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The climate system can be regarded as a dynamic nonlinear system. Thus, traditional linear statistical methods fail to model the nonlinearities of such a system. These nonlinearities render it necessary to find alternative statistical techniques. Since artificial neural network models (NNM) represent such a nonlinear statistical method their use in analyzing the climate system has been studied for a couple of years now. Most authors use the standard Backpropagation Network (BPN) for their investigations, although this specific model architecture carries a certain risk of over-/underfitting. Here we use the so called Cauchy Machine (CM) with an implemented Fast Simulated Annealing schedule (FSA) (Szu, 1986) for the purpose of attributing and detecting anthropogenic climate change instead. Under certain conditions the CM-FSA guarantees to find the global minimum of a yet undefined cost function (Geman and Geman, 1986). In addition to potential anthropogenic influences on climate (greenhouse gases (GHG), sulphur dioxide (SO2)) natural influences on near surface air temperature (variations of solar activity, explosive volcanism and the El Nino = Southern Oscillation phenomenon) serve as model inputs. The simulations are carried out on different spatial scales: global and area weighted averages. In addition, a multiple linear regression analysis serves as a linear reference. It is shown that the adaptive nonlinear CM-FSA algorithm captures the dynamics of the climate system to a great extent. However, free parameters of this specific network architecture have to be optimized subjectively. The quality of the simulations obtained by the CM-FSA algorithm exceeds the results of a multiple linear regression model; the simulation quality on the global scale amounts up to 81% explained variance. Furthermore the combined anthropogenic effect corresponds to the observed increase in temperature Jones et al. (1994), updated by Jones (1999a), for the examined period 1856–1998 on all investigated scales. In accordance to recent findings of physical climate models, the CM-FSA succeeds with the detection of anthropogenic induced climate change on a high significance level. Thus, the CMFSA algorithm can be regarded as a suitable nonlinear statistical tool for modeling and diagnosing the climate system.
Attribution and detection of anthropogenic climate change using a backpropagation neural network
(2002)
The climate system can be regarded as a dynamic nonlinear system. Thus traditional linear statistical methods are not suited to describe the nonlinearities of this system which renders it necessary to find alternative statistical techniques to model those nonlinear properties. In addition to an earlier paper on this subject (WALTER et al., 1998), the problem of attribution and detection of the observed climate change is addressed here using a nonlinear Backpropagation Neural Network (BPN). In addition to potential anthropogenic influences on climate (CO2-equivalent concentrations, called greenhouse gases, GHG and SO2 emissions) natural influences on surface air temperature (variations of solar activity, volcanism and the El Niño/Southern Oscillation phenomenon) are integrated into the simulations as well. It is shown that the adaptive BPN algorithm captures the dynamics of the climate system, i.e. global and area weighted mean temperature anomalies, to a great extent. However, free parameters of this network architecture have to be optimized in a time consuming trial-and-error process. The simulation quality obtained by the BPN exceeds the results of those from a linear model by far; the simulation quality on the global scale amounts to 84% explained variance. Additionally the results of the nonlinear algorithm are plausible in a physical sense, i.e. amplitude and time structure. Nevertheless they cover a broad range, e.g. the GHG-signal on the global scale ranges from 0.37 K to 1.65 K warming for the time period 1856-1998. However the simulated amplitudes are situated within the discussed range (HOUGHTON et al., 2001). Additionally the combined anthropogenic effect corresponds to the observed increase in temperature for the examined time period. In addition to that, the BPN succeeds with the detection of anthropogenic induced climate change on a high significance level. Therefore the concept of neural networks can be regarded as a suitable nonlinear statistical tool for modeling and diagnosing the climate system.
Simulation of global temperature variations and signal detection studies using neural networks
(1998)
The concept of neural network models (NNM) is a statistical strategy which can be used if a superposition of any forcing mechanisms leads to any effects and if a sufficient related observational data base is available. In comparison to multiple regression analysis (MRA), the main advantages are that NNM is an appropriate tool also in the case of non-linear cause-effect relations and that interactions of the forcing mechanisms are allowed. In comparison to more sophisticated methods like general circulation models (GCM), the main advantage is that details of the physical background like feedbacks can be unknown. Neural networks learn from observations which reflect feedbacks implicitly. The disadvantage, of course, is that the physical background is neglected. In addition, the results prove to be sensitively dependent from the network architecture like the number of hidden neurons or the initialisation of learning parameters. We used a supervised backpropagation network (BPN) with three neuron layers, an unsupervised Kohonen network (KHN) and a combination of both called counterpropagation network (CPN). These concepts are tested in respect to their ability to simulate the observed global as well as hemispheric mean surface air temperature annual variations 1874 - 1993 if parameter time series of the following forcing mechanisms are incorporated : equivalent CO2 concentrations, tropospheric sulfate aerosol concentrations (both anthropogenic), volcanism, solar activity, and ENSO (all natural). It arises that in this way up to 83% of the observed temperature variance can be explained, significantly more than by MRA. The implication of the North Atlantic Oscillation does not improve these results. On a global average, the greenhouse gas (GHG) signal so far is assessed to be 0.9 - 1.3 K (warming), the sulfate signal 0.2 - 0.4 K (cooling), results which are in close similarity to the GCM findings published in the recent IPCC Report. The related signals of the natural forcing mechanisms considered cover amplitudes of 0.1 - 0.3 K. Our best NNM estimate of the GHG doubling signal amounts to 2.1K, equilibrium, or 1.7 K, transient, respectively.