year lag indicated above. The weighted averages for San Diego, Psw when regressed on the weighted averages for Mazatlan, Pmw lagged by 7 gave:

Psw = 0.658 Pmw-7 + 35.3 + 16.2%;
r = 0.60, n = 73 (2)

To test the stability of the correlation, the data sets were split arbitrarily into two periods, 1880-1920 and 1921-65. The resulting relationships are respectively:

Psw = 0.421 Pmw-7 + 56.9 + 14.6%;
r = 0.38, n = 35 (3a)


Psw = 0.765 Pmw-7 + 24.3 + 17.1%;
r = 0.67, n = 39 (3b)

The correlation coefficients are significant at the 1% level using the Bartlett formulation to allow for serial correlation in the time series and for reduction in numbers of degrees of freedom. The difference in the correlation coefficients may be due to the 19th and early 20th century precipitation in California differing somewhat from that of the later period (Granger,1977).

Smoothed areal means for the whole period (1880-1965) and for the sub-period (1921-65) were subjected to regression analysis as before and produced respectively:

Pcwa =0.696 Pmwa-7 + 30.9 + 13.4%;
r = 0.51, n = 73 (4a)


Pcwa = 0.919 Pmwa-7 + 7.7 + 15%;
r = 0.48, n = 34 (4b)

where the sub-scripts C = California, M = Mexico, A = Areal means, and W = weighted cumulative averages. Again the correlation coefficients are significant at the 1% level.

Equations 2 and 3b and 4a and 4b were used to predict the smoothed seasonal precipitation of San Diego from that of Mazatlan and the California areal from the Mexican areal for the independent test period 1966-76. Verification scores expressed in terms of an absolute error e, and a root mean square error RMSE, were calculated. The results are shown in Table 2. The predictive performance of the equations is quite good. The null hypothesis that the mean of the observed and forecast samples were not significantly different could not be rejected at p < 0.01 on a F-ratio test. As an additional test of the predictive consistency of the lag effect, Los Angeles and Sacramento which lie 190 km and 780 km respectively from San Diego were selected. Following identical procedures as for equations 2 and 3b, predictive relationships were derived. The outlooks based on them are consistent with those for San Diego and have similar statistical characteristics. We have demonstrated elsewhere that results from the statistical relationships given above can, with care, be mathematically disaggregated to provide actual seasonal precipitation estimates. The outlook for 1977-78 based on one such disaggregation appears to be more accurate than outlooks produced for California by other researchers using other methods.

Despite the accuracy of the equations the problem of causality still remains unsolved although a solution was, and is being vigorously sought. We are convinced that the lag effect is related in some way to the time and space distribution of sea-surface temperature anomalies in the north Pacific. Unfortunately, comprehensive sea-surface temperature data for a sufficiently long period are not now available to provide adequate resolution on the times scales over which the lag appears to be most important. Michaelsen (1977) has found some significant relationships but they appear to be temporally unstable.

We further suspect that the lag effect is part of a global-scale coupling between tropical and mid-latitude systems. Studies by Nicholls (1977) in Australasia and Namias (1957) in northwestern Europe found similar though shorter lags between tropical and mid-latitude systems. The California-Mexico precipitation connection is evidently a complicated one as evidenced by the result of the frequency domain analysis and several mechanisms may be involved, and from the results of Byrne, Granger and Monteverdi (1978) it is probable that an analogous connection with similar forcing mechanism(s) exists between analogous areas in the Old World. We are at present exploring the nature of these connections as far as available data will allow.

As far as we know the foregoing approach to seasonal precipitation outlooks has not been used elsewhere; we do know, however, that it provides California with a seven-year lead time in seasonal precipitation outlooks which is potentially advantageous to water resource planners, agriculturalists, forest management experts, and all those concerned with water availability in central and southern lowland California. If results from research now underway confirm that the lag effect is more than just a north Pacific phenomenon, similar outlooks for other areas of the world will provide an invaluable input into forest management decisions.

TABLE 2. Forecasts of smoothed seasonal precipitation1

Weighted mean centred on






























































































e = 4.8%

= 4.6%

e = - 7.9%

= - 9.8%

RMSE = 16.1%

= 16.9%

RMSE = 14.7%

= 16.8%

1 Using equations 2 and 3b and 4 together with verification scores expressed as average absolute error e, and root mean square error (RMSE). The season is given in which the January-April period falls.

ACKNOWLEDGMENTS: Dr. Roger Byrne and Graduate Students Joel Michaelsen and John Monteverdi collaborated in the initial research project from which some of the above results were taken and the university of California, Berkeley provided the subsidized computer time without which the analysis could not be performed.


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