Using genetic programming for symbolic regression to detect climate change signatures

In contrast to some of the recent investigations, this study shows that far less number of tide gauge stations experienced statistically significant accelerations in sea level rise during the 20thcentury. Twenty-seven tide gauge stations with century long data were analyzed for the presence of an acceleration in global sea level rise using a kinematic model inclusive of a secular trend, acceleration, and compounded periodicities with autocorrelated random effects. Eight out of twenty-seven stations revealed statistically significant but slow sea level rise acceleration (p<0.01) within the 0.01-0.02 mm/yr2range compared to the sixteen stations with accelerations estimated using the models by the previous investigations,which did not account for the compounded periodicities and autocorrelations in sea level changes.

<p>Symbolic regression (SR) is a function identification process, the task of which is to identify and express the relationship between the input and output variables in mathematical models. SR is named to emphasise its ability to find the structure and coefficients of the model simultaneously. Genetic Programming (GP) is an attractive and powerful technique for SR, since it does not require any predefined model and has a flexible representation. However, GP based SR generally has a poor generalisation ability which degrades its reliability and hampers its applications to science and real-world modeling. Therefore, this thesis aims to develop new GP approaches to SR that evolve/learn models exhibiting good generalisation ability. This thesis develops a novel feature selection method in GP for high-dimensional SR. Feature selection can potentially contribute not only to improving the efficiency of learning algorithms but also to enhancing the generalisation ability. However, feature selection is seldom considered in GP for high-dimensional SR. The proposed new feature selection method utilises GP’s built-in feature selection ability and relies on permutation to detect the truly relevant features and discard irrelevant/noisy features. The results confirm the superiority of the proposed method over the other examined feature selection methods including random forests and decision trees on identifying the truly relevant features. Further analysis indicates that the models evolved by GP with the proposed feature selection method are more likely to contain only the truly relevant features and have better interpretability. To address the overfitting issue of GP when learning from a relatively small number of instances, this thesis proposes a new GP approach by incorporating structural risk minimisation (SRM), which is a framework to estimate the generalisation performance of models, into GP. The effectiveness of SRM highly depends on the accuracy of the Vapnik-Chervonenkis (VC) dimension measuring model complexity. This thesis significantly extends an experimental method (instead of theoretical estimation) to measure the VC-dimension of a mixture of linear and nonlinear regression models in GP for the first time. The experimental method has been conducted using uniform and non-uniform settings and provides reliable VC-dimension values. The results show that our methods have an impressively better generalisation gain and evolve more compact model, which have a much smaller behavioural difference from the target models than standard GP and GP with bootstrap, The proposed method using the optimised non-uniform setting further improves the one using the uniform setting. This thesis employs geometric semantic GP (GSGP) to tackle the unsatisfied generalisation performance of GP for SR when no overfitting occurs. It proposes three new angle-awareness driven geometric semantic operators (GSO) including selection, crossover and mutation to further explore the geometry of the semantic space to gain a greater generalisation improvement in GP for SR. The angle-awareness brings new geometric properties to these geometric operators, which are expected to provide a greater leverage for approximating the target semantics in each operation, and more importantly, to be resistant to overfitting. The results show that compared with two kinds of state-of-the-art GSOs, the proposed new GSOs not only drive the evolutionary process fitting the target semantics more efficiently but also significantly improve the generalisation performance. A further comparison on the evolved models shows that the new method generally produces simpler models with a much smaller size and containing important building blocks of the target models.</p>

<div><span>Model-based projections of ice-sheet thresholds and global sea-level rise are severely constrained by </span><span>instrumental observations being only decadal to century-long. As we improve our understanding of these processes, projections just a few years old are now considered conservative, raising concerns about our ability to successfully plan for abrupt future change. </span><span>Past periods of abrupt and extreme warming offer ‘process analogues’ that can provide new insights into the future rate of response of polar ice sheets to warming of the Earth system. The Last Termination </span><span>(20,000-10,000 years ago or 20-10 ka BP) </span>in the North Atlantic region was characterised by a series of abrupt climatic changes including rapid warming at 14.7 ka BP (the start of the “Bølling”, or GI-1 in the Greenland ice-core isotope stratigraphy) which was accompanied by an Antarctic Cold Reversal (ACR) in the south. Potentially important, during the onset of GI-1, warming persisted in the south for some 256±133 calendar years before the ACR, providing a period of time during which both polar regions experienced increasing temperatures. Sometime around the onset of GI-1 and the ACR, Meltwater Pulse 1A (MWP-1A) formed an abrupt sea level rise of ~15 metres, and was coincident with a period of enhanced iceberg flux in the Southern Ocean. It seems likely the majority of the sea level rise came from the Northern Hemisphere – up to 5-6 metres from the Laurentide Ice Sheet – though the timing remains uncertain. The contribution of Antarctic Ice Sheets (AIS) to global mean sea level (GMSL) rise during MWP-1A range from ‘high-end’ scenarios (>10 m contributing over half of the total GMSL rise), to ‘low-end’ (scenarios with little to no contribution). Here we report the results of a multidisciplinary study, with refined age and Antarctic ice-sheet modelling of the MWP-1A sea-level rise. With the recently released international radiocarbon calibration curve (IntCal20), our Bayesian age modelling of terrestrial ages from flooded mangrove swamps suggests global <span>sea level rose across a mean age range of 14.58 ka BP to 14.42 ka BP, with a mean rate of sea-level rise of 0.94 metres per decade (14.97 metres over 160 years). Because the calibrated age range at 95% confidence overlaps in this age model, it is possible the 15 metre rise during MWP1A could have taken place essentially instantaneously. Even the most conservative age modelling we have undertaken indicates an extraordinary rapid rate of sea-level rise; two orders of magnitude larger than the mean rate of global sea level rise since 1993 (0.03±0.003 metres per decade). Our ice-sheet modelling suggests a substantial and rapid loss of Antarctic ice mass (mostly from the Weddell Sea Embayment and the Antarctic Peninsula), synchronous with warming and ice loss in the North Atlantic. The drivers and mechanisms of the observed near-synchronous interhemispheric changes will be discussed, with implications for the future.</span></div>

Gradient-based local optimization has been shown to improve results of genetic programming (GP) for symbolic regression. Several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms such as the Levenberg-Marquardt algorithm for local optimization. The effectiveness of NLS algorithms depends on appropriate scaling and conditioning of the optimization problem. This has so far been ignored in symbolic regression and GP literature. In this study we use a singular value decomposition of NLS Jacobian matrices to determine the numeric rank and the condition number. We perform experiments with a GP implementation and six different benchmark datasets. Our results show that rank-deficient and ill-conditioned Jacobian matrices occur frequently and for all datasets. The issue is less extreme when restricting GP tree size and when using many non-linear functions in the function set.

Increased sea level rise accelerates carbon sequestration in a macro-tidal salt marsh.

Twentieth century sea-level rise inferred from tide gauge, geologically derived and thermosteric sea-level changes

<p>corresponding author: N.Flokos</p><p>flksnik@gmail.com</p><p>ABSTRACT</p><p>Sea level change is one of the key indicators of climate change with numerous effects such as flooding, erosion of beaches, salt intrusion.  The detailed global picture of sea level and the monitoring of its spatial-temporal changes is performed by Satellite Altimetry (SA). Nowadays, SA data compare well with measurements from the global tide gauge network, but the aim of 0.3 mm/year accuracy in the altimeter derived rate of global mean sea level rise is still not fully met. </p><p>Whilst the precise determination of global and regional sea level rise from SA data is promising, there is however an observational gap in our knowledge regarding the coastal zone. While Tide Gauges (TG) are usually located at the coast, therefore providing coastal sea level measurements, altimeters have difficulties there. Filling this gap becomes important when considering that the impact of sea level rise can be devastating on the coast with effects on society and ecosystems. This makes it even more significant knowing that there are many stretches of the world’s coast that still do not possess in situ level measuring devices.  </p><p>This work aims to discuss the available data and methods that link the SA measurements of sea level rise with TG measurements. Whilst there is rich literature on relevant applications, it is important to have a clear and concise methodology on this.</p><p>Tide gauge data</p><p>Several post processing steps need to be applied to the raw TG data to enrich the raw Sea Surface Heights (SSH) values and make them comparable with SA data. There are several geophysical corrections, such as pressure and wind effects, which can be applied to TG data in order to deduce  Sea Level (SL) and be consistent with altimeter data. High frequency atmospheric effects on TG data are corrected using the Dynamic Atmospheric Correction (DAC) provided by AVISO. One other large uncertainty is the vertical stability of the TG benchmark over time. TG data must be corrected for the Vertical Land Motion (VLM) to enable the comparison of two sea level measurements (TG and SA) and their later integration within the surfaces of the absolute sea heights. The main VLM dataset can be obtained from SONEL database (SONEL 2016) which provides crustal velocities from the continuous GNSS measurements at sites collocated to the TG.</p><p>Satellite altimetry data</p><p>Whilst Satellite Altimetry over the open ocean is a mature discipline, global altimetry data collected over the coastal ocean remain still largely unexploited. This is because of intrinsic difficulties in the corrections and issues of land contamination in the footprint that have so far resulted in systematic flagging and rejection of these data. In this work, the relevant methodology to overcome these problems and extend the capabilities of current and future altimeters to the coastal zone (coastal altimetry) will be discussed and a number of coastal altimetry data sets will be used (eg SARvatore, X-TRACK, RADS etc). Finally, a practical example using real data sets over the Aegean Sea will be presented. </p><p> </p><p> </p>

<p>    Global warming-related SLR (sea level rise) constitutes a substantial threat to Macau, due to its low elevation, small size and ongoing land reclamation. This study was devised to determine the long-term variation of sea level change in Macau, as well as to develop future projections based on tide gauge and satellite data and GCM simulations, aiming to provide knowledge for SLR mitigation and adaptation.</p><p>    Based on local tide gauge records, sea level in Macau is now rising at an accelerated rate: 1.35 mm yr<sup>−1</sup> over 1925–2010 and jumping to 4.2 mm yr<sup>−1</sup> over 1970–2010, reflecting an apparent acceleration of SLR. Furthermore, the sea level near Macau rose 10% faster than the global mean during the period from 1993 to 2012. In addition, the rate of VLM (vertical land movement) at Macau is estimated at -0.153mm yr<sup>-1</sup>, contributing little to local sea level change.</p><p>    In the future, as projected by a suite of climate models, the rate of SLR in Macau will be about 20% higher than the global average. This is induced primarily by a greater-than-average rate of oceanic thermal expansion in Macau, together with enhanced southerly anomalies that lead to a piling up of sea water. Specifically, the sea level is projected to rise 8–12, 22–51 and 35–118 cm by 2020, 2060 and 2100 with respect to the 1986–2005 baseline climatology, respectively, depending on the emissions scenario and climate sensitivity. If we consider the medium emissions scenario RCP4.5 along with medium climate sensitivity, Macau can expect to experience an SLR of 10, 34 and 65 cm by 2020, 2060 and 2100. If the worst case happens (RCP8.5 plus high climate sensitivity), the SLR will be far higher than that in the medium case; namely, 12, 51 and 118 cm by 2020, 2060, and 2100, respectively. The SLR under the lower emissions scenario is expected to be less severe than that under the higher emissions scenarios: by 2100, an SLR of 65–118 cm in Macau under RCP8.5, almost twice as fast as that under RCP2.6. The key source of uncertainty stems from the emissions scenario and poor knowledge of climate sensitivity. By 2020, the uncertainty range is only 4 cm, yet by 2100 the range will be increased to 83 cm.</p>

Low frequency oscillation assessment methods based on measured data have attracted increasing attention from research and industry stakeholders in power systems engineering. Among those existing methods, empirical mode decomposition (EMD) is a multi-resolution signal processing method used for analysis of non-stationary signals. In recent years, EMD has been a most widely used method in practice. However, it has some disadvantages such as end effect, mode mixing, etc. If a signal contains more than two individual components whose frequencies fall within an octave, it cannot be decomposed by standard and the frequency heterodyne EMD methods. To improve the frequency resolution, a lower sideband frequency shift EMD (LSB-EMD) is proposed in this paper. The method includes an advanced approach on how to select an appropriate modulation frequency so as to can enlarge the component frequency ratios and avoid frequencies turn over. The improved frequency shift EMD is integrated with the procedure of the standard EMD. Consequently, the complex signal can be decomposed by the method. This method can be applied for the analysis of low-frequency oscillations, as well as other power-system signals such as power quality signals and inrush currents. The effectiveness of the method to separate closely spaced modal components is demonstrated by both numerical simulation and field measurements.

Envelope modified versions of the empirical mode decomposition (EMD) method such as the B‐spline interpolation‐based EMD (B‐EMD) method and cardinal spline interpolation‐based EMD (C‐EMD) method have been proposed recently for purpose of improving its effectiveness. To shed further light on their performance, the behaviours of these EMD‐type methods in the presence of white Gaussian noises are investigated in this study based on extensive numerical experiments. Similarly to the EMD method, it turns out that the envelope modified EMD methods also act as filter banks essentially. However, the spectra among the first several intrinsic mode functions of the B‐EMD method have fewer overlaps than those of the EMD and C‐EMD methods, which indicate that the B‐EMD method has a better ability to alleviate the mode mixing problem for signals with higher frequencies. On the other hand, the C‐EMD method is shown to perform better than the EMD and B‐EMD methods on separating tones with lower frequencies.

Measuring very low frequency sea level variations using satellite altimeter data

Sea level data from the Chesapeake Bay are used to test a novel new analysis method for studies of sea level rise (SLR). The method, based on Empirical Mode Decomposition and Hilbert‐Huang Transformation, separates the sea level trend from other oscillating modes and reveals how the mean sea level changes over time. Bootstrap calculations test the robustness of the method and provide confidence levels. The analysis shows that rates of SLR have increased from ∼1–3 mm y−1 in the 1930s to ∼4–10 mm y−1 in 2011, an acceleration of ∼0.05–0.10 mm y−2 that is larger than most previous studies, but comparable to recent findings by Sallenger and collaborators. While land subsidence increases SLR rates in the bay relative to global SLR, the acceleration results support Sallenger et al.'s proposition that an additional contribution to SLR from climatic changes in ocean circulation is affecting the region.

Projections of global sea-level rise into the future have become more pessimistic over the past five years or so. A global rise by more than one metre by the year 2100 is now widely accepted as a serious possibility if greenhouse gas emissions continue unabated. That is witnessed by the scientific assessments that were made since the last IPCC report was published in 2007. The Delta Commission of the Dutch government projected up to 1.10 m as a 'high-end' scenario (Vellinga et al 2009). The Scientific Committee on Antarctic Research (SCAR) projected up to 1.40 m (Scientific Committee on Antarctic Research 2009), and the Arctic Monitoring and Assessment Programme (AMAP) gives a range of 0.90–1.60 m in its 2011 report (Arctic Monitoring and Assessment Programme 2011). And recently the US Army Corps of Engineers recommends using a 'low', an 'intermediate' and a 'high' scenario for global sea-level rise when planning civil works programmes, with the high one corresponding to a 1.50 m rise by 2100 (US Army Corps of Engineers 2011).

Sea-level rise (SLR) is magnifying the frequency and severity of extreme sea levels (ESLs) that can cause coastal flooding. The rate and amount of global mean sea-level (GMSL) rise is a function of the trajectory of global mean surface temperature (GMST). Therefore, temperature stabilization targets (e.g. 1.5 °C and 2.0 °C of warming above pre-industrial levels, as from the Paris Agreement) have important implications for coastal flood risk. Here, we assess, in a global network of tide gauges, the differences in the expected frequencies of ESLs between scenarios that stabilize GMST warming at 1.5 °C, 2.0 °C, and 2.5 °C above pre-industrial levels. We employ probabilistic, localized SLR projections and long-term hourly tide gauge records to estimate the expected frequencies of historical and future ESLs for the 21st and 22nd centuries. By 2100, under 1.5 °C, 2.0 °C, and 2.5 °C GMST stabilization, the median GMSL is projected to rise 48 cm (90% probability of 28–82 cm), 56 cm (28–96 cm), and 58 cm (37–93 cm), respectively. As an independent comparison, a semi-empirical sea level model calibrated to temperature and GMSL over the past two millennia estimates median GMSL rise within 7–8 cm of these projections. By 2150, relative to the 2.0 °C scenario and based on median sea level projections, GMST stabilization of 1.5 °C spares the inundation of lands currently home to about 5 million people, including 60 000 individuals currently residing in Small Island Developing States. We quantify projected changes to the expected frequency of historical 10-, 100-, and 500-year ESL events using frequency amplification factors that incorporate uncertainty in both local SLR and historical return periods of ESLs. By 2150, relative to a 2.0 °C scenario, the reduction in the frequency amplification of the historical 100 year ESL event arising from a 1.5 °C GMST stabilization is greatest in the eastern United States, with ESL event frequency amplification being reduced by about half at most tide gauges. In general, smaller reductions are projected for Small Island Developing States.

Multiple lines of observational evidence indicate that the global climate has been getting warmer since the early 20th century. This warmer climate has led to a global mean sea level rise of about 18 cm during the 20th century, and over 6 cm for the first 15 years of the 21st century. Regionally the sea level rise is not uniform due in large part to internal climate variability. To better serve the community, the uncertainties of predicting/projecting regional sea level changes associated with internal climate variability need to be quantified. Previous research on this topic has used single-model large ensembles with perturbed atmospheric initial conditions (ICs). Here we compare uncertainties associated with perturbing ICs in just the atmosphere and just the ocean using a state-of-the-art coupled climate model. We find that by perturbing the oceanic ICs, the uncertainties in regional sea level changes increase compared to those with perturbed atmospheric ICs. Thus, in order for us to better assess the full spectrum of the impacts of such internal climate variability on regional and global sea level rise, approaches that involve perturbing both atmospheric and oceanic initial conditions are necessary.