LONG RANGE FORECASTING OF LOW RAINFALL

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 19: (1999) LONG RANGE FORECASTING OF LOW RAINFALL IAN CORDERY* School of Ci il and En ironmental Engineering, The Uni ersity of New South Wales, Sydney 2052, Australia Recei ed 23 April 1997 Re ised 25 June 1998 Accepted 16 August 1998 ABSTRACT Strong relationships have been developed between a global parameter, the southern oscillation index (SOI), and a more local parameter, the geopotential height (GpH), in one season and precipitation in the next season. These relationships, which have only been examined for part of eastern Australia at this stage, explain 50% of the variance in one-season ahead precipitation for areas up to km 2 and 80% of the variance for smaller areas. The relationships, which are essentially simple linear regressions between precipitation in the target season and GpH or SOI in the previous season, apply when a third variable is in a particular range during the previous season. The success of this forecasting scheme is apparent in all four seasons of the year. This form of forecasting, which is based on the partitioning of observed data, has the potential to provide reliable 3-months ahead forecasts of precipitation for large regions. Copyright 1999 Royal Meteorological Society. KEY WORDS: long-range forecasting; low rainfall; SOI; geopotential height; Australia 1. Introduction Around the globe there are regions where precipitation is related to broad scale atmospheric phenomena, such as the El Niño Southern Oscillation, which is numerically defined by the southern oscillation index (SOI; Pittock, 1973), 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 into the possibilities of forecasting rainfall. If reliable forecasts can be produced, then there is a possibility of preparing for, and perhaps alleviating, some of the socially undesirable effects of sudden, unexpected occurrences of extremes such as droughts, floods and widespread fires. Investigation of the relationships between SOI and low rainfall in eastern Australia has been particularly encouraging, but unfortunately it has not led to relationships which have been sufficiently consistent to provide a sound basis for forecasting (Opoku-Ankomah and Cordery, 1993; Nicholls, 1984a). A different approach which is able to provide 3-months ahead forecasts of low precipitation using the same input data is presented here. The accuracy of the forecasts is such that they should gain the confidence of potential users. Strong relationships between concurrent atmospheric or sea surface parameters and precipitation have little practical value. The need, in terms of possibilities for forecasting, is to have a phenomenon easily measured in 1 month related to precipitation one, or preferably several, months later. Although there has been considerable research along these lines (Nicholls, 1984b; Cordery et al., 1993; Opoku-Ankomah and Cordery, 1993, 1994), there have been few instances of the use of such relationships, either because 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. Examples of forecast systems are the Australian Bureau of Meteorology s Seasonal Outlook, 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 * Correspondence to: School of Civil and Environmental Engineering, The University of New South Wales, Sydney 2052, Australia. CCC /99/ $17.50 Copyright 1999 Royal Meteorological Society

2 464 I. CORDERY parts of western USA, indicating the volume of meltwater likely to be observed in subsequent months (McCabe and Legates, 1995). Hastenrath and Greischar (1993) have shown that it is possible to explain up to 70% of the variance in precipitation several months ahead for north-eastern Brazil. In addition, a possible forecasting system has been presented for the Pacific Islands (He and Barnston, 1996) with lead times of up to 13 months, but this approach has only proved capable of explaining 50% of the variance in the target precipitation in one instance, with less than 35% of the variance being explained in most cases. With the exceptions noted, most proposed forecasting schemes explain 35% of the variance in the target precipitation, thus failing to provide the basis for a credible forecasting service. 2. INCONSISTENCIES IN RELATIONSHIPS BETWEEN PRECIPITATION AND OTHER PHENOMENA Although there are strong relationships between SOI and precipitation in eastern Australia, important deficiencies exist. For example, in the approximately 110 years for which concurrent precipitation and SOI observations are available (1880s to the present), there have been two important droughts during which the SOI remained close to its long-term average (1919 and 1937) and two occasions when very low SOI values occurred (usually suggesting drought conditions) concurrent with either average or above average precipitation (1905 and 1987). During these 110 years, there were 16 droughts and 16 occasions when the SOI was more than 1 S.D. below its long-term mean for several months in succession. The general strength of SOI precipitation relationships in many parts of the world suggests that they are not statistical artefacts. Rather, they are reflections of the real influence of the southern oscillation phenomenon on changes in dominant wind directions over the equatorial Pacific Ocean and the associated equatorial ocean currents, as well as that of regions where ascending or descending air is dominant. However the anomalies in SOI precipitation relationships listed above suggest that precipitation over eastern Australia is not entirely dominated by this global scale phenomenon. Local scale phenomena also appear to exert considerable influence. There have been several allusions to this possibility, in addition to demonstrations that other phenomena (e.g. latitude of west east passage of anticyclones, SSTs of various ocean regions) are related to precipitation. Recently, it has been shown that GpH is related to precipitation in various parts of the world (Kozuchowski and Wibig, 1992; Drosdowsky, 1993; McCabe and Legates, 1995; McCabe, 1996) and that for a large part of eastern Australia, using a seasonal time interval, the relationships between GpH and precipitation are stronger than those between SOI and precipitation (Nazemosadat and Cordery, 1997). Unfortunately, GpH data have only been routinely obtained over the last 50 years and therefore it is not possible to examine long-term relationships between GpH and precipitation. In order to consider the possibility of assessing the influence of several phenomena on precipitation, it is necessary to develop a model of their interactions. At present, 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. This means that a multiple regression between precipitation and SOI, SST and GpH cannot be useful in estimating precipitation from the others, 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 of 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 the time intervals for which 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

3 LONG RANGE FORECASTING OF LOW RAINFALL 465 Australia, there may be a strong relationship between GpH and precipitation. Hence, a partitioning strategy for January for example, 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 simple model includes the effects of both global (SOI) and local (GpH) influences on precipitation without compromising the requirement for valid use of regressions A ailable data The data available for this study comprised the monthly district precipitation for all 30 rainfall districts in New South Wales, Australia, which has an area of km 2. These data, supplied by the Australian Bureau of Meteorology, comprise a mean of the monthly precipitation observed in each district; SOI data were provided from the Bureau of Meteorology archive. SOI is defined as the sea level pressure difference between Papeete (Tahiti) and Darwin (Australia) normalised for each month to have a mean of zero and a standard deviation of 10 (Pittock, 1973). GpH data were available in the form of average monthly altitudes at which the particular pressure was observed. Data were initially obtained for four radiosonde observation locations and for pressures of 1000, 900, 850, 800, 700 and 500 hpa. Later, GpH data were obtained for a wider range of radiosonde stations around Australia. Seasonal rather than monthly analysis was used, because it has been shown that the strength of association between precipitation and SOI varies with the data interval used, with the highest association being observed for a 2-month interval, closely followed by 3 months (Opoku-Ankomah and Cordery, 1993). Since 3 months comprises a season and would appear to be a worthwhile forecasting period, this interval was adopted for the analytical work. 3. SEASONAL RELATIONSHIPS BETWEEN LOW PRECIPITATION AND GpH Partitioning of seasonal data was accomplished by identifying the years in which either GpH was very high or SOI was low. Data were available for and GpH data for the years (inclusive) could not initially be obtained from the Bureau of Meteorology archive. The seasons were defined as autumn being from March to May, winter from June to August etc. The seasonal data were assembled into time series, in order that the autumn series comprised autumn 1950, autumn 1951 etc. To partition the data, the years having the ten highest Woomera 800 hpa GpH values for the particular season were selected. For these selected years, precipitation for that season was in turn regressed against SOI and GpH. This provided regressions of concurrent autumn precipitation ersus autumn SOI and of concurrent autumn precipitation ersus autumn GpH for the 10 years having the highest autumn GpH. In summer, neither variable was correlated with precipitation. In autumn and spring, precipitation was correlated with GpH in the partitioned years with r 0.6 for small areas only. In winter, the correlation between SOI and precipitation for years having high GpH at Woomera was very high, with r 0.8 for 60% of New South Wales, or km 2 and r 0.9 for 15% or km 2,as shown in Figure 1. A physical justification for this form of partitioned relationship must also be found. Nazemosadat and Cordery (1997) provided a tentative explanation for high GpH over inland Australia being associated with drier than average conditions over south-eastern Australia. The combination of low SOI associated with descending air over the western Pacific, with high GpH which is also associated with below-average precipitation, presumably reinforce each other in winter. In this season, anticyclones cross Australia from west to east at S latitude. To the south of these anticyclones, the air motion over most of the southern part of the continent is westerly with cool, moist, cloudy southern maritime air masses from the Indian and southern oceans. These air masses are usually dominant at latitudes 30 S (central and southern New South Wales). Orographic and frontal lifting of these air masses produce much of the winter rainfall in New South Wales, particularly on the western slopes of the Great Dividing Range. In winter, Woomera (31 S) is located close to the average path of the

4 466 I. CORDERY anticyclones where air is generally descending. However, below-average GpH at Woomera is an indication that southern ocean depressions with their ascending air will intrude further to the north and influence a large part of New South Wales. Precipitation occurs as a result of this cool ascending air, especially on the western side of the Great Dividing Range. The north of the state lies in the track of the anticyclones, so that when the 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. Nazemosadat and Cordery (1997) observed that in winter, the GpH at Woomera reflects the latitudinal position of the anticyclones and is more strongly related to precipitation than is SOI. 4. LAG RELATIONSHIPS While strong relationships between concurrent SOI, GpH and precipitation are of great interest, they have a limited practical value for forecasting precipitation unless they can be used with forecasts of SOI and GpH values, which may be produced by global climate modelling. To be useful for forecasting, the precipitation in one season needs to be related to parameters in an earlier season. Lag relationships, between, for example, SOI in one season and precipitation in the next season, are generally not sufficiently strong to have any potential for forecasting, although exceptions to this have been demonstrated by Hastenrath and Greischar (1993) for a specific region, and globally by Stone et al. (1996). To examine the possibility of using a partition model for forecasting, the years having the ten highest spring GpH values were identified. For these years, the spring SOI was regressed against the summer precipitation. As shown in Figure 2, for this relationship the correlation coefficient exceeded 0.7 for an area of about km 2 and for km 2 it exceeded 0.6. When these ten highest spring GpH values were regressed against summer precipitation, the area with r 0.7 increased to km 2, while r 0.6 included km 2, Figure 1. New South Wales: isopleths of the correlation coefficient (as a percentage) between winter SOI and winter precipitation for the 10 years having the highest winter GpH (800 hpa at Woomera). Period of record,

5 LONG RANGE FORECASTING OF LOW RAINFALL 467 Figure 2. New South Wales: isopleths of the correlation coefficient (as a percentage) between spring SOI and summer precipitation for the 10 years having the highest spring GpH (800 hpa at Woomera). Period of record, or more than half the state, as shown in Figure 3. However, for these two different models with summer precipitation related to spring SOI or GpH, the regions in which the strong relationships occurred were quite different, as can be seen from comparison of Figures 2 and 3. The reasons for the differences are not obvious, particularly since strong relationships are not limited to one side of the Great Dividing Range, nor do they correspond to any defined climatic zone. Later, GpH data for other stations were used and it was found that stronger relationships covering larger areas were obtainable. For example, when the partitioning variable was the 700 hpa height at Perth, 2000 km to the west of the region for which precipitation data were available, values of r 0.7 were obtained for km 2 when the independent variable was spring SOI, as shown in Figure 4. Here, the relationship between SOI and precipitation is stronger than that shown in Figure 2, but at this stage it is not possible to suggest any physical reason why data from a particular location would provide stronger relationships. As an example, there was weaker correlation between Perth GpH in spring and summer precipitation for these partitioned years, compared with the degree of association shown in Figure 3. Further examination of lag relationships using data partitioned in the same manner as described above enabled the development of strong relationships for all seasons. For example, for spring and autumn precipitation, partitioned relationships were developed with Woomera GpH and SOI in the previous season having correlation coefficients 0.7 for km 2 for spring precipitation and km 2 for autumn precipitation. Between autumn GpH or SOI and winter precipitation, strong relationships were found for more limited areas. When data on autumn SOI were partitioned, a relationship between autumn Figure 3. New South Wales: isopleths of the correlation coefficient (as a percentage) between spring GpH (800 hpa at Woomera) and summer precipitation for the 10 years having the highest spring GpH. Period of record,

6 468 I. CORDERY Figure 4. New South Wales: isopleths of the correlation coefficient (as a percentage) between spring SOI and summer precipitation for the 10 years having the highest spring GpH (700 hpa at Perth). Periods of records, and GpH at Alice Springs and winter precipitation was found, with correlation coefficients 0.7 for km 2. It is apparent from the above reported results that there are large regions where precipitation is strongly related to SOI or GpH in the previous season for those years when GpH is high. The reverse situation, that of strong correlation between precipitation and SOI or GpH in the previous season, also occurs in years of low SOI; an example of this is shown in Figure 5. There was very little correlation between the Alice Springs GpH in autumn and winter precipitation, and the general correlations shown in Figure 5 cannot be considered very strong; however, there is clearly a degree of association over a large area of the north of New South Wales west of the Great Dividing Range. It would appear that if other combinations of data were examined (e.g. partition using SOI or GpH for different pressure levels or for different locations) relationships would probably be found which would allow forcasting of precipitation one season ahead from regressions with correlation coefficients 0.7 (explaining 50% of the variance) and possibly 0.8 for all locations. However, to find these many relationships that will allow forecasting for any location and any season would require a systematic search over a huge database and will require considerable time. Figure 5. New South Wales: isopleths of the correlation coefficient (as a percentage) between autumn GpH (700 hpa at Alice Springs) and winter precipitation for the 10 years having the lowest autumn SOI. Periods of records, and

7 LONG RANGE FORECASTING OF LOW RAINFALL 469 Table I. Precipitation forecasts of winter rain for years for which data was not used in model development Winter of year District 55 a District 64 b Forecast rainfall (mm) Observed winter Forecast rainfall (mm) from autumn rainfall (mm) from autumn Observed winter rainfall (mm) 1988 Not low 123 Not low Not low 177 Not low Not low 201 Not low Not low 174 Not low 216 a District 55, median winter rainfall: 129 mm, lowest 25th percentile, winter rainfall 94 mm. b District 64, median winter rainfall: 126 mm, lowest 25th percentile, winter rainfall 97 mm. 5. THE SIMPLE FORECASTING MODEL To demonstrate the potential of this simple partitioning model for provision of useable forecasts, the case shown in Figure 5 will be used. From the periods and , the years having the ten lowest autumn SOI values were selected (approximately 25% of the 37 years), and for these years regressions were developed between the average autumn 700 hpa height at Alice Springs and the winter precipitation for each of the 30 rainfall districts in New South Wales. Those developed for Districts 55 and 64, which are just to the east of the area of 90% correlation shown in Figure 5, will be used as examples. For these two districts, the linear correlation coefficients between the autumn GpH and the winter rainfall for the years selected by the partitioning were 0.74 and 0.78, respectively. 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 independent data set. Table I shows the observed winter rainfalls and the estimated (forecast) values. In the columns of forecast values the words not low occur where the autumn SOI value was not in the lowest 25% of the observed values to which the partitioned relationship applied, and therefore no value could be estimated except to forecast that the value should be above the lowest 25% of all observed winter rainfalls. Although the results shown in Table I do not appear very impressive at first glance, they are quite consistent with the correlation coefficient values. In the years 1988 to 1990 and 1996, the forecasts are completely correct in that all the observed values were in the vicinity of, or above, the median values. In 1995, the forecasts were approximately correct in that they were for values equal to the lowest 25% of observations and the observed values were in this (drought) range. For 1994, the forecasts were incorrect. 6. CAUSES OF PREDICTIVE RELATIONSHIPS Nazemosadat and Cordery (1997) have given suggestions for GpH over central Australia being related to precipitation in eastern Australia. However those suggestions only apply to concurrent observations. It is not yet apparent why a combination of global and more local atmospheric features in one season would influence precipitation in the next season, three months later. There is a degree of autocorrelation between monthly values of SOI, but since both seasonal GpH and precipitation appear to be totally independent, autocorrelation of the variables cannot be the cause of the observed relationships. Alternatively, the relationships cannot be statistical accidents because they are too consistent, occur for all four seasons and in one season or another provide strong correlations with precipitation in all parts of the land area studied. Low precipitation can be forecast 3 months ahead using a model which takes as input both global and local climatic data. The model requires local data from different locations in order to provide forecasts

8 470 I. CORDERY for each particular target location. In the future, it seems likely that it will be possible to forecast low precipitation for any location in New South Wales and any season, once the location of the GpH that has the greatest influence on precipitation at that location has been found. However, it is imperative that the physical basis for success of this type of model is found, both to avoid unexpected forecasting inaccuracies and to provide a more sound basis for the models. A physical understanding of the processes should lead to even more reliable forecasting. 7. CONCLUSION For many years, significant relationships have been known to exist between precipitation and global variables, such as SOI and SSTs. Although these relations have been statistically significant, they have not been strong enough to provide consistently reliable estimates since the proportion of the variance they have been able to explain in the target precipitation has generally been 35%. In addition, the strong relationships have been between concurrent variables, and lag relationships in 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 one season earlier, and that these relationships are strong enough to explain 50% of the variance in the precipitation over large areas of eastern Australia. Not only have relationships been developed which can provide a 3-month forecast of precipitation, but they have been developed for all four seasons. REFERENCES Australian Bureau of Meteorology. Seasonal outlook, Various dates. Cordery, I., Yao, S.L. and Opoku-Ankomah, Y Forecasting drought is it possible?, Hydrology and Water Res. Symp., Inst. Eng. Aust., Nat. 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 Greischar, L Further work on the prediction of northeast Brazil rainfall anomalies, J. Clim., 6, He, Y.X. and Barnston, A.G Long-lead forecasts of seasonal precipitation in the tropical Pacific islands using CCA, J. Clim., 9, Kozuchowski, K. and Wibig, J Connections between air temperature and precipitation and the geopotential height of the 500 hpa level in a meridional cross-section in Europe, Int. J. Climatol., 12, McCabe, G.J Effects of winter atmospheric circulation on temporal and spatial variability in annual streamflow in the western United States, Hydrol. Sci. J., 41, McCabe, G.J. and Legates, D.R Relationships between 700 hpa height anomalies and 1 April snowpack accumulations in western USA, Int. J. Climatol., 15, Nazemosadat, M.J. and Cordery, I The influence of geopotential heights on New South Wales rainfall, Meteorol. Atmos. Phys., 63, Nicholls, N. 1984a. Toward the prediction of major Australian droughts, Aust. Meteorol. Mag., 33, Nicholls, N. 1984b. The stability of empirical long-range forecast techniques: a case study, J. Clim. Appl. Meteorol., 23, Opoku-Ankomah, Y. and Cordery, I Temporal variation of relations between New South Wales rainfall and the southern oscillation, Int. J. Climatol., 13, Opoku-Ankomah, Y. and Cordery, I Atlantic sea surface temperatures and rainfall variability in Ghana, J. Clim., 7, Pittock, A.B Global meridional interaction in the stratosphere and troposphere, Q. J. R. Meteorol. Soc., 99, Ropelewski, C.F. and Halpert, M.S Quantifying southern oscillation precipitation relationships, J. Clim., 9, Stone, R.C., Hammer,G.L. and Marcussen, T Prediction of global rainfall probabilities using phases of the Southern Oscillation Index, Nature, 384,