Climate network and complexity based El Niño forecast for 2021
CClimate network and complexity based El Ni˜noforecast for 2021
Josef Ludescher , Jun Meng , and Jingfang Fan Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China School of Systems Science, Beijing Normal University, 1000875 Beijing, China
Abstract
The El Ni˜no Southern Oscillation (ENSO) is the most important driver of interannualclimate variability and can trigger extreme weather events and disasters in various parts ofthe globe. Recently, we have developed two approaches for the early forecasting of El Ni˜no.The climate network-based approach allows forecasting the onset of an El Ni˜no event about 1year ahead [1]. The complexity-based approach allows additionally to forecast the magnitudeof an upcoming El Ni˜no event in the calendar year before [2]. Here we communicate theforecasts of both methods for 2021. The methods indicate a high probability (about 89% and90%, respectively) for the absence of an El Ni˜no in 2021.
The El Ni˜no-Southern Oscillation (ENSO) phenomenon [3–9] can be perceived as a self-organizeddynamical see-saw pattern in the Pacific ocean-atmosphere system, featured by rather irregularwarm (“El Ni˜no”) and cold (“La Ni˜na”) excursions from the long-term mean state. The ENSOphenomenon is quantified by the Oceanic Ni˜no Index (ONI), which is based on the average sea-surface temperature (SST) in the Ni˜no3.4 region in the Pacific (see Fig. 1).The ONI is defined as the three-month running-mean SST anomaly in the Ni˜no3.4 region andis a principal measure for monitoring, assessing and predicting ENSO. We will refer to the ONIalso as the Ni˜no3.4 index. An El Ni˜no episode is said to occur when the index is at least 0.5 ° Cabove the climatological average for at least 5 months. A regularly updated table of the ONI canbe found at [10].Since strong El Ni˜no episodes can wreak havoc in various parts of the world (through extremeweather events and other environmental perturbations) [9, 12–16], early-warning schemes basedon robust scientific evidence are highly desirable. Sophisticated global climate models taking intoaccount the atmosphere-ocean coupling, as well as statistical approaches like the dynamical systemsschemes approach, autoregressive models and pattern-recognition techniques, have been proposedto forecast the pertinent index with lead times between 1 and 24 months [4, 17–36].Unfortunately, so far, the forecasting methods in operation have quite limited anticipationpower. In particular, they generally fail to overcome the so-called “spring barrier” (see, e.g.,[37, 38]), which shortens their warning time to around 6 months.To resolve this problem, we have recently introduced two alternative forecasting approaches[1, 2], which considerably extend the probabilistic prediction horizon. The first approach [1] (seealso [39]) is based on complex-networks analysis [40–45]. The method provides forecasts for theonset of an El Ni˜no event, but not for its magnitude, in the year before the event starts. The secondapproach [2] relies on the System Sample Entropy (SysSampEn), i.e., an information entropy, inthe Ni˜no3.4 area. It provides forecasts for the onset and magnitude of an El Ni˜no event at the endof the foregoing year. Both methods predict the absence of an El Ni˜no event in 2021 with roughly90% probability. In the following Sections, we describe the methods and their forecasts.1 a r X i v : . [ phy s i c s . a o - ph ] F e b igure 1: The ONI and the “climate network”. The network consists of 14 grid points in the“El Ni˜no basin” (solid red symbols) and 193 grid points outside this domain (open symbols). Thered rectangle denotes the area where the ONI (Ni˜no3.4 index) is measured. The grid points areconsidered as the nodes of the climate network that we use here to forecast El Ni˜no events. Eachnode inside the El Ni˜no basin is linked to each node outside the basin. The nodes are characterizedby their surface air temperature (SAT), and the link strength between the nodes is determinedfrom their cross-correlation (see below). Figure from [1]. The climate network-based approach exploits the remarkable observation that a large-scale coop-erative mode linking the “El Ni˜no basin” (i.e., the equatorial Pacific corridor) and the rest of thePacific ocean (see Fig. 1) builds up in the calendar year before an El Ni˜no event. An appropriatemeasure for the emerging cooperativity can be derived from the time evolution of the telecon-nections (“links“) between the atmospheric temperatures at the grid points (”nodes“) inside andoutside of the El Ni˜no basin. The strengths of those links are represented by the values of therespective cross-correlations (for details, see [1, 39]). The crucial entity is the mean link strength S ( t ) as obtained by averaging over all individual links in the network at a given instant t [1, 39]. S ( t ) rises when the cooperative mode builds up and drops again when this mode collapses ratherconspicuously with the onset of the El Ni˜no event. The rise of S ( t ) in the year before an El Ni˜noevent starts serves as a precursor for the event.For the sake of concrete forecasting, we employed in [1] daily surface air temperature (SAT)anomalies for the 1950-2011 period. The data have been obtained from the National Centers forEnvironmental Prediction/National Center for Atmospheric Research Reanalysis I project [46, 47].The optimized algorithm [1, 39] involves an empirical decision threshold Θ. Whenever S crosses Θfrom below while the most recent ONI is below 0.5 ° C, the algorithm sounds an alarm and predictsan El Ni˜no inception in the following year. For obtaining and testing the appropriate thresholds,we divided the data into two halves. In the first part (1950-1980), which represents the learningphase, all thresholds above the temporal mean of S ( t ) were considered and the optimal ones, i.e.,those that lead to the best predictions in the learning phase, have been determined. We foundthat Θ-values between 2 .
815 and 2 .
834 lead to the best performance [1], with a false alarm rate of1/20. In the second part of the data set (1981-2011), which represents the prediction (hindcasting)phase, the performance of these thresholds has been tested. We found that the thresholds between2.815 and 2.826 gave the best results (see Fig. 2, where Θ = 2 . .
827 and 2 .
981 1990 2000 2010
Year -1012 N I NO . [ ° C ] S Θ Figure 2: The network-based forecasting scheme (hindcasting phase). We compare the averagelink strength S ( t ) in the climate network (red curve) with a decision threshold Θ (horizontal line,here Θ = 2 . ° C, we give an alarm and predict that an El Ni˜no episode will start inthe following calendar year. The El Ni˜no episodes (when the Ni˜no3.4 index is at or above 0 . Based on this hindcasting capacity, the approach has already been used in [48] to extend theprediction phase from the end of 2011 until November 2013 and later in [39] until October 2019. Welike to emphasize that in the forecasting phase, the algorithm does not contain any fit parameterssince the decision thresholds are fixed and the mean link strengths only depend on the atmospherictemperature data.Eight out of nine real predictions into the future for the years 2012-2020 turned out to becorrect (see Fig. 3). These predictions were not trivial. For example, as late as August 2012, theClimate Prediction Center/International Research Institute for Climate and Society (CPC/IRI)Consensus Probabilistic ENSO forecast yielded a 3 in 4 likelihood for an El Ni˜no event in 2012,which turned out to be incorrect only a few months later [10,11]. In contrast, the network approachalready forecasted the absence of an El Ni˜no at the end of 2011. In 2013, our algorithm predictedthe return of an El Ni˜no event in 2014, since, in September 2013, S ( t ) transgressed the alarmthreshold band while the last available ONI (JJA 2013) was below 0.5 ° C, indicating the return ofEl Ni˜no in 2014 (see Fig. 3). This early prediction was also correct: The El Ni˜no event started inNovember 2014 (and ended in May 2016) [10]. For comparison, the furthest into the future (ASO2014) IRI/CPC plume forecast probabilities in December 2013 were 46% for a neutral event, 44%for an El Ni˜no, and 10% for a La Ni˜na. In 2014, 2015, 2016 and 2018, S ( t ) did not cross thethreshold from below, thus indicating the absence of an El Ni˜no onset in the respectively followingyears, which all turned out to be correct (see Fig. 3). In November 2017, S ( t ) transgressed frombelow the lower threshold band between S = 2 .
815 and 2.826. Since the last ONI, for ASO 2017,was below 0.5 ° C (-0.4 ° C), this indicated the return of El Ni˜no in 2018 (see Fig. 3), which turnedout to be correct.In September 2019, S ( t ) transgressed all thresholds, while the last ONI, JJA 2019, was below0.5 ° C (0.3 ° C). This indicated the onset of an El Ni˜no in 2020 with 80% probability. This predictionturned out to be incorrect since in 2020 a La Ni˜na started. This was the first forecast error of themethod and the first hindcast of forecast error since 2009 when the method missed the 2009/103 ON I [ ° C ] S Figure 3: The climate network-based forecasting phase. Same as Fig. 2 but for the period betweenJanuary 2011 and December 2020. Throughout 2020 the average link strength S ( t ) stayed abovethe threshold, i.e., no alarm for an El Ni˜no in 2021 was given. In the hindcasting and forecastingphase (1981-2019), our algorithm predicted 28 times (25 of which were correct) the absence of anEl Ni˜no onset. Thus the likelihood based on the past performance of the climate network approachfor the absence of an El Ni˜no in 2021 is 89%.El Ni˜no.Before coming to the forecast for the next year, let us discuss the probability that the same or abetter outcome could be obtained by simply guessing using the climatological El Ni˜no probabilities.In the 71 years between 1950 and 2020, 23 El Ni˜nos have started. Accordingly, the probabilitythat an El Ni˜no starts in a certain year is 23 /
71. The probability to correctly forecast the ElNi˜no onsets or their absences between 2012 and 2020 (the forecasting phase) is, therefore, p =(23 / (48 / ≈ . p =7(23 / (48 / ≈ . p ≈ . p ≈ . · − .In 2020 S ( t ) stayed above the threshold throughout the year (see Fig. 3), thus predicting theabsence of an El Ni˜no in 2021 with 89% probability. We like to note that in the entire past whereoutside of an ongoing El Ni˜no episode, a correct prediction for the absence of an El Ni˜no onsetwas made, in 19 out of 22 cases, S ( t ) was below the threshold at the end of the year. Thus 2020does not represent the typical case. The SysSampEn was introduced in [2] as an analysis tool to quantify the complexity (disorder) ina complex system, in particular, in the temperature anomaly time series in the Ni˜no3.4 region. Itis a generalization of sample entropy (SampEn) and Cross-SampEn [49]. SampEn was introducedas a modification of approximate entropy [50, 51]. It measures the complexity related to theKolmogorov entropy [52], the rate of information production, of a process represented by singletime series. The Cross-SampEn was introduced to measure the degree of asynchrony or dissimilaritybetween 2 related time series [49, 53]. Both have been widely used in physiological fields, however,a complex system such as the climate system is usually composed of several related time series(e.g., curves in Fig. 4). Therefore, the SysSampEn [2] was introduced as a measure of the systemcomplexity, to quantify simultaneously the mean temporal disorder degree of all of the time seriesin a complex system and the asynchrony among them. Specifically, it is approximately equal tothe negative natural logarithm of the conditional probability that 2 subsequences similar (within acertain tolerance range) for m consecutive data points remain similar for the next p points, wherethe subsequences can originate from either the same or different time series (e.g., black curves in4igure 4: The Ni˜no3.4 area and the SysSampEn input data. The red circles indicate the 22 nodes inthe Ni˜no 3.4 region with a spatial resolution of 5 × SysSampEn ( m, p, l eff , γ ) = − log ( AB ) , (1)where A is the number of pairs of similar subsequences of length m + p , B is the number of pairsof similar subsequences of length m , l eff ≤ l is the number of data points used in the calculationfor each time series of length l , and γ is a constant which determines the tolerance range. Thedetailed definition of SysSampEn for an arbitrary complex system composed of N time series isdescribed in detail in [2]. When N = 1, p = 1, and l eff = l , the definition is equivalent to theclassical SampEn [49].As is the case for SampEn and Cross-SampEn, before the SysSampEn can be used as an effectivetool, appropriate parameter values have to be identified since only certain value combinationscan be used to estimate a system’s complexity with considerable accuracy. The method how tochoose parameter values, which yield to a high accuracy when estimating a system’s complexity,is described in detail in [2]. We like to note that identifying the parameters, which yield to a highaccuracy, is fully independent of any El Ni˜no magnitude analysis or forecasts. In [2], it was foundthe previous year’s ( y −
1) SysSampEn exhibits a strong positive correlation ( r = 0 .
90 on average)with the magnitude of an El Ni˜no in year y when parameter combinations are used that are ableto quantify a system’s complexity with high accuracy.The linear relationship between SysSampEn and El Ni˜no magnitude enables the prediction ofthe magnitude of an upcoming El Ni˜no when the current ( y −
1) SysSampEn is inserted into thelinear regression equation between the two quantities. If the result is below 0 . ° C and the SysSampEn isabove a certain threshold.
Here we use as input data the daily near-surface (1000 hPa) air temperatures of the ERA5 reanalysisfrom the European Centre for Medium-Range Weather Forecasts (ECMWF) [54] analysed at a 5resolution. The most recent months (Nov-Dec) in 2020 are from the initial data release ERA5T,which in contrast to ERA5, only lags a few days behind real-time. We preprocess the daily timeseries by subtracting the corresponding climatological mean and then dividing by the climatologicalstandard deviation. We start in 1984 and use the previous years to calculate the first anomalies.5
985 1990 1995 2000 2005 2010 2015 2020
Year -202 O N I ( C ) Figure 5: Forecasted and observed El Ni˜no magnitudes. The magnitude forecast is shown as theheight of rectangles in the year when the forecast is made, i.e., one year ahead of a potentialEl Ni˜no. The forecast is obtained by inserting the regarded calendar year’s SysSampEn valueinto the linear regression function between SysSampEn and El Ni˜no magnitude. To forecast thefollowing year’s condition, we use the ERA5 daily near-surface (1000 hPa) temperatures with theset of SysSampEn parameters ( m = 30, p = 30, γ = 8 and l eff = 330), which were obtained in [2].The red curve shows the ONI and the red shades indicate El Ni˜no periods. The blue rectanglesshow the correct prediction of an El Ni˜no in the following calendar year. The absence of an El Ni˜noonset in the following year is predicted if the forecasted magnitude is below 0 .
5C or if the currentyear’s December ONI is ≥ . m = 30, p = 30, γ = 8 and l eff = 330.Figure 5 shows the results of the analysis. The magnitude forecast is shown as the height ofrectangles in the year when the forecast is made, i.e., one year ahead of a potential El Ni˜no. Theforecast is obtained by inserting the regarded calendar year’s SysSampEn value into the linearregression function between SysSampEn and El Ni˜no magnitude. The regression function forthe 2021 forecast is obtained from the best linear fit between the two quantifies for all correctlyhindcasted El Ni˜no events before 2020. The red curve shows the ONI and the red shades indicateEl Ni˜no periods. The blue rectangles show the correct prediction of an El Ni˜no in the followingcalendar year and grey rectangles with a violet border show false alarms. There are 13 cases wherethe forecasted magnitude is above 0 .
5C while the ONI in December is below 0 . .
5C ONI in December. In 9 out of these 10 cases, the hindcast was correct. The forecastedmagnitude for 2021 is far below 0 . . .
35. Thus the method predicts with 90%probability the absence of an El Ni˜no in 2021. 6 cknowledgements
We thank the East Africa Peru India Climate Capacities (EPICC) project, which is part of theInternational Climate Initiative (IKI). The Federal Ministry for the Environment, Nature Conser-vation and Nuclear Safety (BMU) supports this initiative on the basis of a decision adopted by theGerman Bundestag.
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