RODRIGO H. NUÑEZ, TODD S. RICHARDS
AND JAMES J. O'BRIEN
Center for Ocean-Atmospheric Prediction Studies 008A Love Bldg.
The Florida State University
Tallahassee, FL 32306 - 3041, U.S.A.
Submitted to International Journal of Climatology, August 1995.
ABSTRACT
Chilean precipitation shows positive anomalies closely related to the warm phase of ENSO. Conversely, dry conditions correspond to the cold phase of this event. The seasonal impact of ENSO on precipitation in Chile is presented using statistical tools such as Empirical Orthogonal Functions and bootstrap.
Temporal patterns are obtained from the EOF analysis of the precipitation records that combined with the results of the bootstrap technique, show the impact of ENSO in Central and Southern Chile. The impact of ENSO on the Southern region is less severe than in the Central region. The Bootstrap analysis allows a more detailed study of the seasonal precipitation anomalies associated with ENSO, even in the case where the length of the records by themselves are not long enough to give a robust estimate of the population statistics. The cumulative probability distribution functions, derived from the bootstrap analysis, are used to estimate the probability of experiencing a wetter, normal, or drier condition for a specific station, during a given season and ENSO categorization.
KEY WORDS: (1) Bootstrap.....(2) Empirical Orthogonal Functions (EOF)..... (3) El Niño Southern Oscillation (ENSO).....(4) El Viejo ( La Niña or cold event)
![](order-form1.gif")
Chile is located along the south eastern boundary of the Pacific Ocean,
between latitudes 18° S and 56° S, with a length of 4100 kilometers and
an average width of 220 kilometers. It has three well defined climatic
regions: Desert, Subtropical and Temperate Oceanic. The desert region is one
of the earth's driest, with areas that receive less than one millimeter of
rainfall per year, with no particular seasonal cycle. The Subtropical region
has a climate with four well defined seasons and most of the precipitation
(around 450 millimeters per year) during fall and winter. Further south, the
Temperate Oceanic region is characterized by year-round precipitation that
keeps the landscape green but limits farming to the growing of more traditional
grains and pasturing animals.
Chile has a long coastline and several different climate regions (Pittock, 1980). All of them are affected by "El Niño Southern Oscillation" (ENSO). The country is a good study case for the impacts of this air-sea interaction phenomenon (figure 1).
The purpose of this study is to analyze the seasonal and interannual effect of ENSO on rainfall in Chile by means of multiple statistical techniques. An Empirical Orthogonal Function analysis, complemented by a Bootstrap analysis (Efron, 1993), will be used to obtain a better understanding of the interannual and seasonal precipitation anomalies associated with ENSO.
2.0.- DESCRIPTION OF DATA AND STATISTICAL ANALYSIS
2.1.- Description of Data
The precipitation data was obtained from the Dirección
Meteorológica de Chile in Santiago, Chile. As indicated in
Figure 1 and Table 1, nine stations
were used for the study. These stations cover the
Central (Subtropical) and Southern (Temperate Oceanic) regions of the country,
from 33° S to 41° S. Monthly precipitation anomalies were calculated
for the nine stations for the 34-year period from 1961 to 1994, by subtracting
the 34-year monthly average from the corresponding monthly value.
The sealevel data was obtained from the Servicio Hidrográfico y Oceanográfico de la Armada de Chile in Valparaíso, Chile. The station used for this study was Caldera and it is shown in Figure 1. The sealevel anomalies were calculated for the 44-year period from 1951 to 1994, by subtracting the 44-year monthly average from the corresponding monthly value. The sealevel anomalies were detrended using a linear least-square fit to remove artificial sealevel increases due to plate tectonic activity in the region (plate convergence in the Perú-Chile Trench).
The Sea Surface Temperature Anomalies (SST) data was obtained from the Japanese Meteorological Agency (JMA) and represents a region located between 4° N and 4° S and between 150° W and 90° W (figure 2). The SST anomalies for the period 1949-1994 were filtered using a five-month running average to calculate the JMA - SST anomaly Index, later used to classified the precipitation data (conceptually similar to the Southern Oscillation Index published by the U.S. - National Meteorological Center).
2.2.- Empirical Orthogonal Function (EOF) Analysis
In order to obtain the spatial and temporal patterns of the precipitation
anomalies in Chile, an EOF analysis was performed on the nine stations. The
result of the analysis was a set of nine rainfall-anomaly spatial patterns
(eigenvectors), each associated with a rainfall-anomaly time series. Each
eigenvector is modulated by its corresponding time series. Physical patterns
are then assigned to particular eigenvectors that account for a large fraction
of the variance.
The first 2 EOF modes account for 79.35% of the variance (first mode 61.09% and second mode 18.26%, respectively). It is very unusual for a data set to be dominated by two patterns accounting for 80 percent of the variance.
Figures 3 and 4 show the spatial patterns for EOF-1 and EOF-2, respectively. There are some very distinctive features in these spatial modes. Figure 3 indicates that all nine stations will behave in the same way for any specific given temporal perturbation, with the largest rainfall anomalies at station 4 (Chillán), station 5 (Concepción) and station 7 (Valdivia). Thus, EOF-1 is a country-wide effect. Figure 4 , in the contrary, indicates that for the second EOF mode the country is divided into two well defined regions. Stations 1 to 5 (central region) will behave oppositely as compared with stations 6 to 9 (southern region). Thus, EOF-2 separates the two different climatic regions.
Figures 5 and 6 show the time series of EOF-1 and EOF-2, respectively. Both time series were filtered using a 12-month running average to eliminate the high frequency noise. This simple filter acts as a "low pass filter" enhancing signals with a period greater than 1 year and helping observers to recognize them in the output time series.
A quick analysis of these time series shows that they are strongly modulated by an ENSO signal. Large positive and negative anomalies exist in both time series at known years where strong and moderated El Niño (warm events) and strong and moderated El Viejo (La Niña or cold events) occurred.
2.3.- Bootstrap Technique "Margin Probability Analysis"
The second aspect of this study involves investigation into the seasonal
impact of ENSO on precipitation in Chile. The technique used is based on
Richards (1995) and Sittel (1994). In order to complete such an analysis,
the data are first separated into ENSO categories based on the Japanese
Meteorological Agency
index (JMA Atlas, 1991). This index defines ENSO years based on sea surface
temperature anomalies in the region defined in
Figure 2 . According to the
index, an El Niño event occurs when the five month running average of
SST anomalies is greater than 0.5°C for at least six consecutive months. In
addition, the series of six consecutive months must begin before October, and
must include October, November, and December. A similar definition is applied
to El Viejo years denoted by SST anomalies less than -0.5°C for at least six
consecutive months. Further, years that fail to fit into one of the categories
are defined as Neutral years. The resulting categorized years are listed in
Table 2. For the purpose of this study,
an ENSO year is defined from October to
September so as to include the entire event.
In order to determine the seasonal impact of ENSO on Chilean rainfall, each of the years of this study are subdivided into three-month seasons. For each of these seasons, three-month means of the data are calculated. Next, a statistical resampling technique known as bootstrapping is applied to the seasonal means to compensate for the small number of years within each ENSO category. That is, the bootstrap technique involves repeated sampling with replacement of the existing nine El Niño years within the period of study, to provide a more robust estimate of the population statistics for those ENSO years.
The bootstrap technique is introduced in Diaconis and Efron (1983), and has been used in other studies (e.g. Inoue and O'Brien, 1984). For this study, a precipitation value for each calendar month of a given three- month season for all years in a given ENSO category is randomly selected. The resulting three values are averaged to produce a mean to represent that given season and ENSO category. The data chosen are replaced. This selection process is repeated one million times. A sample contains many random amounts of the seven hundred and twenty-nine possible combinations for the nine El Niño years. The one million means are then averaged to produce a single mean for a given three-month season and ENSO category. This mean is equivalent to that computed before the bootstrapping (source).
The bootstrapping process is completed for the ten three-month seasons from October-November- December (OND) through July-August-September (JAS) within each of the three ENSO categories at all nine stations. The means which are produced are based on one million samples. By comparing the means from each ENSO category, during each of the ten seasons, the seasonal effects on ENSO are determined for the individual stations. In addition, the bootstrap samples are then used to produce an estimate of the population distribution of the original data. By comparing the distributions for each of the three ENSO categories during a given three-month season, at a particular station, further evidence of the seasonal impact of each category can be seen.
In this study, at all nine stations, ten thousand of the bootstrapped samples from each ENSO category are selected and used to produce cumulative probability distribution functions for each season. These cumulative probability distribution functions can be used to estimate the probability of experiencing a wetter, normal, or drier condition for a specific station, during a given season and ENSO categorization.
Comparing the means from each ENSO category provides insight into the relationship between ENSO and Chilean precipitation, however, this study goes a step further. Probability estimates of above or below average precipitation associated with ENSO years are computed by calculating marginal probabilities.
Because precipitation is not normally distributed, and is in fact more log-normal in shape, a more easily defined and variable distribution is used to estimate the continuous probability distributions of the data. This study utilizes a least squares approximation to fit Weibull distributions as detailed by Pavia and O'Brien (1986). The Weibull curves were chosen because they are easy to define and can approximate the curve for the precipitation data. Each Weibull curve is defined by two parameters, a shape parameter, and a scaling factor. By least squares fitting these Weibull parameters to the precipitation data, continuous distribution curves result for each station, three-month period, and ENSO category. The area under these curves is then utilized to calculate probability estimates.
The marginal probabilities are defined as the probability of precipitation for a given ENSO event being greater than one standard deviation above or below the mean of the entire data set during a particular season. These probabilities are calculated by relating the area under each best fit Weibull curve for both ENSO extremes (e.g. El Niño and El Viejo) to the area represented by the overall mean plus or minus one standard deviation at each station for all three-month seasons. By computing such probabilities, the variability of the data is accounted for, and more insight into the magnitude and timing of precipitation anomalies in Chile associated with each ENSO category is provided.
3.0.- RESULTS
The EOF analysis indicates that Chile can be divided into two regions, the
Central region, and the Southern region (figure 4)
. One representative
station is chosen within each of these two regions for further analysis.
Station Concepción for the Central region and station Puerto Montt for
the Southern region The results from the chosen stations are indicative of the
results from each station within the particular region. Graphs for the other stations
are available through web browser at the following URL location
"http://www.coaps.fsu.edu/~nunez/Paper1/
figures7-8.html".
The first result of the bootstrap analysis is mean precipitation. Comparisons are made between the bootstrapped mean precipitation values from each ENSO category. These comparisons are made for each three-month season of the ENSO year, resulting in the discovery of definite temporal patterns within the data.
Over the span of an ENSO year, the Central and Southern regions display dissimilar results. In general, stations within the Central region experience an increase in precipitation during El Niño winter and spring seasons. Conversely, the Southern region sees El Viejo summers in which the mean precipitation is above that of the Neutral years ( figures 7 and 8).
The mean precipitation pattern for the Central region of study is characterized by examining the results from Concepción (see figure 1). At this particular station as well as in each of the four other stations within this region, the spring and winter seasons are wetter during El Niño years. In particular, the June-July-August (JJA) season shows an increase in precipitation during El Niño of 33.4 mm when compared to the Neutral years (figure 7). This is an increase of almost 20 percent over the mean JJA precipitation. The summer and fall seasons, however, show a reversal in the pattern. That is, following the DJF season, the El Niño mean precipitation values are less than the Neutral means. This is most evident in the March-April-May (MAM) season when the El Niño mean is 22.3 mm below the Neutral mean for that season. This represents a decrease of almost 25 percent from the overall mean for MAM.
In the case of El Viejo, the summer and fall seasons show a decrease in mean precipitation from the Neutral case by as much as 34.7 mm (figure 7) , which is a 38 percent decrease from the overall mean in that season. This negative precipitation anomaly persists through the May-June-July season.
The above mentioned pattern seen at Concepción, which can also be seen by analyzing cumulative probability functions of the precipitation for each of the seasons (figure 9), holds true for the entire Central region of study.
The precipitation pattern in the Southern region is described by investigating the results from Puerto Montt (see figure 1). In Puerto Montt, as well as in the other three Southern region stations, the El Niño signal is not pronounced. Instead, the dominate signal is that of El Viejo. During El Viejo years, the fall season is drier than the Neutral years (figure 8). This negative anomaly is most apparent in the MAM season with the El Viejo mean 29.6 mm below that of the Neutral category. That is a decrease of nearly 20 percent from the overall mean for MAM. This pattern, which diminishes with the onset of winter, can also be seen through cumulative probability functions of the precipitation for each of the seasons (figure 10). Opposite behavior can be seen for the summer season, where precipitation anomalies increase compare to Neutral years.
Another result that can be derived from the bootstrap analysis is the marginal probability study. This investigation relates the mean and standard deviation for the entire data set for each season to precipitation values within each ENSO category. The resulting marginal probabilities reveal the potential for receiving much above or below normal precipitation given the occurrence of a particular ENSO extreme(i.e. El Niño or El Viejo). In order to define a reference value of significance for the marginal probabilities, a value of 16 percent is adopted (similar to the 16 percent obtained for one standard deviation of the mean value in a Gaussian distribution). The curves for El Niño and El Viejo years are compared to the curve for all of the years combined. Any probability estimates which are greater than 16 percent represent definite shifts in the curves from the "all years" curve. These shifts can be interpreted as effects of El Niño or El Viejo on precipitation.
Four separate marginal probabilities are calculated for each season at every station: probability of much above normal precipitation given El Niño or El Viejo, as well as the probability of below normal precipitation given El Niño or El Viejo. The results of the probability study mirror the comparison of the means discussed earlier. In general, the Central region shows a greater impact from El Niño during spring and winter seasons, while results for the summer season in the Southern region are dictated by El Viejo.
In the Central region, results from Concepción show a greater than 20 percent chance of mean precipitation being greater than one standard deviation above the overall mean, given an El Niño, throughout the winter and spring seasons (figure 11). The maximum probability of 38 percent occurs in the OND season. Given El Viejo, the probability of drier than normal conditions is above 20 percent for the summer and early fall seasons (figure 12). These results hold true for each of the stations within the Central region.
The Southern region is represented by Puerto Montt. The marginal probability analysis indicates, as expected from the EOF analysis, that the effect of the ENSO signal is not as pronounced in the Southern region as it is in the Central region The probability of receiving much below normal precipitation given an El Viejo is greater than twenty percent throughout the fall season (figure 13). The peak in probability occurs in MAM and is almost 33 percent. This peak occurs during the same season as the peak difference in precipitation means.
4.0.- CONCLUSIONS
The EOF analysis gives us temporal patterns
(figures 5 and
6)
that are easily recognized as being modulated by an ENSO signal, with large
positive anomalies existing in the years in which strong or moderate warm
events occurred in the equatorial Pacific (i.e. 1972, 1983 and 1987).
Conversely, minima in both time series occur during some of the years when
strong or moderate colds events occurred. The spatial pattern of EOF-1
(figure 3) indicates that all stations
will behave in the same way for any specific
given temporal perturbation. In contrast, the spatial pattern of EOF-2
(figure 4) indicates that the four southern
most stations will behave oppositely as
compared with the stations located in the Central region of the country. The
spatial pattern of EOF-2 is supported by the results of previous studies
(Pittock, 1980; Rutllant and Fuenzalida, 1991) and it is interpreted as the
geographic separation of two well defined climatic regions. Because of these
distinctive climate characteristics, the impact of ENSO on the Southern region
is less severe than in the Central region. The spatial distribution of EOF-2
shows that EL Niño event will produce a negative precipitation anomaly
that tends to cancel a portion of the positive precipitation anomaly of EOF-1,
resulting in a less severe positive anomaly. During El Viejo years, the effect
will be opposite, keeping the resulting negative precipitation anomaly
smaller.
The Bootstrap analysis proved to be a powerful tool that complements the EOF analysis and allows a more detailed study of the seasonal precipitation anomalies associated with ENSO, even in the case where the length of the records by themselves are not long enough to give a robust estimate of the population statistics. The cumulative probability distribution functions are used to estimate the probability of experiencing a wetter, normal, or drier condition for a specific station, during a given season and ENSO categorization.
As a result of applying bootstrap analysis, we discovered definite temporal (seasonal) patterns within the data that can be related to ENSO. Stations in the Central region experienced an increase in precipitation during El Niño winter and spring seasons. Conversely, the Southern region experienced an increase in precipitation during El Viejo summers.
The purpose of the cross-correlation analysis was to estimate the time-shift among the rise and fall of the sealevel associated with the propagation of coastal trapped Kelvin waves along the South American coast, the variability in the precipitation patterns and the appearance of anomalies in the SST record in the tropical east Pacific ocean. The analysis shows that rise and fall of sealevel in Caldera has a strong correlation with the JMA - SST anomaly index. This correlation coefficient is around 0.5 when there is a two-month lag of the sealevel with respect to JMA - SST index. This lag is reasonable and represents the average travel time of a Kelvin wave from the equator to Caldera.
The correlation coefficient for the cross-correlation between sealevel and EOF-1 time series is around 0.34 when there is a four-month lead of the sealevel. The sealevel change alters the local heat balance of the ocean off Chile by decreasing the amount of cool upwelled water. At the same time, teleconnections in the atmosphere from the equator, will interact with the modified ocean climate along the Chilean coast, producing perturbations in the precipitation climate for Chile.
5.0.- ACKNOWLEDGMENTS
The authors thank Dr. Steve
Meyers for his contructive
comments and Mr. J. Stricherz for his help setting up this "web-page". Special
thanks are due to the Director of the Hydrographic and
Oceanographic Service of the Chilean Navy and the Director of the Chilean
Meteorological Service for supplying the sealevel and precipitation data,
respectively. Support for this research through the following agencies and
their grants is gratefully acknowledged: 1) Chilean Navy - Hydrographic and
Oceanographic Service, 2) Department of Defense grants N00014-85-J-1240 and
N00014-93-1-1132.
COAPS, FSU, recieves its base support from the Secretary of the Navy Grant, Physical Oceanography, ONR. This was also supported by NOAA, Office of Global Programs (OGP).
6.0.- REFERENCES
Diaconis, P. and Efron, B. 1983. Computer-intensive methods in statistics.
Sci. Amer.,
248, 116-130.
Efron, B. and Tibshirani, R. J. 1993. An Introduction to the Bootstrap, Chapman and Hall, New York. 436 pp.
Inoue, M. and O'Brien, J.J. 1984. A forecasting model for the onset of a major El Niño. Mon. Wea. Rev., 112, 2326-2337.
Japan Meteorological Agency, Marine Department. 1991. Climate Charts of Sea Surface Temperatures of the Western North Pacific and the Global Ocean. 51 pp.
Pittock, A. B. 1980. Patterns of climatic variation in Argentina and Chile - I. Precipitation, 1931-60. Mon. Wea. Rev., 112, 2326-2337.
Pavia, E. G., and O'Brien, J. J. 1986. Weibull statistics of wind speed over the ocean, J. Climate Appl. Meteor., 25, 1324-1332.
Richards, T. S. 1995. Marginal Probabilities for Florida Precipitation Related to ENSO. Submitted to Journal of Climate, 1995.
Rutllant, J. and Fuenzalida, H. 1991. Synoptic aspects of the Central Chile rainfall variability associated with the southern oscillation. International Journal of Climatology, 11, 63-76.
Sittel, M. C. 1994. Marginal probability of the extremes of ENSO events for temperature and precipitation in the southeastern United States. Center for Ocean-Atmospheric Prediction Studies, The Florida State University. Technical Report 94-1.
<== click on this icon to send me email
<== click on this icon to go back to Rodrigo's Front Page
<==click on this icon to go back to COAPS Home Page