A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective

Does the Danube exist? Versions of reality given by various regional climate models and climatological datasets

We present an intercomparison and verification analysis of several regional climate models (RCMs) nested into the same run of the same Atmospheric Global Circulation Model (AGCM) regarding their representation of the statistical properties of the hydrological balance of the Danube river basin for 1961-1990. We also consider the datasets produced by the driving AGCM, from the ECMWF and NCEP-NCAR reanalyses. The hydrological balance is computed by integrating the precipitation and evaporation fields over the area of interest. Large discrepancies exist among RCMs for the monthly climatology as well as for the mean and variability of the annual balances, and only few datasets are consistent with the observed discharge values of the Danube at its Delta, even if the driving AGCM provides itself an excellent estimate. Since the considered approach relies on the mass conservation principle and bypasses the details of the air-land interface modeling, we propose that the atmospheric components of RCMs still face difficulties in representing the water balance even on a relatively large scale. Their reliability on smaller river basins may be even more problematic. Moreover, since for some models the hydrological balance estimates obtained with the runoff fields do not agree with those obtained via precipitation and evaporation, some deficiencies of the land models are also apparent. NCEP-NCAR and ERA-40 reanalyses result to be largely inadequate for representing the hydrology of the Danube river basin, both for the reconstruction of the long-term averages and of the seasonal cycle, and cannot in any sense be used as verification. We suggest that these results should be carefully considered in the perspective of auditing climate models and assessing their ability to simulate future climate changes.Comment: 25 pages 8 figures, 5 table

Prevailing climatic trends and runoff response from Hindukush–Karakoram–Himalaya, upper Indus Basin

Largely depending on the meltwater from the Hindukush–Karakoram–Himalaya, withdrawals from the upper Indus Basin (UIB) contribute half of the surface water availability in Pakistan, indispensable for agricultural production systems, industrial and domestic use, and hydropower generation. Despite such importance, a comprehensive assessment of prevailing state of relevant climatic variables determining the water availability is largely missing. Against this background, this study assesses the trends in maximum, minimum and mean temperatures, diurnal temperature range and precipitation from 18 stations (1250–4500 m a.s.l.) for their overlapping period of record (1995–2012) and, separately, from six stations of their long-term record (1961–2012). For this, a Mann–Kendall test on serially independent time series is applied to detect the existence of a trend, while its true slope is estimated using the Sen's slope method. Further, locally identified climatic trends are statistically assessed for their spatial-scale significance within 10 identified subregions of the UIB, and the spatially (field-) significant climatic trends are then qualitatively compared with the trends in discharge out of corresponding subregions. Over the recent period (1995–2012), we find warming and drying of spring (field-significant in March) and increasing early melt season discharge from most of the subregions, likely due to a rapid snowmelt. In stark contrast, most of the subregions feature a field-significant cooling within the monsoon period (particularly in July and September), which coincides well with the main glacier melt season. Hence, a decreasing or weakly increasing discharge is observed from the corresponding subregions during mid- to late melt season (particularly in July). Such tendencies, being largely consistent with the long-term trends (1961–2012), most likely indicate dominance of the nival but suppression of the glacial melt regime, altering overall hydrology of the UIB in future. These findings, though constrained by sparse and short observations, largely contribute in understanding the UIB melt runoff dynamics and address the hydroclimatic explanation of the Karakoram Anomaly

Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean–atmosphere model on a β-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme, and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing to the temperature field. The increase in the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The Kaplan–Yorke dimension of the attractor increases as well. The convergence rate of the rate function for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric timescale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated with the ocean dynamics, is not fully resolved because of its associated long timescales, even at intermediate orders. As expected, increasing the mechanical atmosphere–ocean coupling coefficient or introducing a turbulent diffusion parametrisation reduces the Kaplan–Yorke dimension and Kolmogorov–Sinai entropy. In all considered configurations, we are not yet in the regime in which one can robustly define large deviation laws describing the statistics of the FTLEs. This paper highlights the need to investigate the natural variability of the atmosphere–ocean coupled dynamics by associating rate of growth and decay of perturbations with the physical modes described using the formalism of the covariant Lyapunov vectors and considering long integrations in order to disentangle the dynamical processes occurring at all timescales

Hydrological cycle over South and Southeast Asian river basins as simulated by PCMDI/CMIP3 experiments

We investigate how the climate models contributing to the PCMDI/CMIP3 dataset describe the hydrological cycle over four major South and Southeast Asian river basins (Indus, Ganges, Brahmaputra and Mekong) for the 20th, 21st (13 models) and 22nd (10 models) centuries. For the 20th century, some models do not seem to conserve water at the river basin scale up to a good degree of approximation. The simulated precipitation minus evaporation (P − E), total runoff (R) and precipitation (P) quantities are neither consistent with the observations nor among the models themselves. Most of the models underestimate P − E for all four river basins, which is mainly associated with the underestimation of precipitation. This is in agreement with the recent results on the biases of the representation of monsoonal dynamics by GCMs. Overall, a modest inter-model agreement is found only for the evaporation and inter-annual variability of P − E. For the 21st and 22nd centuries, models agree on the negative (positive) changes of P − E for the Indus basin (Ganges, Brahmaputra and Mekong basins). Most of the models foresee an increase in the inter-annual variability of P − E for the Ganges and Mekong basins, thus suggesting an increase in large low-frequency dry/wet events. Instead, no considerable future change in the inter-annual variability of P − E is found for the Indus and Brahmaputra basins

Seasonality of the hydrological cycle in major South and Southeast Asian river basins as simulated by PCMDI/CMIP3 experiments

In this study, we investigate how PCMDI/CMIP3 general circulation models (GCMs) represent the seasonal properties of the hydrological cycle in four major South and Southeast Asian river basins (Indus, Ganges, Brahmaputra and Mekong). First, we examine the skill of the GCMs by analysing their performance in simulating the 20th century climate (1961–2000 period) using historical forcing (20c3m experiment), and then we analyse the projected changes for the corresponding 21st and 22nd century climates under the SRESA1B scenario. The CMIP3 GCMs show a varying degree of skill in simulating the basic characteristics of the monsoonal precipitation regimes of the Ganges, Brahmaputra and Mekong basins, while the representation of the hydrological cycle over the Indus Basin is poor in most cases, with a few GCMs not capturing the monsoonal signal at all. While the model outputs feature a remarkable spread for the monsoonal precipitation, a satisfactory representation of the western mid-latitude precipitation regime is instead observed. Similarly, most of the models exhibit a satisfactory agreement for the basin-integrated runoff in winter and spring, while their spread is large for the runoff during the monsoon season. For the future climate scenarios, most models foresee a decrease in the winter P − E over all four basins, while agreement is found on the decrease of the spring P − E over the Indus and Ganges basins only. Such decreases in P − E are mainly due to the decrease in precipitation associated with the western mid-latitude disturbances. Consequently, for the Indus and Ganges basins, the runoff drops during the spring season while it rises during the winter season. Such changes indicate a shift from rather glacial and nival to more pluvial runoff regimes, particularly for the Indus Basin. Furthermore, the rise in the projected runoff, along with the increase in precipitation during summer and autumn, indicates an intensification of the summer monsoon regime for all study basins