NP5.2

The El Niño Southern Oscillation (ENSO) is one of the most prominent interannual climate phenomena. Early and reliable ENSO forecasting remains a crucial goal, due to its serious implications for economy, society, and ecosystem. Despite the development of various dynamical and statistical prediction models in the recent decades, the “spring predictability barrier” remains a great challenge for long-lead-time (over 6 mo) forecasting. To overcome this barrier, here we develop an analysis tool, System Sample Entropy(SysSampEn), to measure the complexity (disorder) of the system composed of temperature anomaly time series in the Niño 3.4 region. When applying this tool to several near-surface air temperature and sea surface temperature datasets, we find that in all datasets a strong positive correlation exists between the magnitude of El Niño and the previous calendar year’s SysSampEn(complexity). We show that this correlation allows us to forecast the magnitude of an El Niño with a prediction horizon of 1 y and high accuracy (i.e., root-mean-square error=0.25^◦C for the average of the individual datasets forecasts). For the recent two 2018 and 2019 El Niño events, our method forecasted weak El Niños with magnitudes of 1.11±0.23^◦C and 0.69±0.25^◦C, both within one root-mean-square error comparing to the observed magnitudes, i.e. 0.9^◦C and 0.6^◦C. Our framework presented here not only facilitates long-term forecasting of the El Niño magnitude but can potentially also be used as a measure for the complexity of other natural or engineering complex systems.

How to cite: Meng, J.: Complexity-based approach for El Nino magnitude forecasting before the spring predictability barrier, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-339, https://doi.org/10.5194/egusphere-egu21-339, 2020.

Most forecasting schemes in the geosciences, and in particular for predicting weather and
climate indices such as the El Niño Southern Oscillation (ENSO), rely on process-based
numerical models [1]. Although statistical modelling[2] and prediction approaches also have
a long history, more recently, different machine learning techniques have been used to predict
climatic time series. One of the supervised machine learning algorithm which is suited for
temporal and sequential data processing and prediction is given by recurrent neural networks
(RNNs)[3]. In this study we develop a RNN-based method that (1) can learn the dynamics
of a stochastic time series without requiring access to a huge amount of data for training, and
(2) has comparatively simple structure and efficient training procedure. Since this algorithm
is suitable for investigating complex nonlinear time series such as climate time series, we
apply it to different ENSO indices. We demonstrate that our model can capture key features
of the complex system dynamics underlying ENSO variability, and that it can accurately
forecast ENSO for longer lead times in comparison to other recent studies[4].

Reference:

[1] P. Bauer, A. Thorpe, and G. Brunet, “The quiet revolution of numerical weather prediction,”
Nature, vol. 525, no. 7567, pp. 47–55, 2015.

[2] D. Kondrashov, S. Kravtsov, A. W. Robertson, and M. Ghil, “A hierarchy of data-based enso
models,” Journal of climate, vol. 18, no. 21, pp. 4425–4444, 2005.

[3] L. R. Medsker and L. Jain, “Recurrent neural networks,” Design and Applications, vol. 5, 2001.

[4] Y.-G. Ham, J.-H. Kim, and J.-J. Luo, “Deep learning for multi-year enso forecasts,” Nature,
vol. 573, no. 7775, pp. 568–572, 2019.

How to cite: hassanibesheli, F., Boers, N., and Kurths, J.: Echo-State Networks for Predicting ENSO Beyond One Year, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4826, https://doi.org/10.5194/egusphere-egu21-4826, 2021.

Interseasonal forecasting of El Niño Southern Oscillation (ENSO), which is traditionally based on data of tropical sea surface temperatures (SST), is in high demand due to the impacts of ENSO on regional climatic conditions around the world as well as the global climate. Improvements in the quality of data in recent decades have led to the active use of statistical ENSO models, which compete with physical models in predictive power. The main disadvantage of statistical forecasts is the pronounced seasonal growth of uncertainty when predicting the upcoming summer-fall ENSO conditions from winter-spring months (so called the spring predictability barrier (SPB)). Recent studies show that Pacific atmospheric circulation anomalies in winter-spring may have a long-term impact on the summer tropical climate via the SST footprint. Here, we infer an index based on sea level pressure (SLP) data from February-March in a single area surrounding Hawaii, and show that this area is the most informative part of the large SLP pattern initiating the SST footprinting mechanism. We define the Hawaiian index (HI) as the mean SLP anomalies in the region (13⁰N-19⁰N, 150⁰W-160⁰W) averaged over February-March and demonstrate that the statistical AR model of the Niño 3.4 index taking the HI as a forcing is better in the Bayesian sense and delivers significantly better multimonth predictions. In fact, the HI forcing in the model substantially lowers the SPB and hence increases the predictability of the whole June-May ENSO cycle for forecasts starting in spring. Thus, we can recommend that modelers test the HI as an additional predictor in statistical ENSO models.

This research was supported by the Russian Science Foundation (Contract 19-42-04121)

How to cite: Feigin, A., Mukhin, D., Gavrilov, A., Seleznev, A., and Buyanova, M.: An atmospheric forcing extending ENSO forecast horizon using statistical models, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2813, https://doi.org/10.5194/egusphere-egu21-2813, 2021.

We investigate the decadal-to-centennial ENSO variability based on nonlinear data-driven stochastic modeling. We construct data-driven model of yearly Niño-3.4 indices reconstructed from paleoclimate proxies based on three different sea-surface temperature (SST) databases at the time interval from 1150 to 1995 [1]. The data-driven model is forced by the solar activity and CO2 concentration signals. We find the persistent antiphasing relationship between the solar forcing and Niño-3.4 SST on the bicentennial time scale. The dynamical mechanism of such a response is discussed.

The work was supported by the Russian Science Foundation (Grant No. 20-62-46056)

1. Emile-Geay, J., Cobb, K. M., Mann, M. E., & Wittenberg, A. T. (2013). Estimating Central Equatorial Pacific SST Variability over the Past Millennium. Part II: Reconstructions and Implications, Journal of Climate, 26(7), 2329-2352.

How to cite: Seleznev, A., Mukhin, D., Gavrilov, A., and Feigin, A.: Data-driven modeling decadal-to-centennial ENSO variability and its response to external forcing, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8370, https://doi.org/10.5194/egusphere-egu21-8370, 2021.

Climate changes globally, yet its impacts strongly vary between different locations in the same region. Today, numerical weather models are able to forecast weather patterns on a scale of several kilometers. However, the extreme weather impacts materialize at a finer scale, interacting with highly local factors such as topography, soil or vegetation type. The relationship between driving variables and Earth’s surface at such local scales remains unresolved by current physical models and is partly unknown; hence, it is a source of considerable uncertainty. Most current efforts to predict the local impacts of extreme weather rely on weather downscaling as an intermediary step. However, weather impacts at high resolution are observed and analyzed on satellite imagery. Thus, we can bypass the weather downscaling step by directly forecasting satellite imagery. This is inherently similar to video prediction, a computer vision task that has been tackled with machine learning models. Here we introduce EarthNet2021, a machine learning challenge to forecast the spatio-temporal evolution of the Earth’s terrestrial surface. The task can be summarized as translating coarse weather projections into high-resolution Earth surface imagery encompassing localized climate impacts. EarthNet2021 is a carefully prepared dataset containing target spatio-temporal Sentinel-2 imagery at 20 m resolution, matching with high resolution topography and mesoscale (1.28 km) weather variables. Comparing multiple Earth surface forecasts is not trivial. Thus, we design the EarthNetScore, a novel ranking criterion for Earth surface models. EarthNet2021 comes with multiple test tracks for evaluation of model validity and robustness as well as model applicability to extreme events and the complete annual vegetation cycle. In addition to forecasting directly observable weather impacts through satellite-derived vegetation indices, capable Earth surface models will enable downstream applications such as crop yield prediction, forest health assessments, coastline management or biodiversity monitoring.

How to cite: Requena Mesa, C., Benson, V., Denzler, J., Runge, J., and Reichstein, M.: EarthNet2021: Self-supervised impact predictions of extreme weather., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1612, https://doi.org/10.5194/egusphere-egu21-1612, 2021.

In light of the rapid recent retreat of Arctic sea ice, the extreme weather events triggering the variability in Arctic ice cover has drawn increasing attention. A non-Gaussian α-stable Lévy process is thought to be an appropriate model to describe such extreme events. The maximal likely trajectory, based on the nonlocal Fokker–Planck equation, is applied to a nonautonomous Arctic sea ice system under α-stable Lévy noise. Two types of tipping times, the early-warning tipping time and the disaster-happening tipping time, are used to predict the critical time for the maximal likely transition from a perennially ice-covered state to a seasonally ice-free one and from a seasonally ice-free state to a perennially ice-free one, respectively. We find that the increased intensity of extreme events results in shorter warning time for sea ice melting and that an enhanced greenhouse effect will intensify this influence, making the arrival of warning time significantly earlier. Meanwhile, for the enhanced greenhouse effect, we discover that increased intensity and frequency of extreme events will advance the disaster-happening tipping time, in which an ice-free state is maintained throughout the year in the Arctic Ocean. Finally, we identify values of the Lévy index α and the noise intensity ε in the αε-space that can trigger a transition between the Arctic sea ice state. These results provide an effective theoretical framework for studying Arctic sea ice variations under the influence of extreme events.

How to cite: Yang, F., Zheng, Y., Duan, J., Fu, L., and Wiggins, S.: The tipping times in an Arctic sea ice system under influence of extreme events, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-996, https://doi.org/10.5194/egusphere-egu21-996, 2021.

Many phenomena in the climate system lie in the gray zone between weather and climate: they are not amenable to deterministic forecast, but they still depend on the initial condition. A natural example is medium-range forecasting, which is inherently probabilistic because it lies beyond the predictability time of the atmosphere. Similarly, one may ask the probability of occurrence of an El Niño event several months ahead of time or the probability of occurrence of a heat wave a few weeks in advance based on the observed atmospheric circulation. In this talk, we introduce a quantity which corresponds precisely to this type of prediction problem: the committor function is the probability for an event to occur in the future, as a function of the current state of the system. 

In the first part of this presentation, we explain the main mathematical properties of this probabilistic concept, and compute it in the case of a low-dimensional stochastic model for El-Niño, the Jin and Timmerman model. This example allows us to show that the ability to predict the probability of occurrence of the event of interest may differ strongly depending on the initial state: in some regions of phase space, the committor function is smooth (intrinsic probabilistic predictability) and in some other regions, it depends sensitively on the initial condition (intrinsic probabilistic unpredictability).  We stress that this predictability concept is markedly different from the deterministic unpredictability arising because of chaotic dynamics and exponential sensivity to initial conditions. 

The second part of the talk is about how to efficiently compute the committor function from data through several data-driven approaches, such as direct estimates, kernel-based methods and neural networks. We discuss two examples: a) the computation of committor function for the Jin and Timmerman model, b) the computation of committor function for extreme heat waves. Both systems are highly nonlinear but, considering the dimensionality of the two, their level of complexity is profoundly different. This therefore allows us to explore and discuss the performance and limits of the different methods proposed. 

Finally, we propose a method for learning effective dynamics by introducing a Markov chain on the data. Using the Markov chain we are able to quickly and easily compute many interesting quantities of the original system, including the committor function. The goal is to overcome some of the limitations of the methods introduced previously and to develop a robust algorithm that can be useful even in the lack of data.

How to cite: Lucente, D., Miloshevich, G., Herbert, C., and Bouchet, F.: Predicting extreme events using dynamics based machine learning. , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14436, https://doi.org/10.5194/egusphere-egu21-14436, 2021.

The spatio-temporal patterns of precipitation are of considerable relevance in the context of understanding the underlying mechanism of climate phenomena. The application of the complex network paradigm as a data-driven technique for the investigation of the climate system has contributed significantly to identifying the key regions influencing the climate variability of a target region of interest and, in particular, to improving the predictability of extreme events. In our work, we conduct a comparative study of precipitation patterns by constructing functional climate networks using two nonlinear event similarity measures – event synchronization (ES) and edit-distance (ED). Event synchronization has been widely applied to identify interactions between occurrences of different climate phenomena by counting the number of synchronized events between two event series. Edit-distance measures the similarity between sequences by minimizing the number of operations required to transform one sequence to another. We suggest edit-distance as an alternative approach for network reconstruction that can measure similarity between two event series by incorporating not only event occurrences but also event amplitudes. Here, we compare the global extreme precipitation patterns obtained from both reconstruction methods based on the topological characteristics of the resulting networks. As a case study, we compare selected features of network representations of East Asian heavy precipitation events obtained using both ES and ED. Our results reveal the complex nature of the interaction between the Indian Summer Monsoon (ISM) and the East Asian Summer Monsoon (EASM) systems. Through a systematic comparison, we explore the limitations of both measures and show the robustness of the network structures.

How to cite: Su, Z., Gupta, S., Marwan, N., Boers, N., and Kurths, J.: A comparative study of extreme precipitation patterns using complex networks, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8740, https://doi.org/10.5194/egusphere-egu21-8740, 2021.

Obtaining an efficient prediction of the Pacific Decadal Oscillation (PDO) phase transition is a worldwide challenge. Here, we employed the climate network analysis to uncover early warning signals prior to a PDO phase transition. This way an examination of cooperative behavior in the PDO region revealed an enhanced signal that propagated from the western Pacific to the northwest coast of North America. The detection of this signal corresponds very well to the time when the upper ocean heat content in the off-equatorial northwestern tropical Pacific reaches a threshold, in which case a PDO phase transition may be expected with the arising of the next El Niño/La Niña event. The objectively detected early warning signal successfully forewarned all the six PDO phase transitions from the 1890s to 2000s, and also underpinned the possible PDO phase transition around 2015, which may be triggered by the strong El Niño event in 2015-2016.

How to cite: Lu, Z., Yuan, N., Yang, Q., Ma, Z., and Kurths, J.: Detecting early warning signal of the Pacific Decadal Oscillation phase  transition using complex network analysis , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2541, https://doi.org/10.5194/egusphere-egu21-2541, 2021.

The global climate system is an aggregate of a huge number of interacting components, each having an intrinsic time scale. Such a complex dynamical system demonstrates nontrivial behavior and can exhibit a variety of possible modes of evolution. Gradual change of the parameters of the global climate system can lead to transitions (e.g., the Mid-Pleistocene Transition or to abrupt climate changes) from the observed to a new mode.
In this work, we investigate the stability of the global climate system against strong sudden perturbations in the last 2.5 million years. This case is fundamentally different from the small perturbations case: in particularly, the system response cannot be described by a linearized evolution operator. To estimate the climate system’s nonlinear stability during the last 2.5 million years, we use a nonlinear data-driven model of climate dynamics in Pleistocene [1] and basin stability criterion [2]. Our results indicate that the stabilityof the Pleistocene climate to large perturbations decreases with time: past climates being much more stable compared to the present one.
This work was supported by RFBR grant 19-02-00502.

1. D. Mukhin, A. Gavrilov, E. Loskutov, J. Kurths, A. Feigin. “Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition”. ScientificReports, 9 7328 (2019).
2. V. Klinshov, S. Kirillov, J. Kurths, V. Nekorkin. “Interval stability for complex systems”. New Journal of Physics, v. 20, p. 043040.

How to cite: Loskutov, E., Vdovin, V., Gavrilov, A., Mukhin, D., and Feigin, A.: Stability of the global climate system against strong perturbations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3454, https://doi.org/10.5194/egusphere-egu21-3454, 2021.

Understanding the interactions between oceanic conditions and streamflow can deepen our knowledge on hydrological aspects. Most studies exploring this relationship only focus on seasonal or annual scales. However, various atmospheric and oceanic phenomena occur at different timescales and need to be accounted to attribute connectivity between sea-surface temperature and streamflow to specific oceanic and climate processes. In this study, we have investigated the influence of sea-surface temperature (SST) on German streamflow at timescales ranging from sub-seasonal to decadal. We apply wavelets' concepts to decompose the time series into multiple frequency signals and fed into complex networks to identify spatial connections. We employ degree centrality metric and average link distance concepts to interpret the outcomes of coupled SST-Streamflow networks. Our results indicate that the SST anomaly at North Atlantic Ocean region has a stable connection with German streamflow at shorter timescales up to annual scale. We also noticed scale-specific connections in the Pacific, Indian and Southern ocean regions at different timescales ranging from seasonal to decadal scale. Scale-specific connections exhibited by the streamflow stations at all timescales makes it difficult to cluster based on degree centrality. We observed that streamflow stations are influenced by short-range local connections at lower timescales and long-range teleconnections at higher time scale. Our preliminary analysis highlight that the low frequent streamflow extremes have long-range connections, usually not captured at the original scale, and geographical proximity plays a role in high-frequency streamflow signals, according to Tobler’s first law of geography. The results obtained from this study reconfirms reported existing streamflow influences and helped gain insights over other possible large-scale climatic influences.

How to cite: Ganapathy, A., Guntu, R. K., Ozturk, U., Merz, B., and Agarwal, A.: Network-based approach to unravel sea-surface temperature and streamflow connectivity at different timescales, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4670, https://doi.org/10.5194/egusphere-egu21-4670, 2021.

The Indian summer monsoon (ISM) dramatically transforms the weather from hot and dry conditions to abundant precipitation within four months. The high temperature in the summer creates a low-pressure monsoon trough. Subsequently, moist winds from the surrounding seas increase the humidity in the atmosphere. Both the temperature and humidity influence the cloud formation over the monsoon region. Outgoing longwave radiation (OLR) indicates convective activity, which is the basis for cloud formation. Thus, the OLR is a crucial characteristic in meteorology to define monsoon's arrival in the state of Kerala. However, certain values of OLR at monsoon onset for different locations remain unknown. That is a scientific challenge to characterize monsoon onset at every location. This study aims to quantify the advance of monsoon and then make predictions.

Recently, Stolbova et al. 2016 [1] showed temperature and relative humidity exhibit a critical transition from pre-monsoon to monsoon in central India, which allowed making a long-term prediction of monsoon onset and withdrawal in Central India [2].  In the current study, we reveal that OLR exhibits a critical transition from high OLR values during the pre-monsoon state to low OLR values in the rainy season state. We prove the existence of criticality by identifying the OLR-critical threshold. Moreover, we show the appearance of the critical phenomena on the eve of the monsoon onset. In particular, we observe a growth of autocorrelation and variance of fluctuations for different regions in temperature, relative humidity, and OLR.
We find that the abruptness of the transition varies along the direction of advance of the monsoon. More abrupt the transition higher the amount of precipitation. These findings allow us to predict the timing of the monsoon advance from South India to central India. Such a forecast provides crucial information for farmers to sow the appropriate crops before the monsoon begins.

[1] Stolbova, V., E. Surovyatkina, B. Bookhagen, and J. Kurths (2016). GRL 43, 1–9 [doi:10.1002/2016GL068392]
[2] https://www.pik-potsdam.de/en/output/infodesk/forecasting-indian-monsoon

NB acknowledges the financial support of the EPICC project (18_II_149_Global_A_Risikovorhersage) funded by BMU; ES acknowledges the Russian Foundation for Basic Research (RFBR) (No. 20-07-01071)

How to cite: George, N. B., Surovyatkina, E., Krishnan, R., and Kurths, J.: Critical transition to monsoon in outgoing long-wave radiation: prediction of the advance of Indian Summer Monsoon, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6453, https://doi.org/10.5194/egusphere-egu21-6453, 2021.

Climate extremes such as heat waves, drought, extreme precipitation or cold surges have huge social and economic impacts that are expected to increase with climate change. Forecasting of such extreme events on the sub-seasonal time scale (from 10 days to about 3 months) is very challenging because of the poor understanding of phenomena that may increase predictability at this time scale. The Madden-Julian Oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on sub-seasonal time scales and can also promote or enhance phenomena such as monsoons and hurricanes in other regions of the world. It is a hierarchically organized structure that propagates across the planet with a period of 30 to 60 days, and its phase represents an important source of sub-seasonal predictability. For this reason, forecasting the MJO phase can improve the predictability of weather extremes. Here we use the index of the MJO based on outgoing longwave radiation (OLR), namely the OLR MJO Index (OMI), which is a popular index used for defining MJO phases. We used the first two principal components to compute the MJO phase and amplitude. With an autoregressive integrated moving average (ARIMA) model we found that winter and summer are slightly more predictable than spring and autumn. We also computed the likelihood of having a warm/cold spell during a given MJO phase. For warm spells, we found that the significantly most likely phase is the 7, and the top three are 7, 8 and 1, which are, as expected, consecutive phases. For cold spells, phases 5 and 1 play important roles, while phase 3 is by far the least likely to have cold spells. Ongoing work is devoted to compare the skill of neural network approaches (long-short term memory, LSTM, and gated recurrent unit, GRU) for the prediction of the MJO phases and warm/cold spells. Acknowledgment: work funded by ITN CAFE.

How to cite: Silini, R., Masoller, C., and Barreiro, M.: On the predictability of the Madden-Julian Oscillation phase , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8015, https://doi.org/10.5194/egusphere-egu21-8015, 2021.

The reconstruction and analysis of palaeoseasonality from speleothem records remains a notoriously challenging task. Although the seasonal cycle is obscured by noise, dating uncertainties and irregular sampling, its extraction can identify regime transitions and enhance the understanding of long-term climate variability. Shifts in seasonal predictability of hydroclimatic conditions have immediate and serious repercussions for agricultural societies.

We present a highly resolved speleothem record (ca. 0.22 years temporal resolution with episodes twice as high) of palaeoseasonality from Yok Balum cave in Belize covering the Common Era (400-2006 CE) and demonstrate how seasonal-scale hydrological variability can be extracted from δ¹³C and δ¹⁸O isotope records. We employ a Monte-Carlo based framework in which dating uncertainties are transferred into magnitude uncertainty and propagated. Regional historical proxy data enable us to relate climate variability to agricultural disasters throughout the Little Ice Age and population size variability during the Terminal Classic Maya collapse.

Spectral analysis reveals the seasonal cycle as well as nonstationary ENSO- and multi-decadal-scale variability. Variations in both the subannual distribution of rainfall and mean average hydroclimate pose limitations on how reliably farmers can predict crop yield. A characterization of year-to-year predictability as well as the complexity of seasonal patterns unconver shifts in the seasonal-scale variability. These are discussed in the context of their implications for rainfall dependent agricultural societies.

How to cite: Braun, T., Breitenbach, S. F. M., Ray, E., Baldini, J. U. L., Baldini, L. M., Lechleitner, F., Asmerom, Y., Prufer, K. M., and Marwan, N.: Two millennia of seasonal rainfall predictability in the neotropics with repercussions for agricultural societies, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11012, https://doi.org/10.5194/egusphere-egu21-11012, 2021.

In 2020, the Arctic Circle warming in Siberia was extraordinary. Strong anticyclones have been dominant over a large area in Northern Siberia through spring. It resulted in an all-time high-temperature record in the Arctic Circle - more than 6°C above the average (1981–2010). Thus, it accelerated the melting of snow, ice, permafrost and has gotten the wildfire in Siberia off to an unusually early and severe start. The Arctic warming has repercussions not only for Siberia but for the entire Eurasia and the Northern Hemisphere. Specifically, the Arctic conditions affect atmospheric circulation in the Pacific Ocean and the strength and direction of trade winds in the tropical zone.

Here, I show that Arctic Circle warming has impacted the timing of monsoon and sea ice seasons. First, I found the observational evidence of Arctic warming causing colder than average temperatures over the east of Eurasia, Central Europe, and Central Asia. Notably, North Pakistan and Northern India saw temperatures distinctly below the long-term average (1981–2010): 4°C below from March to December. Second, I took this evidence into account while developing a new method for forecasting the sea-ice timing and the recent long-range forecasting method of monsoon season [1]. Third, based on the forecast results for 2020, I found that utilizing only recent trends is an inadequate strategy for predictions. However, considering the current Arctic warming outcomes in specific regions overcomes this problem and results in successful forecasts for both sea-ice and monsoon seasons.

The results imply that when North Pakistan's temperature is cooler than usual: (i) it slows down an advance of monsoon, (ii) it accelerates the cooling of the entire Indian subcontinent during withdrawal from northern Pakistan to the east coast of central India. Hence, North Pakistan's cooling in 2020 caused a protracted offensive and early end of the Indian summer monsoon, thus, shortening its duration. As a result, it led to the early onset of the seasonal wind reversal in the eastern Pacific Ocean in the middle of October and, therefore, to the surprisingly early onset of the winter monsoon in South Asia and India [2]. The consequences of this change in monsoon timing strongly affected 70% of the Indian population directly related to farming.

In the Sea of Okhotsk in 2020, the sea ice retreated early due to heatwaves in Siberia. In December, the onset date of ice season was around average, but ice grew faster than average, creating a hazard to navigation safety.

Hence, the proposed forecasting methodology applied to India and the Sea of Okhotsk opens new possibilities to forecasting monsoon and sea ice seasons around the globe.

The author acknowledges financial support from RFBR, project number 20-07-01071 .

[1] Stolbova, V., E. Surovyatkina, B. Bookhagen, and J. Kurths (2016): Tipping elements of the Indian monsoon: Prediction of onset and withdrawal. GRL 43, 1–9 [doi:10.1002/2016GL068392]

[2] https://www.pik-potsdam.de/en/output/infodesk/forecasting-indian-monsoon

How to cite: Surovyatkina, E.: The impact of Arctic warming on the timing of Indian monsoon and ice season in the Sea of Okhotsk, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13582, https://doi.org/10.5194/egusphere-egu21-13582, 2021.

Model-free gradation of predictability of a geophysical system is essential to quantify how much inherent information is contained within the system and evaluate different forecasting methods' performance to get the best possible prediction. We conjecture that Multiscale Information enclosed in a given geophysical time series is the only input source for any forecast model. In the literature, established entropic measures dealing with grading the predictability of a time series at multiple time scales are limited. Therefore, we need an additional measure to quantify the information at multiple time scales, thereby grading the predictability level. This study introduces a novel measure, Wavelet Entropy Energy Measure (WEEM), based on Wavelet entropy to investigate a time series's energy distribution. From the WEEM analysis, predictability can be graded low to high. The difference between the entropy of a wavelet energy distribution of a time series and entropy of wavelet energy of white noise is the basis for gradation. The metric quantifies the proportion of the deterministic component of a time series in terms of energy concentration, and its range varies from zero to one. One corresponds to high predictable due to its high energy concentration and zero representing a process similar to the white noise process having scattered energy distribution. The proposed metric is normalized, handles non-stationarity, independent of the length of the data. Therefore, it can explain the evolution of predictability for any geophysical time series (ex: precipitation, streamflow, paleoclimate series) from past to the present. WEEM metric's performance can guide the forecasting models in getting the best possible prediction of a geophysical system by comparing different methods. 

How to cite: Guntu, R. K. and Agarwal, A.: Wavelet Entropy Energy Measure (WEEM): A multiscale measure to grade a geophysical system's predictability, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-703, https://doi.org/10.5194/egusphere-egu21-703, 2021.

Since acquisition costs for sensors and data collection decrease rapidly especially in the geo-scientific fields, researchers often have to deal with a large amount of multivariable data, which they would need to automatically analyze in an appropriate way. In nonlinear time series analysis, phase space reconstruction often makes the very first step of any sophisticated analysis, but the established methods are either unable to reliably automate the process or they can not handle multivariate time series input. Here we present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data.

How to cite: Kraemer, H., Datseris, G., Kurths, J., Kiss, I., Ocampo-Espindola, J. L., and Marwan, N.: A unified and automated approach to attractor reconstruction, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1495, https://doi.org/10.5194/egusphere-egu21-1495, 2021.

  Reduced-order dynamical models play a central role in developing our
  understanding of predictability of climate irrespective of whether
  we are dealing with the actual climate system or surrogate climate
  models. In this context, the Linear Inverse Modeling (LIM) approach,
  by helping capture a few essential interactions between dynamical
  components of the full system, has proven valuable in being able to
  provide insights into the dynamical behavior of the full system.

  We demonstrate that Reservoir Computing (RC), a form of machine
  learning suited for learning in the context of chaotic dynamics,
  provides an alternative nonlinear approach that improves on the LIM
  approach. We do this in the example setting of predicting sea
  surface temperature in the North Atlantic in the pre-industrial
  control simulation of a popular earth system model, the Community
  Earth System Model version 2 (CESM2) so that we can compare the
  performance of the new RC based approach with the traditional LIM
  approach both when learning data is plentiful and when such data is
  more limited. The useful predictive skill of the RC approach over a
  wider range of conditions---larger number of retained EOF
  coefficients, extending well into the limited data regime,
  etc.---suggests that this machine learning approach may have a use
  in climate predictability studies. While the possibility of
  developing a climate emulator---the ability to continue the
  evolution of the system on the attractor long after failing to be
  able to track the reference trajectory---is demonstrated in context
  of the Lorenz-63 system, it is suggested that further development of
  the RC approach may permit such uses of the new approach in settings
  of relevance to realistic predictability studies.

How to cite: Nadiga, B.: Reservoir Computing as a Tool for Climate Predictability Studies, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1561, https://doi.org/10.5194/egusphere-egu21-1561, 2021.

Tracing the spatio-temporal distribution of water isotopologues (e.g., H₂¹⁶O, H₂¹⁸O,HD¹⁶O, D₂¹⁶O), in the atmosphere allows insights in to the hydrological cycle and surface-atmosphere interactions. Strong relationships between atmospheric circulation and isotopologue variability exist, mitigated by fractionation during phase transitions of water. Isotopic gradients correlate with precipitation amount, temperature, with distance to source areas of evaporation and often follow topographic features. Isotope-enabled general circulation models (iGCMs) have been established to explicitly simulate the processes that lead to these distributions, in response to the changes in radiative forcing, boundary conditions, and including effects of internal variability of the climate system. However, few of these iGCMs^1,2 of varying complexity exist to date and isotopic tracers decrease their computational efficiency.

Here, we evaluate the potential of replacing the explicit simulation of the isotopic component in the water cycle by statistical learning for offline model evaluation at interannual to multi-millennial timescales. This is challenging. While the relevant fractionation processes are well understood, the climate system is a chaotic, nonstationary system of high dimensionality. Therefore, successful statistical prediction requires the (so far elusive) understanding of the timescale-dependent relationships in the climate system. We present a case study on the feasibility of this approach.

We focus on the impact of variable selection (primarily surface temperature, precipitation and sea-level pressure) and boundary conditions (CO₂ concentrations, ice sheet distribution). We also compare different approaches to dimensionality reduction, and compare the performance of different machine-learning approaches including simple linear regression, random forests, Gaussian Processes and different types of neural networks. The accuracy of the predictions is evaluated using regional and global area-weighted mean squared errors across training and evaluation data from individual GCM simulations and across climatic states. We find a high spatial variability of prediction accuracy, modest in many locations with the presently employed approaches. We obtain encouraging results for the prediction of isotope variability in Greenland and the Antarctic.

References

[1] Tindall, J. C., P. J. Valdes, and Louise C. Sime. "Stable water isotopes in HadCM3: Isotopic signature of El Niño–Southern Oscillation and the tropical amount effect." Journal of Geophysical Research: Atmospheres 114.D4 (2009)

[2] Werner, Martin, et al. "Glacial–interglacial changes in H 2 18 O, HDO and deuterium excess–results from the fully coupled ECHAM5/MPI-OM Earth system model." Geoscientific Model Development 9.2 (2016): 647-670.

How to cite: Rehfeld, K., Wider, J., Theisen, N., Werner, M., Köthe, U., and Weitzel, N.: The potential of machine learning for modeling spatio-temporal properties of water isotopologue distributions in precipitation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2979, https://doi.org/10.5194/egusphere-egu21-2979, 2021.

A multitude number of satellite precipitation products developed as an alternative to ground-based measurements. However, these products suffer from considerable errors and uncertainties due to their retrieval algorithms and sensor capabilities. The uncertainties vary from region to region depending on the topography and also with the rainfall intensities. This study evaluated the accuracy of Tropical Rainfall Measuring Mission (TRMM3B42), Integrated Multi-satellitE Retrievals for GPM (IMERG), Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks - Climate Data Record (PERSIANN-CDR), Climate Prediction Center morphing method (CMORPH), Climate Hazards Group InfraRed Precipitation with Station (CHIRPS) and European Centre for Medium-Range Weather Forecasts Reanalysis 5th Generation (ERA5) during the monsoon season over the coastal Vamsadhara river basin in India. We have also developed a quantile based Bayesian model averaging (QBMA) to merge these products. QBMA is compared with traditional methods, namely, simple model averaging and one outlier removed. Two cases of merging, each with three sub-cases, were experimented: In the first case, we combined various for of TRMM (Linear Scaling bias-corrected, Local Intensity Scaling bias-corrected) PERSIANN and CMORPH. In the second case we had various combination of IMERG (Linear Scaling bias-corrected, Local Intensity Scaling bias-corrected), CHIRPS and ERA5. In all the cases, the coefficients were calibrated using 2001 to 2013 daily monsoon rainfall data and validated for 2014 to 2018. The results indicate that linear scaling bias-corrected QBMA  outperformed the other methods in the first case. For the second case, the one outlier removed method performed better in terms of the correlation coefficient. However, the relative root mean square error is lowest for linear scaling bias-corrected QBMA. The second case outperformed the first case. Our results imply that the improvement of accuracy depends on the method and products used in merging.

How to cite: Yumnam, K., Guntu, R. K., Agarwal, A., and Rathinasamy, M.: Merging of satellite precipitation products: A quantile based Bayesian model averaging approach, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3024, https://doi.org/10.5194/egusphere-egu21-3024, 2021.

The problem of modeling interaction between processes with different time scales is very important in geoscience. In this report, we propose a new form of empirical evolution operator model based on the analysis of multiple time series representing processes with different time scales. We assume that the time series are given on the same time interval.

To construct the model, we extend the previously developed general form of nonlinear stochastic model based on artificial neural networks and designed for the case of time series with constant sampling interval [1]. This sampling interval is related to the main time scale of the process under consideration, which is described by the deterministic component of the model, while the faster time scales are modeled by its stochastic component, possibly depending on the system’s state. This model also includes slower processes in the form of weak time-dependence, as well as external forcing. The structure of the model is optimized using Bayesian approach [1]. The model has proven its efficiency in a number of applications [2-4].

The idea of modeling time series with different time scales is to formulate the above-described model individually for each time scale, and then to include the parameterized influence of the other time scales in it. Particularly, the influence of “slower” time series is included in the form of parameter trends, and the influence of “faster” time series is included by time-averaging their statistics. The algorithm and first results of comparison between the new model and the model without cross-interactions will be discussed.

The work was supported by the Russian Science Foundation (Grant No. 20-62-46056).

1. Gavrilov, A., Loskutov, E., & Mukhin, D. (2017). Bayesian optimization of empirical model with state-dependent stochastic forcing. Chaos, Solitons & Fractals, 104, 327–337. http://doi.org/10.1016/j.chaos.2017.08.032

2. Mukhin, D., Kondrashov, D., Loskutov, E., Gavrilov, A., Feigin, A., & Ghil, M. (2015). Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models. Journal of Climate, 28(5), 1962–1976. http://doi.org/10.1175/JCLI-D-14-00240.1

3. Gavrilov, A., Seleznev, A., Mukhin, D., Loskutov, E., Feigin, A., & Kurths, J. (2019). Linear dynamical modes as new variables for data-driven ENSO forecast. Climate Dynamics, 52(3–4), 2199–2216. http://doi.org/10.1007/s00382-018-4255-7

4. Mukhin, D., Gavrilov, A., Loskutov, E., Kurths, J., & Feigin, A. (2019). Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Scientific Reports, 9(1), 7328. http://doi.org/10.1038/s41598-019-43867-3

How to cite: Gavrilov, A., Seleznev, A., Mukhin, D., and Feigin, A.: Data-driven stochastic model for cross-interacting processes with different time scales, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4199, https://doi.org/10.5194/egusphere-egu21-4199, 2021.

Complex network is a relatively young, multidisciplinary field with an objective to unravel the spatiotemporal interaction in natural processes. Though network theory has become a very important paradigm in many fields, the applications in the hydrology field are still at an emerging stage.  In this study, we employed the Pearson correlation coefficient and Spearman correlation coefficient as a similarity measure with varying threshold ranges to construct the precipitation network of the Ganga River Basin (GRB). Ground-based observed dataset (IMD) and satellite precipitation product (TRMM) are used. Different network properties such as node degree, degree distribution, clustering coefficient, and architecture were computed on each resultant precipitation network of GRB. We also ranked influential grid points in the precipitation network by using weighted degree betweenness to identify the importance of each grid station in the network Our results reveal that the choice of correlation method does not significantly affect the network measures and reconfirm that the thresholds significantly influence network construction and network properties in the case of both datasets. The spatial distribution of the clustering coefficient value is high to low from center to boundary and inverse in the case of degree.  In addition, there is a positive correlation between the average neighbor degree and node degree. Again, we analyzed the architecture of precipitation networks and found that the network has a small world with random network behavior.   Our results also indicated that both products have similar network measures and showed similar kinds of spatial patterns.

How to cite: Gadhawe, M., Guntu, R. K., and Agarwal, A.: Network-based approach to explore basin network comparing observed and satellite dataset, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4840, https://doi.org/10.5194/egusphere-egu21-4840, 2021.

An analysis of the climate system is usually complicated by its very high dimensionality and its nonlinearity which impedes spatial and time scale separation. An even more difficult problem is to obtain separate estimates of the climate system’s response to external forcing (e.g. anthropogenic emissions of greenhouse gases and aerosols) and the contribution of the climate system’s internal variability into recent climate trends. Identification of spatiotemporal climatic patterns representing forced signals and internal variability in global climate models (GCMs) would make it possible to characterize these patterns in the observed data and to analyze dynamical relationships between these two types of climate variability.

In contrast with real climate observations, many GCMs are able to provide ensembles of many climate realizations under the same external forcing, with relatively independent initial conditions (e.g. LENS [1], MPI-GE [2], CMIP ensembles of 20th century climate). In this report, a recently developed method of empirical spatio-temporal data decomposition into linear dynamical modes (LDMs) [3] based on Bayesian approach, is modified to address the problem of self-consistent separation of the climate system internal variability modes and the forced response signals in such ensembles. The LDM method provides the time series of principal components and corresponding spatial patterns; in application to an ensemble of realizations, it determines both time series of the internal variability modes of current realization and the time series of forced response (defined as signal shared by all realizations). The advantage of LDMs is the ability to take into account the time scales of the system evolution better than some other linear techniques, e.g. traditional empirical orthogonal function decomposition. Furthermore, the modified ensemble LDM (E-LDM) method is designed to determine the optimal number of principal components and to distinguish their time scales for both internal variability modes and forced response signals.

The technique and results of applying LDM method to different GCM ensemble realizations will be presented and discussed. This research was supported by the Russian Science Foundation (Grant No. 18-12-00231).

[1] Kay, J. E., Deser, C., Phillips, A., Mai, A., Hannay, C., Strand, G., Arblaster, J., Bates, S., Danabasoglu, G., Edwards, J., Holland, M. Kushner, P., Lamarque, J.-F., Lawrence, D., Lindsay, K., Middleton, A., Munoz, E., Neale, R., Oleson, K., Polvani, L., and M. Vertenstein (2015), The Community Earth System Model (CESM) Large Ensemble Project: A Community Resource for Studying Climate Change in the Presence of Internal Climate Variability, Bulletin of the American Meteorological Society, doi: 10.1175/BAMS-D-13-00255.1, 96, 1333-1349 

[2] Maher, N., Milinski, S., Suarez-Gutierrez, L., Botzet, M., Dobrynin, M., Kornblueh, L., Kröger, J., Takano, Y., Ghosh, R., Hedemann, C., Li, C., Li, H., Manzini, E., Notz, N., Putrasahan, D., Boysen, L., Claussen, M., Ilyina, T., Olonscheck, D., Raddatz, T., Stevens, B. and Marotzke, J. (2019). The Max Planck Institute Grand Ensemble: Enabling the Exploration of Climate System Variability. Journal of Advances in Modeling Earth Systems, 11, 1-21. https://doi.org/10.1029/2019MS001639

[3] Gavrilov, A., Kravtsov, S., Mukhin, D. (2020). Analysis of 20th century surface air temperature using linear dynamical modes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(12), 123110. https://doi.org/10.1063/5.0028246

How to cite: Buyanova, M., Kravtsov, S., Gavrilov, A., Mukhin, D., Loskutov, E., and Feigin, A.: Application of linear dynamical mode decomposition to ensembles of climate simulations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4869, https://doi.org/10.5194/egusphere-egu21-4869, 2021.

Complex network approaches have been recently emerging as novel and complementary concepts of nonlinear time series analysis which are able to unveil many features that are hidden to more traditional analysis methods. In this talk, we focus on one particular approach of ordinal pattern transition networks (OPTNs) for characterizing time series data. In particular, we introduce a suite of OPTN based complexity measures to infer the coupling direction between two dynamical systems from pairs of time series. For several examples of both coupled stochastic processes and chaotic Henon maps, we demonstrate that our approach is able to successfully identify interaction delays of both unidirectional and bidirectional coupling configurations.

Furthermore, we focus on applying these methods to characterize the recent extreme drought events in the semiarid region of Northeast Brazil (NEB) where has been experiencing a continuous dry condition since 2012. Therefore, we propose a three-step strategy to establish the episodic coupling directions on intraseasonal time scales from the surrounding ocean to the precipitation patterns in the NEB, focusing on the distinctive roles of the oceans during the recent extreme drought events of 2012-2013 and 2015-2016. Our algorithm involves: (i) computing drought period length from daily precipitation anomalies to capture extreme drought events, (ii) characterizing the episodic coupling delays from the surrounding oceans to the precipitation by applying Kullback-Leibler divergence (KLD) of complexity measure which is based on OPTN representation of time series, and (iii) calculating the ratio of high temperature in the ocean during the extreme drought events with proper time lags that are identified by KLD measures. From the viewpoint of climatology, our analysis provides data-based evidence of showing significant influence from the North Atlantic in 2012-2013 to the NEB, but in 2015-2016 the Pacific played a dominant role than that of the Atlantic. The episodic intra-seasonal time scale properties are potential for monitoring and forecasting droughts in the NEB, in order to propose strategies for drought impacts reduction.

In conclusion, our results suggest that ordinal partition transition networks can be used as complementary tools for causal inference tasks and provide insights into the potentials and theoretical foundations of time series networks.

References:

[1] H. Y. Wu, Y. Zou, L. M. Alves, E. E. N. Macau, G. Sampaio, and J. A. Marengo. Uncovering episodic influence of oceans on extreme drought events in Northeast Brazil by ordinal partition network approaches. Chaos, 30, 053104, 2020.

[2] Y. J. Ruan, R. V. Donner, S. G. Guan, and Y. Zou. Ordinal partition transition network based complexity measures for inferring coupling direction and delay from time series. Chaos, 29, 043111, 2019.

[3] Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, and J. Kurths. Complex network approaches to nonlinear time series analysis. Physics Reports, 787, 1 – 97, 2019.

How to cite: Zou, Y., Macau, E., and Donner, R.:  Ordinal partition transition network based complexity measures for climate data analysis, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7847, https://doi.org/10.5194/egusphere-egu21-7847, 2021.

Complex network theory provides a powerful framework to study the collective dynamics of the interacting units that constitute a complex system. Functional climate network analysis has been widely applied to study the evolution of climate phenomena such as the South American Monsoon and El Niño which occur over seasonal to (inter-)annual time scales. In this work, we use an evolving climate network approach for the study of tropical cyclones (TCs), which are highly localized extreme weather phenomena occurring over very short time scales (typically 3-10 days). We construct time-evolving climate networks of overlapping short-length (10-14 days) time windows using ERA5 reanalysis mean sea level pressure. We focus on studying the dynamics of the cyclones in the North Indian Ocean and the tropical Atlantic Ocean TC basins. We compute topological measures such as degree centrality as well as the local and global clustering coefficients for successive networks during the cyclone season. We find that, during a TC, the network undergoes a characteristic spatial reorganization in a way that localized structures with high clustering and low degree emerge along the TC track. We also compare the spatial scales involved in the regional weather system in the absence and presence of a TC, within the time span of the network. Our results show that weather variability at daily time scales, and in particular tropical cyclones, can be captured effectively by evolving climate networks.

How to cite: Gupta, S., Boers, N., Pappenberger, F., and Kurths, J.: A Complex Network approach for studying Tropical Cyclones, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8964, https://doi.org/10.5194/egusphere-egu21-8964, 2021.

Extreme events such as earthquakes, tsunamis, heat weaves, droughts, floods, heavy precipitation, or tornados -- affect the human communities and cause tremendous loss of property and wealth, but can be related to multiple and complex sources. For example, a flood is a natural event caused by many drivers such as extreme precipitation, soil moisture, or temperature. We are interested in understanding the direct and indirect coupling between flood events with different climatological and hydrological drivers such as soil moisture and temperature.

We use multivariate recurrence plot and recurrence quantification analysis as a powerful framework to study the couplings between the different systems, especially the direction of coupling. The standard delay-embedding method is not a suitable for the recurrence analysis of event-like data. Therefore, we apply the novel edit-distance method to compute recurrence plots of time series of flood events and use the standard recurrence plot method for the continuous varying time series such as soil moisture and temperature. The coupling analysis is performed using the mean conditional probabilities of recurrence derived from the different recurrence plots. We demonstrate this approach on a prototype system and apply it on the hydrological data. Using this approach we are able to indicate the coupling direction and lag between the different coupled systems.

How to cite: Banerjee, A., Goswami, B., Marwan, N., Merz, B., and Kurths, J.: Recurrence based coupling analysis between event-like data and continuous data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14831, https://doi.org/10.5194/egusphere-egu21-14831, 2021.

Ecological systems typically can exhibit various states ranging from extinction to coexistence of different species in oscillatory states. The switch from one state to another is called bifurcation. All these behaviours of a specific system are hidden in a set of describing differential equations (DE) depending on different parametrisations. To model such a system as DE requires full knowledge of all possible interactions of the system components. In practise, modellers can end up with terms in the DE that do not fully describe the interactions or in the worst case with missing terms.

The framework of universal differential equations (UDE) for scientific machine learning (SciML) [1] allows to reconstruct the incomplete or missing term from an idea of the DE and a short term timeseries of the system and make long term predictions of the system’s behaviour. However, the approach in [1] has difficulties to reconstruct the incomplete or missing term in systems with bifurcations. We developed a trajectory-based loss metric for UDE and SciML to tackle the problem and tested it successfully on a system mimicking algal blooms in the ocean.

[1] Rackauckas, Christopher, et al. "Universal differential equations for scientific machine learning." arXiv preprint arXiv:2001.04385 (2020).

How to cite: Vortmeyer-Kley, R., Nieters, P., and Pipa, G.: A trajectories' guide to the state space - learning missing terms in bifurcating ecological systems, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16159, https://doi.org/10.5194/egusphere-egu21-16159, 2021.