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Approaches to climate change study and neural network modelling Antonello Pasini CNR - Institute of Atmospheric Pollution Rome, Italy Summer School on Climate Change UniKore, 6-10 September 2008 1 Outline • Climate science and dynamical modelling; • neural network model; • assessment on the past; • about predictability in past and future scenarios; • NN downscaling; • conclusions and prospects. Summer School on Climate Change UniKore, 6-10 September 2008 2 Climate scientists as grown-up babies If you give a child a toy, he will eventually open it up. Let’s open it up! Summer School on Climate Change UniKore, 6-10 September 2008 3 Climate scientists as grown-up babies Let’s understand how it works... … and let’s reassemble it! Summer School on Climate Change UniKore, 6-10 September 2008 4 Decomposing the system Summer School on Climate Change UniKore, 6-10 September 2008 5 Theoretical knowledge We possess theoretical knowledge of single sub-systems from experiments in “real laboratories” (e.g., laws from fluiddynamics and thermodynamics of oceans and atmosphere). In order to recompose the complexity of the system, we need a “virtual laboratory”... Summer School on Climate Change UniKore, 6-10 September 2008 6 Recomposing in a model Summer School on Climate Change UniKore, 6-10 September 2008 7 From dynamical modelling... • Physical characterization and forecasting in the climate system is a very difficult task, if we adopt an approach with complete dynamics. • Global Climate Models (GCMs) are the standard tools for grasping this complexity. • They permit to recognize the role of some cause-effect relationships. Summer School on Climate Change UniKore, 6-10 September 2008 8 From dynamical modelling... Summer School on Climate Change UniKore, 6-10 September 2008 9 From dynamical modelling... • However, the results of GCMs could crucially depend on the delicate balance (fine tuning) among the relative strength of feedbacks and the various parameterization routines doubtful results . • Furthermore, they show limits in reconstruction and forecasting at regional and local scales. • So, an independent (more “holystic”) analysis could be interesting. Summer School on Climate Change UniKore, 6-10 September 2008 10 … to a different strategy • The simplest idea: application of a multivariate linear model to the analysis of influence/causality: forcings (which influence temperature) vs. temperature itself • Bad results: the linear model is too simple neural networks! Summer School on Climate Change UniKore, 6-10 September 2008 11 … to a different strategy A biological “inspiration” Summer School on Climate Change UniKore, 6-10 September 2008 12 … to a different strategy Natural inputs Climatic behaviour Anthropogenic inputs Summer School on Climate Change UniKore, 6-10 September 2008 13 A neural network model 1 sigmoid output 0.8 n=3 0.6 n=8 n=20 0.4 n=50 0.2 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 weighted sum g j hj Summer School on Climate Change UniKore, 6-10 September 2008 1 h j 1 exp nhl 14 A neural network model Oi gi Wij g j Summer School on Climate Change j k w jk I k 1 E Ti Oi 2 i UniKore, 6-10 September 2008 2 15 A neural network model W t = W t g h T O V mW t W t 1 Wij t 1 Wij t E m Wij t Wij t 1 ij ij Summer School on Climate Change i i i i j UniKore, 6-10 September 2008 ij ij 16 A neural network model w t t + g h W g h T O I mw t w E w jk t 1 w jk t m w jk t w jk t 1 jk w jk j j ij i i i i k jk jk t 1 i Summer School on Climate Change UniKore, 6-10 September 2008 17 A neural network model • Tool for short historical time series of data (“all-frame” or “leave-one-out” procedure); • early stopping method. Summer School on Climate Change UniKore, 6-10 September 2008 18 Assessment on the past Global case study; regional case study. Summer School on Climate Change UniKore, 6-10 September 2008 19 Global case study Input data: • solar irradiance and stratospheric optical thickness as indices of natural forcings coming from Sun and volcanoes; • CO2 concentration and sulfate emissions as anthropogenic forcings; • SOI index (ENSO) as a circulation pattern in ocean and atmosphere which can be important for better catching the interannual temperature variability. Summer School on Climate Change UniKore, 6-10 September 2008 20 Global case study 4 case studies: a) natural forcings only; b) anthropogenic forcings only; c) natural + anthropogenic forcings; d) natural + anthropogenic forcings + ENSO. In cases when anthropogenic forcings are considered, a strong improvement in the reconstruction performance is achieved by neural modelling (vs. linear modelling). Summer School on Climate Change UniKore, 6-10 September 2008 21 Global case study Anthropogenic forcings 0.6 0.6 0.4 0.4 Temperature anomalies [°C] Temperature anomalies [°C] Natural forcings 0.2 0 -0.2 -0.4 0.2 0 -0.2 -0.4 -0.6 1860 1880 1900 1920 1940 1960 1980 2000 -0.6 1860 1880 Years Summer School on Climate Change 1900 1920 1940 1960 1980 Years UniKore, 6-10 September 2008 22 2000 Global case study Natural + anthropogenic forcings + ENSO 0.6 0.6 0.4 0.4 Temperature anomalies [°C] Temperature anomalies [°C] Natural + anthropogenic forcings 0.2 0 -0.2 -0.4 0.2 0 -0.2 -0.4 -0.6 1860 1880 1900 1920 1940 1960 1980 2000 -0.6 1860 1880 Years Summer School on Climate Change 1900 1920 1940 1960 1980 Years UniKore, 6-10 September 2008 23 2000 Remarks • Anthropogenic forcings appear as a main probable cause of the changes in T; • the input related to ENSO acts as a 2ndorder corrector to the estimation obtained by anthropogenic and natural forcings (nevertheless, in a nonlinear system we cannot separate the single contributions to the final result); • the amount of variance not explained by our final model is low Summer School on Climate Change UniKore, 6-10 September 2008 24 Remarks Is this low amount due to the natural variability of climate system or to some hidden dynamics coming from one or more neglected dynamical causes? Look at the residuals! Three tests: •Fourier spectrum; •autocorrelation function; •MonteCarlo Singular Spectrum Analysis (MCSSA). Summer School on Climate Change UniKore, 6-10 September 2008 25 The residuals No particular peak and periodicity; the spectrum trend is almost flat… … but, decrease in the amplitude above 3 cycles per 10 years; we cannot exclude red or pink noise. Summer School on Climate Change UniKore, 6-10 September 2008 26 The residuals The autocorrelation function is almost completely confined inside the white noise limits; some oscillations are visible but more uncoupled than in previous results. Summer School on Climate Change UniKore, 6-10 September 2008 27 The residuals The plots show results obtained applying MCSSA: due to some points exceeding the confidence limits provided by an AR(1) process, the presence of components different from red noise is suggested. Summer School on Climate Change UniKore, 6-10 September 2008 28 The residuals No undoubted conclusion can be reached by our analysis of the residuals (besides, it is well known how is difficult to distinguish between noise and chaotic dynamical signals in short time series). Anyway, we can be confident that the major causes of temperature change have been considered and only 2nd-order dynamics has been neglected in our study. Summer School on Climate Change UniKore, 6-10 September 2008 29 Regional case study We want to analyze the fundamental elements that drive the temperature behaviour at a regional scale, with the same strategy adopted in the previous global case study. It is well known that the North Atlantic Oscillation (NAO) correlates quite well with temperatures in a period called “extended winter” (December to March). We want to assess the relative influences of global forcings and NAO on temperature in Central England. Summer School on Climate Change UniKore, 6-10 September 2008 30 Regional case study NAO - Summer School on Climate Change NAO + UniKore, 6-10 September 2008 31 Regional case study (CET) CET series in extended winters 7 Temperature [°C] 6 5 4 3 2 1 1860 1880 1900 1920 1940 1960 1980 2000 3 case studies and input data: a) global (natural + anthropogenic) forcings; b) NAO only; c) global forcings + NAO. Years Summer School on Climate Change UniKore, 6-10 September 2008 32 Regional case study (CET) Case (a) (b) (c) Bias [°C] -0.002 0.117 -0.037 MAE [°C] 0.995 0.601 0.651 Residuals [°C] (b) 5 4 3 2 1 0 -1 -2 -3 -4 1860 1880 1900 1920 1940 1960 1980 2000 Years (c) 5 4 3 2 1 Residuals [°C] Residuals [°C] (a) 0 -1 -2 -3 -4 5 4 3 2 1 0 -1 -2 -3 -4 1860 1880 1900 1920 1940 1960 1980 2000 1860 1880 1900 1920 1940 1960 1980 2000 Years Years Summer School on Climate Change UniKore, 6-10 September 2008 33 Regional case study (CET) Global forcings have a very little influence on the behaviour of temperatures in the Central England during extended winter. NAO - driving force: when NAO is considered the values of linear correlation coefficients (estimated T vs. observed T) are about 0.72 0.75 in the two cases. These values are lower than in the analogous situations of the previous global case study (about 0.88). This is probably due to the enhanced interannual variability of climate at regional scale. Summer School on Climate Change UniKore, 6-10 September 2008 34 Discussion A non-dynamical approach allows us to obtain simple assessments in a complex system. At a global scale we are able to reconstruct the global temperature behaviour only if we take the anthropogenic forcings into account. Furthermore, we are able to recognize the influence of ENSO in better catching the inter-annual variability of our global time series of temperature. Summer School on Climate Change UniKore, 6-10 September 2008 35 Discussion At a regional scale, the recognition of the major influence of NAO on the CET time series appears very important (a further discussion in the afternoon exercise session). In general, our results can be used in order to identify the fundamental elements for obtaining both: • successful dynamical regional models • and reliable statistical downscaling of GCMs in the past and for future scenarios. Summer School on Climate Change UniKore, 6-10 September 2008 36 Discussion We possess a phenomenological tool for obtaining preliminary assessments on the past in the climate system. In particular it is worthwhile: • to consider an extension to inputs related to other kinds of forcings, circulation patterns and oscillations; • to apply our method to other regions of the world; • to extend our treatment to the reconstruction of precipitation regimes. Summer School on Climate Change UniKore, 6-10 September 2008 37 Impact studies (animals) How rainfall, snow cover and temperature affect them? Summer School on Climate Change UniKore, 6-10 September 2008 38 Impact studies (animals) Bivariate linear and nonlinear analyses (meteo-climatic forcings vs. rodent density) From Pasini et al. (submitted) Summer School on Climate Change UniKore, 6-10 September 2008 39 Impact studies (animals) Neural reconstruction of rodent density in the Apennines starting from data of meteoclimatic forcings From Pasini et al. (submitted) Summer School on Climate Change UniKore, 6-10 September 2008 40 Impact studies (animals) Neural “backcast” of rodent density in the Apennines starting from data of meteoclimatic forcings From Pasini et al. (submitted) Summer School on Climate Change UniKore, 6-10 September 2008 41 Predictability • Paper by Lorenz (1963) and the discovery of “deterministic chaos” in meteo-climatic systems; • predictability problem and change of perspective in the forecasting activity at medium- and long-range; • ensemble integrations for estimating the predictability horizon in different meteorological situations. Summer School on Climate Change UniKore, 6-10 September 2008 42 Preliminary considerations Ensemble 25 10m WIND SPEED (KTS) 20 15 10 5 Deterministic Summer School on Climate Change 0 TIME (12 - hours interval) UniKore, 6-10 September 2008 43 Preliminary considerations Is the Lorenz-63 model important only for historical reasons? In the present situation, we deal with very complex meteo-climatic models (107 degrees of freedom); inside these models, their physical behaviour can be obscured and also the ensemble strategy cannot be fully followed up (because of the large amount of computer time needed). Summer School on Climate Change UniKore, 6-10 September 2008 44 Preliminary considerations In this framework, the Lorenz-63 model represents a toy model which mimics some features of both the atmosphere and the climate system: for instance, their chaotic behaviour … … and the presence of preferred states or “regimes”. Furthermore, the local predictability on the Lorenz attractor resembles the predictability of single real states. Summer School on Climate Change UniKore, 6-10 September 2008 45 The Lorenz system dx/dt = (y-x) dy/dt = rx - y - xz dz/dt = xy - bz Our choice of the parameters: = 10, b = 8/3, r = 28 chaotic solutions. Summer School on Climate Change UniKore, 6-10 September 2008 46 The forced Lorenz system dx/dt = (y-x) + f0 cos dy/dt = rx - y - xz + f0 sin dz/dt = xy - bz Our choice of the parameters: f0 = 2.5 5, = /2 still chaotic solutions. Toy simulation of an increase of anthropogenic forcings in the climate system Summer School on Climate Change UniKore, 6-10 September 2008 47 The Lorenz system Summer School on Climate Change UniKore, 6-10 September 2008 48 Unforced vs. forced Summer School on Climate Change UniKore, 6-10 September 2008 49 Predictability (dynamics) Summer School on Climate Change UniKore, 6-10 September 2008 50 Predictability (dynamics) The concept of bred vector: • Bred vectors are simply the difference v between two model runs after a certain number (n) of time steps, if the second run is originated from slightly perturbed initial conditions v0. • We define the bred-growth rate as: g = 1/n ln(v/v0). • g can be used to identify regions of distinct predictability on the attractor. Summer School on Climate Change UniKore, 6-10 September 2008 51 Predictability (dynamics) n=8 Blue: g < 0 Green: 0 g < 0.04 Yellow: 0.04 g < 0.064 Red: g 0.064 Summer School on Climate Change UniKore, 6-10 September 2008 52 Predictability (dynamics) Unforced Summer School on Climate Change Forced UniKore, 6-10 September 2008 53 Predictability (dynamics) Summer School on Climate Change UniKore, 6-10 September 2008 54 Predictability studies by NNs The idea to forecast future states of the Lorenz system by NN is not new… … but previous works considered the prediction of the time series for a single variable (usually the x variable) in order to reconstruct the complete dynamics under the conditions of the Takens theorem; this permits to mimic the reconstruction of an unknown dynamics by observational data in a complex system. Summer School on Climate Change UniKore, 6-10 September 2008 55 Predictability studies by NNs Here, we consider the full 3D dynamics of the Lorenz system and try to estimate the predictability on its attractor in several regions (related to bred-growth classes), by considering changes in NN forecasting performance: • network topology: 3 - 15 - 3; • single-step forecast from t0 to t0+n (n=8); • total set of Lorenz simulated data (20,000 input-target patterns) divided into a training set (80%) and a validation/test set (20%); Summer School on Climate Change UniKore, 6-10 September 2008 56 Predictability studies by NNs • the 3D-Euclidean distance between output and target points as a measure of our forecast performance. • The NN forecast performance “feels” increased predictability in forced situations. Summer School on Climate Change UniKore, 6-10 September 2008 57 Predictability studies by NNs Distributions of distance errors for each class Yellow class 20 18 18 16 16 14 14 NN forecast error (distance) Summer School on Climate Change UniKore, 6-10 September 2008 45 41 37 33 29 25 21 45 41 37 33 0 29 0 25 2 21 2 17 4 13 4 9 6 5 6 17 8 13 8 10 9 10 12 5 12 1 Frequency (%) 20 1 Frequency (%) Blue class NN forecast error (distance) 58 Predictability studies by NNs In short, the average forecast error decreases in the forecasting activity on the forced system. This can be obviously due to a more frequent permanence of the system’s state in regions of high predictability (blue points). Can this be due to a change in local predictability of single points in the Euclidean 3D-space, too? Is this due to both of these factors? Summer School on Climate Change UniKore, 6-10 September 2008 59 Predictability studies by NNs Some points: • Of course, the Lorenz system is only a toy model of the atmosphere and the climate system; • operationally, we would like to obtain an estimate of predictability for future times, when observations are not still available, while here the recognition of distinct predictability regions are obtained by NN just in comparison with the “observed” states in Lorenz models (obtained after dynamical integration). Summer School on Climate Change UniKore, 6-10 September 2008 60 Predictability studies by NNs Thus, we obtain just an a posteriori recognition of the predictability over the Lorenz attractors is it possible to obtain an operational estimation of predictability? Yes, by forecasting (via NNs) the bred-growth rates directly (1 output). Main result: NNs are able to forecast g and a statistical significant increase of performance is shown when the external forcing is applied. Summer School on Climate Change UniKore, 6-10 September 2008 61 Predictability studies by NNs Related to the forecast of g Thus, not only the presence of an external forcing permits to better forecast the future states over the attractors (as shown previously), but also the NN estimation of the predictability itself is improved in these forced situations. Summer School on Climate Change UniKore, 6-10 September 2008 62 Provisional conclusions • Neural modelling is able to distinguish regions of distinct predictability over Lorenz attractors. • Increased predictability has been found in the forced case (confirmed by dynamical quantities) and operational estimation of g has been obtained (here, it is an exercise, but it could become important as emulation of dynamical computations for predictability assessments in real dynamical models, where ensemble runs are very time-consuming). Summer School on Climate Change UniKore, 6-10 September 2008 63 Prospects Our NN performance is not very good improvements can be envisaged by: • obtaining extended data sets by prolonged Runge-Kutta integrations; • consideration of different input sets (e.g., truncated time series of delayed data); • application of other NN architectures and learning paradigms. Summer School on Climate Change UniKore, 6-10 September 2008 64 NN downscaling • Up to now we have considered NNs as a strategy which is alternative to dynamical modelling. • In doing so we have obtained both results comparable with those coming from GCMs (in the case of influence analysis on the past) and new results (e.g., in the predictability case study on unforced and forced Lorenz systems). Summer School on Climate Change UniKore, 6-10 September 2008 65 NN downscaling • As a matter of fact, these strategies are based on two distinct view-points for the analysis of a system: a dynamical decomposition-recomposition approach vs. an analysis of the system as a whole by learning directly on data. • The challenge of complexity is extremely hard and different view-points (and the associated strategies) are welcome! Summer School on Climate Change UniKore, 6-10 September 2008 66 NN downscaling • Probably, these strategies can be seen more appropriately as complementary than as alternative. • A concrete example of “synergies” between them is represented by the case of GCMs downscaling via NNs. • In what follows we will discuss this complementary approach and the work in progress about it. Summer School on Climate Change UniKore, 6-10 September 2008 67 The rationale Summer School on Climate Change UniKore, 6-10 September 2008 68 The rationale GCMs are not able to determine climate at regional/local scale. So, there is a need for downscaling. It can be achieved either dynamically or statistically, so that we have two cases: • dynamical downscaling (regional climate models - RCMs); • statistical downscaling (regression models, weather classification, weather generators). Summer School on Climate Change UniKore, 6-10 September 2008 69 The rationale Here we do not discuss about weather classification and weather generators: see Wilby et al. (2004) in the references. In short, statistical downscaling is based on the view-point that the regional/local climate is conditioned by two factors: • the large scale climatic state; • the regional/local physiographic features (e.g., topography, land/sea distribution, land use). Summer School on Climate Change UniKore, 6-10 September 2008 70 The rationale So the process for a statistical downscaling is as follows: • to establish a statistical model which is able to link large-scale climate variables (predictors) with regional/local variables (predictands); • to feed the large-scale output of a GCM to the statistical model; • to estimate the corresponding regional/local climate characteristics. Summer School on Climate Change UniKore, 6-10 September 2008 71 Pros and Cons Advantages of a statistical downscaling: • the techniques used for building and applying the statistical model are usually quite inexpensive from the computer-time point of view; • they can be used to provide site-specific information, which can be critical for many climate change impact studies. Summer School on Climate Change UniKore, 6-10 September 2008 72 Pros and Cons A major theoretical weakness: • we are not able to verify the basic assumption that underlies these models; • that is to say, we cannot be sure that the statistical relationships developed for the present-day climate also hold under the different forcing conditions of possible future climates (“stationarity” assumption); • however, this is a limitation that affects also physical parameterizations of GCMs. Summer School on Climate Change UniKore, 6-10 September 2008 73 Be aware... • Predictors relevant to a regional/local predictand should be adequately reproduced by the GCM to be downloaded (e.g., remind NAO as an important element to determine European climate); • therefore, predictors have to be chosen on the balance of their relevance to the target predictand and their accurate representation by climate models. Summer School on Climate Change UniKore, 6-10 September 2008 74 NNs in downscaling • Among the regression models, NNs appear particular for their characteristic feature of achieving nonlinear relationships between predictors and predictands. • This feature is obviously important in the nonlinear climate system and it becomes increasingly crucial when dealing with regional/local variables (predictands) which are heterogeneous and discontinuous in space and time, such as daily precipitation. Summer School on Climate Change UniKore, 6-10 September 2008 75 A simple example • I would like to present just a simple example of application (by Trigo & Palutikof, 1999). • Reconstruction on the past and future scenarios for minimum and maximum daily temperatures in Coimbra (Portugal). • Feed-forward networks with one hidden layer and backpropagation training. • Training and validation on the past; test on future scenarios. Summer School on Climate Change UniKore, 6-10 September 2008 76 A simple example 6 variables + values of the same variables for the previous day + sin and cos (Julian day) Predictor 24 h mean (nearest grid point) 24 h north-south gradient 24 h east-west gradient 24 h geostrophic vorticity Summer School on Climate Change 500hPa * * * UniKore, 6-10 September 2008 SLP * * * 77 A simple example Validation Summer School on Climate Change UniKore, 6-10 September 2008 78 A simple example Future scenarios Summer School on Climate Change UniKore, 6-10 September 2008 79 Recent advances • Recently, a particular attention has been devoted to the combination of dynamical and moisture variables as predictors; • furthermore, some researchers stressed the importance of a cross-validation of the downscaling model from observational data for periods that represent independent or different climate regimes (thus somewhat validating the “stationarity” assumption). Summer School on Climate Change UniKore, 6-10 September 2008 80 Recent advances • Recently, NNs used for downscaling were extended to SOM (Kohonen networks); • inter-comparisons of NNs and other methods for a statistical downscaling show that neural network modelling is one of the best methods to do so (see more in Pasini (2008)). • At present, in general the scores of methods of statistical downscaling are comparable with those coming from dynamical downscaling (RCMs). Summer School on Climate Change UniKore, 6-10 September 2008 81 Conclusions and prospects • Modelling the dynamics of the climate system is a difficult task. • In this framework, neural network modelling begins to help in grasping this complexity, both as an alternative strategy to dynamical modelling, and as a complementary technique that may be used together with GCMs. • Climate change studies represent a field in which NNs (and, more generally, AI techniques) can be applied successfully. Summer School on Climate Change UniKore, 6-10 September 2008 82 Essential references • Climate modelling: A. Pasini (2005), From Observations to Simulations: a conceptual introduction to weather and climate modelling, World Scientific, www.worldscibooks.com /environsci/5930.html Summer School on Climate Change UniKore, 6-10 September 2008 83 Essential references • Assessment on the past: A. Pasini, M. Lorè, F. Ameli (2006), Ecological Modelling 191, 5867. • Predictability: A. Pasini (2007), Predictability in past and future climate conditions: a preliminary analysis by neural networks using unforced and forced Lorenz systems as toy models, in Proceedings of the 87th AMS annual meeting (5th AI Conference), San Antonio, AMS, CD-ROM. Summer School on Climate Change UniKore, 6-10 September 2008 84 Essential references • NN downscaling: R.L. Wilby et al. (2004), Guidelines for use of climate scenarios developed from statistical downscaling methods. IPCC Task Group TGICA, http://ipccddc.cru.uea.ac.uk/guidelines/StatDown_Guide .pdf (and references therein). • R.M. Trigo & J.P. Palutikof (1999), Climate Research 13, 45-59. Summer School on Climate Change UniKore, 6-10 September 2008 85 Essential references • All these topics are now reviewed in A. Pasini (2008), Neural network modeling in climate change studies, in Artificial Intelligence Methods in the Environmental Sciences (S.E. Haupt, A. Pasini and C. Marzban eds.), Springer (in press). Summer School on Climate Change UniKore, 6-10 September 2008 86 For Italian readers... [email protected] Summer School on Climate Change UniKore, 6-10 September 2008 87