the variance in the precipitation fo regions of p to 500,000 km and more than 35% of

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1 WATER RESOURCES RESEARCH, VOL. 36, NO. 3, PAGES , MARCH 2000 A model for forecasting drought from teleconnections Ian Cordery School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia Mark McCall Australian Bureau of Meteorology, Sydney, Australia Abstract. Strong relationships have been developed between both global and local phenomena in one season and precipitation in the next four seasons for years when the precipitation is likely to be low (drought years) The relations explain more than 65% of the variance in the precipitation fo regions of p to 500,000 km and more than 35% of the variance for up to 1.3 x 106 km 2 in eastern Australia. The strong relationships occurred when precipitation was regressed against one of the variables in years that were selected on the basis of the magnitude of a third, so-called partitioning, variable. The relations are shown to be able to provide forecasts of low precipitation in all seasons of the year. Statistical tests show that the strong forecasting relations could not occur by chance. 1. Introduction Around the globe, there are regions where precipitation is related to broadscale atmospheric phenomena such as E1 Nino-southern oscillation, which is numerically defined by the southern oscillation index (SO!), sea surface temperatures (SST), and geopotential height (GpH). The demonstration of these relatively strong relationships for many regions [Ropelewski and Halpert, 1996] has aroused considerable interest and encouraged investigation of the possibilities of forecasting rainfall and perhaps alleviating some of the socially undesirabl effects of sudden, unexpected occurrences of extremes such as droughts, floods, and widespread fires. Investigation of relations between SOI and low rainfall in eastern Australia has been particularly encouraging, but unfortunately it has not led to relationships that have been sufficiently consistento provide a sound basis for forecasting [Nicholls, 1984a; Opoku-Ankomah and Cordery, 1993]. In addition, strong relationships between concurrent atmospheric or sea surface variables and precipitation have little practical value. The need in terms of possibilities for forecasting is to have an easily measured phenomenon in one month, related to precipitation one, or preferably several months later. Though there has been considerable research along these lines [Nicho!ls, 1984b; Cordery et al., 1993; Ropelewski and Halpert, 1996], there have been few instances of use of such relationships because either the relationships developed have not been strong enough or the delay between data collection and the forecast event has been too short to permit any action. An exception to this is the forecasting model developed by Hastenrath and Greischar [1993] for northeast Brazil. Other examples of forecast systems are the Australian Bureau of Meteorology's "Seasonal outlook" I/lust. Bur. Met., various dates], which attempts to qualitatively indicate the precipitation to be expected during the following 3 months, and the estimation of snowpack water content from GpH in parts of western United States [McCabe Copyright 2000 by the American Geophysical Union. Paper number 1999WR /00/1999 WR and Legates, 1995]. A possible forecasting system has been presented by He and Barnston [1996] with lead times of up to 13 months, but this approach has only been able to explain 50% of the variance in the target precipitation in one instance, with less than 35% of the variance being explained in most cases, providing an insufficient basis for a credible forecasting service. Since atmospheric and ocean surface phenomena have been shown to be quite strongly related to local precipitation, both concurrently and with a delay of several months, an investigation was undertaken to attempt to determine causes of changes in relationships in the hope of being able to develop relations that would allow consistent forecasting of precipitation in eastern Australia. In this research the aim was to forecast drought. Hence effort was focused on developing relationships that would allow estimation of the occurrence of below average precipitation. 2. Inconsistencies in Relations Between Precipitation and Other Phenomena The variables most widely used in relationships with precipitation have been the Southern Oscillation Index (SOI) and SSTs. SOI is determined as the difference between sea level atmospheric pressures at Papeete (Tahiti) and Darwin, normalized to have a mean of zero and standard deviation of 10 [Troup, 1965]. While it has been possible to relate precipitation to SOI and SSTs, in general, the relations have not been very strong. Experience in Australia was similar to that in other places [McBride and Nicholls, 1983; Lough, 1992] in that the relations with precipitation were stronger than could occur by chance but were not strong enough to provide a basis for forecasting precipitation, except for one or two restricted locations. In the 110 or so years for which concurrent precipitation and SOI observations are available, there have been two important droughts in Australia (1919 and 1937) during which the SOI remained close to its long-term average and two occasions when very low SOI values occurred, but drought conditions were not observed (1905 and 1957). There were 16 droughts and 16 occasions when the SOI was more than one

2 764 CORDERY AND MCCALL: FORECASTING DROUGHT FROM TELECONNECTIONS standard deviation below its long-term mean for several months in succession. The anomalies in SOI-precipitation relations listed above suggesthat precipitation over eastern Australia is not totally dominated by this global-scale phenomenon. Local-scale phenomena also appear to exert considerable influence. Recently, it has been shown that geopotential height is related to precipitation in various parts of the world [McCabe and Legates, 1995; Drosdowsky, 1993; Kozuchowski and Wibig, 1992; Mc- Cabe, 1996] and that for a large part of eastern Australia, using a seasonal time interval, relationships between GpH and precipitation are stronger than those between SOI and precipitation [Nazemosadat and Cordery, 1997]. Unfortunately, GpH data have only been routinely collected over the last 50 years and so it is not possible to examine very long term relations between GpH and precipitation, such as is possible for relations between SOI and precipitation (from the 1870s). In order to consider the possibility of assessing the influence of several phenomena on precipitation, there is a need to develop a model of their interactions. At this stage, practically nothing is known of the physics of the interaction between these phenomena except that they are observed to change in concert with each other and that they all tend to be correlated with each other. This means that a simple exploratory model such as multiple regression between precipitation and variables such as SOI, SST, and GpH cannot be useful in estimating precipitation since the simple linear correlation coefficients between SOI, SST, and GpH, using a seasonal time interval, are of the order of 0.7, whereas valid use of multiple regression requires independence of the predictor variables Partitioning Data Another means of examining the influence of two correlated variables on a third variable is to use one variable as a marker to partition the data. Where the three variables are in the form of concurrent time series, one variable could be used as a means of selecting occasions when the relationship between the remaining two variables is to be examined. For example, if both SOI and GpH influence precipitation, it is possible that when SOI is low, which usually indicates below average rainfall in eastern Australia, there may be a strong relationship between GpH and precipitation. Hence a partitioning strategy, for say, January, could be to select the years when the January SOI is in the lowest 25% of all January SOIs. For these years the January GpH-precipitation regression could be examined. This is a conditional model where the regression relation depends on the value of the partition variable (SOI). This conditional model includes the effects of both global (SOI) and local (GpH) influences on precipitation without compromising the requirements for valid use of regression as a prediction model Data Available Data available for this study were supplied by the Australian Bureau of Meteorology. Precipitation data comprised monthly values for all 107 districts into which Australia is divided for reporting purposes. The districts vary in size from a few hundred square kilometers in the larger cities to -500,000 km 2 in the arid regions. A district monthly data value comprises the average of the values reported. Provided that the number of stations used to estimate the mean for each month is high, say, greater than 10, the time series for each district should be relatively homogeneous. SO1 and GpH data were provided from the Bureau of Meteorology archive. GpH data were available in the form of average monthly altitudes at which the particular pressure was observed. Data were obtained for the radiosonde observation locations with the longest records that were Woomera, Alice Springs, Perth, and Melbourne (Figure 1) and for pressures of 1000, 900, 850, 700, and 500 hpa. Seasonal analysis was used rather than monthly because it has been shown that the strength of association between precipitation and SOI varies with the data interval used, the highest association occurring for a 2-month interval, dosely followed by 3 months [Opoku-Ankomah and Cordery, 1993]. Since 3 months is a season and provides a worthwhile forecasting period, this interval was adopted for the analytical work. Autumn was defined as March to May, winter June to August, etc. When seasonal data were used, they were assembled in a time series for each season, so that the autumn series comprised autumn 1950, autumn 1951, etc. 3. Seasonal Relationships Between Precipitation and GpH Partitioning of seasonal data was accomplished by identifying the years in which the GpH was very high. Data were available for and GpH data for years inclusive were initially not available in the Bureau of Meteorology archive. To partition the data, the years with the 10 highest GpH values for the particular season were selected. A sample size of 10 was adopted becaus experimentation showed that the strongest relations between seasonal precipitation and either SOI or GpH occurred for between 8 and 11 data points, and also 10 years gives -25% of the available GpH data. For the selected season and years, precipitation was regressed against SOI and GpH for the same season. This provided regressions of concurrent autumn precipitation versus autumn SOI and of concurrent autumn precipitation versus autumn GpH, in both cases for the years with the highest autumn GpH. In summer, autumn and winter strong relationships were found to occur over large areas of eastern and northern Australia. In spring a large area, shown in Figure 1, had strong relations between GpH at Woomera and precipitation, when SOI was lowest, with correlation co- efficients exceeding 0.6 for -1.3 x 106 km 2 and exceeding 0.8 for an area of-200,000 km 2. A physical justification for this form of partitioned relationship also needs to be found. Nazemosadat and Cordery [1997] have provided a tentative explanation for high GpH over inland Australia being associated with drier than average condi- tions over south eastern Australia. The combination of low SOI, which is associated with descending air over the tropical western Pacific, with high GpH at Woomera, which is also associated with below average precipitation, presumably rein- force each other. In winter, anticyclones cross Australia from west to east at 25ø-30øS latitude. To the south of these anticyclones the air motion over most of the southern part of the continent is westerly with cool, moist, southern maritime airmasses from the Indian and Southern Oceans. Orographic and frontal lifting of these airmasses produce much of the winter rainfall acros southern Australia. Woomera (31øS) is located close to the average path of the anticyclones in winter, and so this is a region where air is generally descending. However, below average GpH at Woomera is an indication that Southern Ocean

3 CORDERY AND MCCALL: FORECASTING DROUGHT FROM TELECONNECTIONS Figure 1. Isopleths of correlation coefficient between spring geopotential height (GpH) (700 hpa at Woomera) and spring precipitation for the 10 years with lowest spring southern oscillation index (SOl). Data period Figure 2. Isopleths of correlation coefficient between winter SOl and spring precipitation for the 10 years with the highest winter GpH (700 hpa at Woomera). Data period and depressions with their ascending air intrude further to the north and influence a large part of southern Australia. Precipitation occurs from this cool ascending air. So when GpH is lower, the precipitation in this region increases, but when GpH is above average, the dominant air movement is downward and the region is dry. Figure 1 shows correlations for GpH versus rainfall when SOI was low, with predominantly descending air and low rainfall over southeastern Australia. 4. Lag Relationships 4.1. The Relationships While strong relationships between concurrent SOI, GpH, and precipitation are of great interest, they have little practical value for predicting precipitation. To be useful for prediction, the precipitation in one season needs to be related to variables observed in an earlier season. tralia for all four seasons. It is noteworthy that strong relations were observed for large areas, not just for individual rainfall districts. Rainfalls in adjacent districts tend to be correlated, but as can be seen in Figures 2 and 3, strong relationships occur over much larger regions than "adjacent districts." For all seasons, correlation coefficients for one season ahead relationships of greater than 0.7 (relations explaining more than half the variance in the rainfall in the target season) were obtained for areas exceeding 106 kltl 2 and correlation coeffi- To examine the possibility of using the partition model for forecasting, the years with the 10 highest winter GpH values were identified. For these years, winter SOI was regressed against spring precipitation for each of the 107 rainfall districts. Depending on the location of the GpH data, different relationships were obtained between winter SOI and spring precipitation. Not only did the SOI-precipitation relations vary with the location of the GpH observations, but the regions where the strongest relationships occurred also changed when the partitioning GpH station was changed. Similarly, when the partitioning and regression variables were interchanged, that is, when winter SOI was used as the partitioning variable and winter GpH was regressed against spring precipitation for the years of lowest winter SOI, similar strong relationships occurred but at different locations. Examples of the correlations for the strong but different sets of relationships are shown in Figure 3. Isopleths of correlation coefficient between winter Figures 2 and 3 for spring precipitation. Similar, strong rela- GpH (700 hpa at Woomera) and spring precipitation for the 10 tionships between variables in one season and precipitation in the next season were obtained for large areas of eastern Ausyears with highest winter GpH (700 hpa at Woomera). Data period and

4 766 CORDERY AND MCCALL: FORECASTING DROUGHT FROM TELECONNECTIONS Table 1. Number of Australian Rainfall Districts for Which Significant Correlations Occur Between Rainfall and Southern Oscillation Index or Geopotential Height for the Forecasting Period Shown No. of Districts With r > 0.6 (Significant at 95% Level) Lag Between Forecast Formulation and Target Season Concurrent (zero lag) data 3 months (one season) 6 months (2 seasons) 12 months (4 seasons) Random Selection of Data Target Partition Model Mean of Standard Deviation Season Selection of Data 500 Runs of Random Runs spring summer autumn winter spring summer autumn winter spring summer autumn winter spring summer autumn winter Total number of districts is 107. cients greater than 0.8 were obtained for areas of -5 x l0 s gression variables that produced strong relations for the largest km 2. number of rainfall districts was Woomera GpH (700 ppa) for When it had been established that relationships strong the 10 years of lowest spring SOI (partition variable), for which enough to provide credible prediction of precipitation one 46 districts had regressions with r > 0.6. However, when season ahead had been obtained, attention was turned to de- autumn GpH (6 months ahead) was used as the partitioning veloping relations for forecasting two and more seasons ahead. variable, strong relationships were obtained between spring It was found that strong partition relations could also be es- GpH and spring precipitation for a larger number of districts tablished for these longer-term forecast intervals. In general, (67) covering most of southern Australias shown in Figure 4. the relations obtained were not as strong as those obtained for The question must be asked, "Why is it possible to obtain one season ahead forecasts and did not include such large stronger correlations using data that are more distant, in time, areas of the country's land surface. However, the relationships were too consistent and covered too large an area to have occurred by chance. As can be seen in the leftmost three columns of Table 1, the number of rainfall districts for which regressions were obtained with r > 0.6 declined as the forecast interval increased from zero to four seasons Anomalies in Lag Relationships At this stage of the development of conditional or partition relationships for forecasting low rainfall, it has not been found possible to provide a physical explanation for the discovered relationships. As mentioned earlier, Nazemosadat and Cordery, [1997] have suggested a physical explanation for concurrent relations, but not for lag relationships. The large energy storage of the oceans could be the cause for SOI in one season being related to precipitation in later seasons. However, upper air pressure phenomenare much more ephemeral, continuously circulating from the west to the east and having a "residence" time over any surface location of just a few days. Why these upper air phenomena would be related to precipitation several months later is not apparent at this time It is not only surprising that GpH in one season should be related to precipitation one or more seasons later, but there are occasions when the lag relationships, or pseudo lag rela- Figure 4. Isopleths of correlation coefficient between spring tionships are stronger than concurrent relationships. For ex- GpH (700 hpa at Woomera) and spring precipitation for the 10 ample, when concurrent relationships were examined for years with highest autumn GpH (700 hpa at Melbourne). Data spring precipitation, the combination of partitioning and re- period

5 CORDERY AND MCCALL: FORECASTING DROUGHT FROM TELECONNECTIONS 767 loo 50 R 2 = 0.80 ß I I m I I I m Figure 5. Relationship between autumn SOI and spring precipitation for Australia Bureau of Meteorology District 26 (centered at 37øS, 140ø15'E). The larger shaded points are those for the 10 years with the highest values of 700 hpa geopotential height at Melbourne in autumn.,sol than with concurrent data?" Anomalous relations such as this have not been found in all seasons, but it is not uncommon for very good concurrent relationships to result from selection of data pairs for the years of highest GpH (partition variable) one or two seasons before the occurrence of the concurrent regression variables. 5. Validity of Regression Relationships SOI and GpH have been shown to be only weakly related to precipitation unless the data are partitioned. The process of partitioning data before developing regression relations could introduce some bias or it is possible the relation may not be linear. A small selection (from the several thousand, one for each of the 107 rainfall districts for each parameter combination) of the regressions was examined. An example is shown in Figure 5. It shows autumn SOI plotted against the following spring precipitation for district 26, which is at 37øS, 140ø15'E, for years , The data points for the years that have the 10 highest values of the partition variable, GpH (700 hpa) at Melbourne in autumn, are highlighted. It should be noted that for the total data there is no relation between autumn SOI and spring precipitation but that for the highlighted data points there is a strong linear relationship (r = 0.89, n = 10). In the absence of a physical basis for the forecasting models, there is a need to demonstrate that the relationships are not accidental occurrences or artefacts of the simple mathematical formulation. One test that was used was to substitute a random process for the simple partitioning device of selecting the data pairs as those with either minimum SOI or maximum GpH at the time of forecast formulation. For example, instead of selecting data for the years when autumn GpH was in the highest quartile of autumn GpH values, a random selection of years was made. For these years the SOI and precipitation were correlated for all 107 precipitation districts. Several hundred runs were undertaken for each forecast period and season, each run with a different, randomly selected set of 10 years for the regression exercise. For a few target periods, strong correlations resulted for a surprisingly large number of precipitation districts as shown in columns 4 and 5 of Table 1. A contribution to the large mean value of districts with strong correlations was the fact that rainfalls tend to be strongly correlated within groups of districts. This can be seen by the size of the standard deviations of numbers of districts for which correlations were significant. In most cases the standard deviation is about equal to the mean. By comparison the proposed partition model in most cases produced strong correlations (including lag relations) in far more districts than result from the random selection process. In column 3 of Table 1 are shown the maximum number of districts with significant relationships produced by the proposed model. The shown maxima result from a range of different combinations of the partition and predictor variables. In most cases the number of districts with significant relationships from the proposed model is more than two standard deviations greater than the number of districts for which significant correlations result from the random selection process. Since there is less than 5% chance of obtaining values more than 2 standard deviations from the mean, and here we are only considering values higher than the mean, there is less than 2.5% chance that the large numbers of districts with strong relationships from the proposed partition model could have occurred by chance. This small experiment demonstrates that it is unlikely that the results obtained are a statistical artefact. Rather, it reinforces the need to understand the processes that might be responsible for such a set of results. It can also be seen from Table 1 that the number of districts for which significant relationships are produced by the proposed model decreases with the lag, but that even with 1 year ahead forecasts, strong relationships were obtained for far more districts than could have occurred by chance. 6. Formulation of a Forecast To demonstrate the way in which a forecasting system such as that proposed here could be used, an independent data set, for the years and , which were not used in developing the forecasting system, were used. From the period and , the years with the 10 lowest autumn SOI values were selected, (---25% of the 37 years), and for these years, regressions were developed between the average autumn 700 hpa height at Alice Springs and winter precipitation for each of the 107 rainfall districts in

6 768 CORDERY AND MCCALL: FORECASTING DROUGHT FROM TELECONNECTIONS Table 2. Precipitation Forecasts for District 55 for Winter for Years for Which Development Data Were Not Used in Model Winter Rain Forecast From Observed Winter Year Autumn, mm Rain, mm 1988 not low not low not low Not low 522 Note that for district 55, median winter rainfall 387 mm. Lowest 25th percentile rainfall 282 mm. which precipitation is related to observations of other variables in previous months, have generally been weak. It has been shown here that precipitation is strongly related to combinations of observations of SOI and GpH up to 1 year earlier, and that these relations are strong enough to explain more than 65% of the variance in the precipitation over large areas of Australia. From these relations a forecasting technique has been developed that can be used to forecast the likelihood of occurrence of low precipitation up to 1 year ahead. Acknowledgment. Facilities to undertake part of the reported work were kindly provided by the Institute of Hydrology, Wallingford, U.K. Monthly precipitation, SOI and GpH data were provided by the Australian Bureau of Meteorology. Australia. For demonstration purposes district 55, which is located at 31øS, 150ø30'E in eastern Australia will be used as an example. The linear correlation coefficient between the autumn GpH and winter rainfall for the conditional relationship was In operational mode a watch would be kept on autumn SOI values. At the end of autumn, if the autumn SOI was in the range of the lowest 25% of values, i.e., below -7.2, then the Alice Springs 700 hpa GpH would be applied to the GpHrainfall regression to obtain an estimate (forecast) of the winter rainfall. After development of the results discussed above, data became available for the missed years and for , and an attempt was made to use the model in forecasting mode with this completely independent data set. Table 2 shows the observed winter rainfalls and the estimated (forecast) values for the independentest years. In the column of forecast values the words "not low" occur where the autumn SOI value was not in the lowest 25% of observed values, to which the partitioned relationship applied, and therefore no value could be estimated, except to forecasthat the value should be above the lowest 25% of all observed winter rains. Though the results shown in Table 2 do not appear very impressive at first glance, they are quite consistent with the correlation coefficient value of 0.74 (explaining 55% of the variance). In the 4 years and 1996 the forecasts are completely correct in that all the observed rainfalls were in the vicinity of, or above the median values. In 1995 the forecast was approximately correct in that it was for a value within the lowest 25 % of observations and the observed value was in this (drought) range. For 1994 the forecast was incorrect. 7. Conclusion For many years, significant relations have been known to exist between precipitation and global variables such as SOI and SSTs. Though these relations have been statistically significant, they have not been strong enough to provide consistently reliable forecasts since the proportion of the variance they have been able to explain in the target precipitation has generally been less than 35%. In addition, the strong relations have been between concurrent variables. Lag relations, in References Australian Bureau of Meteorology. Seasonal outlook. Various dates. Cordery, I., S. L. Yao, and Y. Opoku-Ankomah, Forecasting drought-is it possible? Hydrol. Water Res. Symp., Inst. Eng. Aust., Natl. Conf. Publ., 93/14, , Drosdowsky, W., An analysis of Australian seasonal rainfall anomalies: , II, Temporal variability and teleconnection patterns, Int. J. Climatol., 13, , Hastenrath, S. and L. Greischar, Further work on the prediction of northeast Brazil rainfall anomalies, J. 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Cordery, The influence of geopotential heights on New South Wales rainfall, Meteorol. Atmos. Phys., 63, , Nicholls, N., The stability of empirical long-range forecast techniques: a case study, J. Clim. Appl. Meteorol., 23, , 1984a. Nicholls, N., Toward the prediction of major Australian droughts, Aust. Meteorol. Mag., 33, , 1984b. Opoku-Ankomah, Y. and I. Cordery, Temporal variation of relations between New South Wales rainfall and the southern oscillation. Int. Jour. Climatology, 13, Ropelewski, C. F., and M. S. Halpert, Quantifying southern oscillation-precipitation relationships, J. Clim., 9, , Troup, A. J., The southern oscillation, Q. J. R. Meteorol. Soc., 91, , I. Cordery, School of Civil and Environmental Engineering, University of New South Wales, Sydney 2052, Australia. M. McCall, Australian Bureau of Meteorology, Sydney 2001, Australia. (Received September 2, 1999; revised October 25, 1999; accepted October 26, 1999.)