Predictability of SST forced climate signals in two atmospheric general circulation models

 The predictability of atmospheric responses to global sea surface temperature (SST) anomalies is evaluated using ensemble simulations of two general circulation models (GCMs): the GENESIS version 1.5 (GEN) and the ECMWF cycle 36 (ECM). The integrations incorporate observed SST variations but start from different initial land and atmospheric states. Five GEN 1980–1992 and six ECM 1980–1988 realizations are compared with observations to distinguish predictable SST forced climate signals from internal variability. To facilitate the study, correlation analysis and significance evaluation techniques are developed on the basis of time series permutations. It is found that the annual mean global area with realistic signals is variable dependent and ranges from 3 to 20% in GEN and 6 to 28% in ECM. More than 95% of these signal areas occur between 35 °S–35 °N. Due to the existence of model biases, robust responses, which are independent of initial condition, are identified over broader areas. Both GCMs demonstrate that the sensitivity to initial conditions decreases and the predictability of SST forced responses increases, in order, from 850 hPa zonal wind, outgoing longwave radiation, 200 hPa zonal wind, sea-level pressure to 500 hPa height. The predictable signals are concentrated in the tropical and subtropical Pacific Ocean and are identified with typical El Ni?o/ Southern Oscillation phenomena that occur in response to SST and diabatic heating anomalies over the equatorial central Pacific. ECM is less sensitive to initial conditions and better predicts SST forced climate changes. This results from (1) a more realistic basic climatology, especially of the upper-level wind circulation, that produces more realistic interactions between the mean flow, stationary waves and tropical forcing; (2) a more vigorous hydrologic cycle that amplifies the tropical forcing signals, which can exceed internal variability and be more efficiently transported from the forcing region. Differences between the models and observations are identified. For GEN during El Ni?o, the convection does not carry energy to a sufficiently high altitude, while the spread of the tropospheric warming along the equator is slower and the anomaly magnitude smaller than observed. This impacts model ability to simulate realistic responses over Eurasia and the Indian Ocean. Similar biases exist in the ECM responses. In addition, the relationships between upper and lower tropospheric wind responses to SST forcing are not well reproduced by either model. The identification of these model biases leads to the conclusion that improvements in convective heat and momentum transport parametrizations and basic climate simulations could substantially increase predictive skill. Received: 25 April 1996 / Accepted: 9 December 1996     

Impact of the convection-wind-evaporation feedback on surface climate simulation in general circulation models

The wind-evaporation-convection feedback in the tropics is demonstrated to strongly affect the mean state of surface climate in atmospheric general circulation models. The feedback is shown to be very effective in channeling perturbations from one component of the climate system to other components, e.g., from evaporation to surface wind and from atmospheric convective activity to evaporation. It also provides an effective channel to pass on atmospheric perturbations in the middle and upper troposphere to the surface. As an illustration, it is shown that surface evaporation over tropical oceans is connected with cloud absorption of shortwave radiation through this feedback. Insufficient shortwave cloud absorption, causing excessive shortwave radiation at the surface as is common in most of the climate models, leads to excessive evaporation. Quantitatively, sensitivity of evaporation to short-wave cloud absorption, when averaged over the whole tropics, can be described by an approximate balance of variations in atmospheric radiative cooling and latent heating. This balance is achieved by the impact of radiation on convection, and then on the surface wind and evaporation. This mechanism calls for the need to include atmospheric processes far beyond the surface for improvements of the quality of surface climate simulation.     

Analysis of rainfall seasonality from observations and climate models

Two new indicators of rainfall seasonality based on information entropy, the relative entropy (RE) and the dimensionless seasonality index (DSI), together with the mean annual rainfall, are evaluated on a global scale for recently updated precipitation gridded datasets and for historical simulations from coupled atmosphere–ocean general circulation models. The RE provides a measure of the number of wet months and, for precipitation regimes featuring a distinct wet and dry season, it is directly related to the duration of the wet season. The DSI combines the rainfall intensity with its degree of seasonality and it is an indicator of the extent of the global monsoon region. We show that the RE and the DSI are fairly independent of the time resolution of the precipitation data, thereby allowing objective metrics for model intercomparison and ranking. Regions with different precipitation regimes are classified and characterized in terms of RE and DSI. Comparison of different land observational datasets reveals substantial difference in their local representation of seasonality. It is shown that two-dimensional maps of RE provide an easy way to compare rainfall seasonality from various datasets and to determine areas of interest. Models participating to the Coupled Model Intercomparison Project platform, Phase 5, consistently overestimate the RE over tropical Latin America and underestimate it in West Africa, western Mexico and East Asia. It is demonstrated that positive RE biases in a general circulation model are associated with excessively peaked monthly precipitation fractions, too large during the wet months and too small in the months preceding and following the wet season; negative biases are instead due, in most cases, to an excess of rainfall during the premonsoonal months.     

The spread amongst ENSEMBLES regional scenarios: regional climate models, driving general circulation models and interannual variability

Various combinations of thirteen regional climate models (RCM) and six general circulation models (GCM) were used in FP6-ENSEMBLES. The response to the SRES-A1B greenhouse gas concentration scenario over Europe, calculated as the difference between the 2021–2050 and the 1961–1990 means can be viewed as an expected value about which various uncertainties exist. Uncertainties are measured here by variance explained for temperature and precipitation changes over eight European sub-areas. Three sources of uncertainty can be evaluated from the ENSEMBLES database. Sampling uncertainty is due to the fact that the model climate is estimated as an average over a finite number of years (30) despite a non-negligible interannual variability. Regional model uncertainty is due to the fact that the RCMs use different techniques to discretize the equations and to represent sub-grid effects. Global model uncertainty is due to the fact that the RCMs have been driven by different GCMs. Two methods are presented to fill the many empty cells of the ENSEMBLES RCM?×?GCM matrix. The first one is based on the same approach as in FP5-PRUDENCE. The second one uses the concept of weather regimes to attempt to separate the contribution of the GCM and the RCM. The variance of the climate response is analyzed with respect to the contribution of the GCM and the RCM. The two filling methods agree that the main contributor to the spread is the choice of the GCM, except for summer precipitation where the choice of the RCM dominates the uncertainty. Of course the implication of the GCM to the spread varies with the region, being maximum in the South-western part of Europe, whereas the continental parts are more sensitive to the choice of the RCM. The third cause of spread is systematically the interannual variability. The total uncertainty about temperature is not large enough to mask the 2021–2050 response which shows a similar pattern to the one obtained for 2071–2100 in PRUDENCE. The uncertainty about precipitation prevents any quantitative assessment on the response at grid point level for the 2021–2050 period. One can however see, as in PRUDENCE, a positive response in winter (more rain in the scenario than in the reference) in northern Europe and a negative summer response in southern Europe.     

2004年临汾市高温的气候特点和环流特征分析

本文从分析亚欧环流形势出发,对比历史资料平均情况,对造成2004年临汾市持续高温的500hPa高度场和850hPa的温度场的实况资料以及平流等物理量作了较详细的分析,找出了临汾市夏季出现高温的可能指标。     

Expected changes in future agro-climatological conditions in Northeast Thailand and their differences between general circulation models

We have studied future changes in the atmospheric and hydrological environments in Northeast Thailand from the viewpoint of risk assessment of future cultural environments in crop fields. To obtain robust and reliable estimation for future climate, ten general circulation models under three warming scenarios, B1, A1B, and A2, were used in this study. The obtained change trends show that daily maximum air temperature and precipitation will increase by 2.6°C and 4.0%, respectively, whereas soil moisture will decrease by c.a. 1% point in volumetric water content at the end of this century under the A1B scenario. Seasonal contrasts in precipitation will intensify: precipitation increases in the rainy season and precipitation decreases in the dry season. Soil moisture will slightly decrease almost throughout the year. Despite a homogeneous increase in the air temperature over Northeast Thailand, a future decrease in soil water content will show a geographically inhomogeneous distribution: Soil will experience a relative larger decrease in wetness at a shallow depth on the Khorat plateau than in the surrounding mountainous area, reflecting vegetation cover and soil texture. The predicted increase in air temperature is relatively consistent between general circulation models. In contrast, relatively large intermodel differences in precipitation, especially in long-term trends, produce unwanted bias errors in the estimation of other hydrological elements, such as soil moisture and evaporation, and cause uncertainties in projection of the agro-climatological environment. Offline hydrological simulation with a wide precipitation range is one strategy to compensate for such uncertainties and to obtain reliable risk assessment of future cultural conditions in rainfed paddy fields in Northeast Thailand.     

Ocean-atmosphere interactions and climate drift in a coupled general circulation model

 We have analysed numerical simulations performed with a global 3D coupled atmosphere-ocean model to focus on the role of atmospheric processes leading to sea surface temperature (SST) drift in the tropics. Negative SST errors occur coherently in space and time with large positive errors in latent heat and momentum fluxes at the tropical air-sea interface, as diagnosed from forced SST simulations. The warm pool in the western Pacific disappears after a few years of simulation. Strong SST gradients enforce regions of high precipitation that are thin and stationary north of the equator. We detail the implications for the ocean-atmosphere system of such upheaval in the deep convection location. A sensitivity experiment to empirically formulate air-sea drag coefficient shows that the rapid warm pool erosion is not sensitive to changes in the formulation of the surface drag coefficient over the oceans because the corresponding changes in turbulent heat fluxes and LW cooling approximately cancel one another. In the eastern Pacific, the improvement in SST is striking and caused by feedbacks between SST, surface turbulent fluxes and boundary layer cloud fraction, which decreases as SST warms. Received: 8 December 1998 / Accepted: 6 January 2000     

Decadal climate variability simulated in a coupled general circulation model

A 1000 year integration of the CSIRO coupled ocean-atmosphere general circulation model is used to study low frequency (decadal to centennial) climate variability in precipitation and temperature. The model is shown to exhibit sizeable decadal variability for these fields, generally accounting for approximately 20 to 40% of the variability (greater than one year) in precipitation and up to 80% for temperature. An empirical orthogonal function (EOF) analysis is applied to the model output to show some of the major statistical modes of low frequency variability. The first EOF spatial pattern looks very much like that of the interannual ENSO pattern. It bears considerable resemblance to observational estimates and is centred in the Pacific extending into both hemispheres. It modulates both precipitation and temperature globally. The EOF has a time evolution that appears to be more than just red noise. Finally, the link between SST in the Pacific with Australian rainfall variability seen in observations is also evident in the model. Received: 29 August 1998 / Accepted: 31 July 1999     

Climate of Russia in the 21st Century. Part 2. Verification of atmosphere-ocean general circulation models CMIP3 for projections of future climate changes

Results of simulation of radiation, cloud cover, surface air temperature, sea-level pressure, and hydrological regime components for Russia with the help of an ensemble of CMIP3 global climate models is analyzed. Despite a large spread among the models, the CMIP3 AOGCM ensemble simulations of the key characteristics of the observed surface climate agree well with observations, anyway in averaging over areas of vast regions, from watersheds of large rivers to the whole of Russia. These means (ensemble-and area-averaged values) often fall into the range of estimates derived from observations. This suggests the existence of uncertainty in the estimates obtained from simulations as well as from observational data. Comparison of different-generation models demonstrates a gradual improvement of the AOGCM simulation of surface climate characteristics. In general, the averaging over the CMIP3 AOGCM ensemble allows us to state that the ensemble is suitable for estimates of future climate changes.     

Stratospheric climate and variability from a general circulation model and observations

The climate and natural variability of the large-scale stratospheric circulation simulated by a newly developed general circulation model are evaluated against available global observations. The simulation consisted of a 30-year annual cycle integration performed with a comprehensive model of the troposphere and stratosphere. The observations consisted of a 15-year dataset from global operational analyses of the troposphere and stratosphere. The model evaluation concentrates on the simulation of the evolution of the extratropical stratospheric circulation in both hemispheres. The December–February climatology of the observed zonal mean winter circulation is found to be reasonably well captured by the model, although in the Northern Hemisphere upper stratosphere the simulated westerly winds are systematically stronger and a cold bias is apparent in the polar stratosphere. This Northern Hemisphere stratospheric cold bias virtually disappears during spring (March–May), consistent with a realistic simulation of the spring weakening of the mean westerly winds in the model. A considerable amount of monthly interannual variability is also found in the simulation in the Northern Hemisphere in late winter and early spring. The simulated interannual variability is predominantly caused by polar warmings of the stratosphere, in agreement with observations. The breakdown of the Northern Hemisphere stratospheric polar vortex appears therefore to occur in a realistic way in the model. However, in early winter the model severely underestimates the interannual variability, especially in the upper troposphere. The Southern Hemisphere winter (June–August) zonal mean temperature is systematically colder in the model, and the simulated winds are somewhat too strong in the upper stratosphere. Contrary to the results for the Northern Hemisphere spring, this model cold bias worsens during the Southern Hemisphere spring (September–November). Significant discrepancies between the model results and the observations are therefore found during the breakdown of the Southern Hemisphere polar vortex. For instance, the simulated Southern Hemisphere stratosphere westerly jet continuously decreases in intensity more or less in situ from June to November, while the observed stratospheric jet moves downward and poleward.This paper was presented at the Third International Conference on Modelling of Global Climate Change and Variability, held in Hamburg 4–8 Sept. 1995 under the auspice of the Max Planck Institute for Meteorology, Hamburg. Editor for these papers is L. Dümenil.     

The Beijing Climate Center atmospheric general circulation model: description and its performance for the present-day climate

The Beijing Climate Center atmospheric general circulation model version 2.0.1 (BCC_AGCM2.0.1) is described and its performance in simulating the present-day climate is assessed. BCC_AGCM2.0.1 originates from the community atmospheric model version 3 (CAM3) developed by the National Center for Atmospheric Research (NCAR). The dynamics in BCC_AGCM2.0.1 is, however, substantially different from the Eulerian spectral formulation of the dynamical equations in CAM3, and several new physical parameterizations have replaced the corresponding original ones. The major modification of the model physics in BCC_AGCM2.0.1 includes a new convection scheme, a dry adiabatic adjustment scheme in which potential temperature is conserved, a modified scheme to calculate the sensible heat and moisture fluxes over the open ocean which takes into account the effect of ocean waves on the latent and sensible heat fluxes, and an empirical equation to compute the snow cover fraction. Specially, the new convection scheme in BCC_AGCM2.0.1, which is generated from the Zhang and McFarlane’s scheme but modified, is tested to have significant improvement in tropical maximum but also the subtropical minimum precipitation, and the modified scheme for turbulent fluxes are validated using EPIC2001 in situ observations and show a large improvement than its original scheme in CAM3. BCC_AGCM2.0.1 is forced by observed monthly varying sea surface temperatures and sea ice concentrations during 1949–2000. The model climatology is compiled for the period 1971–2000 and compared with the ERA-40 reanalysis products. The model performance is evaluated in terms of energy budgets, precipitation, sea level pressure, air temperature, geopotential height, and atmospheric circulation, as well as their seasonal variations. Results show that BCC_AGCM2.0.1 reproduces fairly well the present-day climate. The combined effect of the new dynamical core and the updated physical parameterizations in BCC_AGCM2.0.1 leads to an overall improvement, compared to the original CAM3.     

A new framework for isolating individual feedback processes in coupled general circulation climate models. Part I: formulation

This paper proposes a coupled atmosphere–surface climate feedback–response analysis method (CFRAM) as a new framework for estimating climate feedbacks in coupled general circulation models with a full set of physical parameterization packages. The formulation of the CFRAM is based on the energy balance in an atmosphere–surface column. In the CFRAM, the isolation of partial temperature changes due to an external forcing or an individual feedback is achieved by solving the linearized infrared radiation transfer model subject to individual energy flux perturbations (external or due to feedbacks). The partial temperature changes are addable and their sum is equal to the (total) temperature change (in the linear sense). The decomposition of feedbacks is based on the thermodynamic and dynamical processes that directly affect individual energy flux terms. Therefore, not only those feedbacks that directly affect the TOA radiative fluxes, such as water vapor, clouds, and ice-albedo feedbacks, but also those feedbacks that do not directly affect the TOA radiation, such as evaporation, convections, and convergence of horizontal sensible and latent heat fluxes, are explicitly included in the CFRAM. In the CFRAM, the feedback gain matrices measure the strength of individual feedbacks. The feedback gain matrices can be estimated from the energy flux perturbations inferred from individual parameterization packages and dynamical modules. The inter-model spread of a feedback gain matrix would help us to detect the origins of the uncertainty of future climate projections in climate model simulations.     

Atlantic watermass and circulation response to persistent freshwater forcing in two coupled general circulation models

The sensitivity of the Atlantic circulation and watermasses to biases in the convergence of moisture into the basin is examined in this study using two different general circulation models. For a persistent positive moisture flux into the tropical Atlantic, the average salinity and temperature in the basin is reduced, mainly below mid-depths and in high latitudes. A transient reduction in the Atlantic overturning strength occurs in this case, with a recovery timescale of 1–2 centuries. In contrast, a similar amount of freshwater directed into the Subpolar North Atlantic results in a persistent reduction in overturning and an increase in basin heat and salt content. In the unperturbed pre-industrial simulations, the Atlantic is unambiguously warmer and saltier than historical observations below mid-depths and in the Nordic Seas. The models’ tropical freshwater flux sensitivities project strongly onto the spatial pattern of this bias, suggesting a common atmospheric deficiency. The integrated Atlantic plus Arctic surface freshwater flux in these models is between ?0.5 and ?0.6 Sv, compared with an observational estimate of ?0.28 Sv. Our results suggest that shortcomings in the models’ ability to reproduce realistic bulk watermass properties are due to an overestimation of the inter-basin moisture export from the tropical Atlantic.     

The deep water stratification of ocean general circulation models

Abstract

A central problem in climate and ocean modelling is the accurate simulation of the climatological state of the oceanic density field. A constant vertical diffusivity for heat and salt is frequently employed in ocean general circulation models (OGCMs) and it is usually assigned a value designed to optimize the depth of the pycnocline. One undesired consequence of this choice is a poor representation of the deep water, which is usually insufficiently stratified. In contrast to the uniform diffusivity of many models, some observational studies suggest that the vertical diffusivity is not constant but increases with depth, possibly in inverse proportion to the local buoyancy frequency. Numerical experiments with an OGCM are presented that demonstrate that allowing the vertical diffusivity to increase below the pycnocline substantially increases the stratification of the abyssal water mass of these models without significantly affecting the pycnocline depth, and hence may lead to a better representation of the vertical density structure.     

Simulating the diurnal cycle of rainfall in global climate models: resolution versus parameterization

The effects of horizontal resolution and the treatment of convection on simulation of the diurnal cycle of precipitation during boreal summer are analyzed in several innovative weather and climate model integrations. The simulations include: season-long integrations of the Non-hydrostatic Icosahedral Atmospheric Model (NICAM) with explicit clouds and convection; year-long integrations of the operational Integrated Forecast System (IFS) from the European Centre for Medium-range Weather Forecasts at three resolutions (125, 39 and 16 km); seasonal simulations of the same model at 10 km resolution; and seasonal simulations of the National Center for Atmospheric Research (NCAR) low-resolution climate model with and without an embedded two-dimensional cloud-resolving model in each grid box. NICAM with explicit convection simulates best the phase of the diurnal cycle, as well as many regional features such as rainfall triggered by advancing sea breezes or high topography. However, NICAM greatly overestimates mean rainfall and the magnitude of the diurnal cycle. Introduction of an embedded cloud model within the NCAR model significantly improves global statistics of the seasonal mean and diurnal cycle of rainfall, as well as many regional features. However, errors often remain larger than for the other higher-resolution models. Increasing resolution alone has little impact on the timing of daily rainfall in IFS with parameterized convection, yet the amplitude of the diurnal cycle does improve along with the representation of mean rainfall. Variations during the day in atmospheric prognostic fields appear quite similar among models, suggesting that the distinctive treatments of model physics account for the differences in representing the diurnal cycle of precipitation.     

Atmospheric circulation in regional climate models over Central Europe: links to surface air temperature and the influence of driving data

The study examines simulation of atmospheric circulation, represented by circulation indices (flow direction, strength and vorticity), and links between circulation and daily surface air temperatures in regional climate models (RCMs) over Central Europe. We explore control simulations of five high-resolution RCMs from the ENSEMBLES project driven by re-analysis (ERA-40) and the same global climate model (ECHAM5 GCM) plus of one RCM (RCA) driven by different GCMs. The aims are to (1) identify errors in RCM-simulated distributions of circulation indices in individual seasons, (2) identify errors in simulated temperatures under particular circulation indices, and (3) compare performance of individual RCMs with respect to the driving data. Although most of the RCMs qualitatively reflect observed distributions of the airflow indices, each produces distributions significantly different from the observations. General biases include overestimation of the frequency of strong flow days and of strong cyclonic vorticity. Some circulation biases obviously propagate from the driving data. ECHAM5 and all simulations driven by ECHAM5 underestimate frequency of easterly flow, mainly in summer. Except for HIRHAM, however, all RCMs driven by ECHAM5 improve on the driving GCM in simulating atmospheric circulation. The influence on circulation characteristics in the nested RCM differs between GCMs, as demonstrated in a set of RCA simulations with different driving data. The driving data control on circulation in RCA is particularly weak for the BCM GCM, in which case RCA substantially modifies (but does not improve) the circulation from the driving data in both winter and summer. Those RCMs with the most distorted atmospheric circulation are HIRHAM driven by ECHAM5 and RCA driven by BCM. Relatively strong relationships between circulation indices and surface air temperatures were found in the observed data for Central Europe. The links differ by season and are usually stronger for daily maxima than minima. RCMs qualitatively reproduce these relationships. Effects of the driving model biases were found on RCMs’ performance in reproducing not only atmospheric circulation but also the links to surface temperature. However, the RCM formulation appears to be more important than the driving data in representing the latter. Differences of the circulation-to-temperature links among the RCA simulations are smaller and the links tend to be more realistic compared to the driving GCMs.     

Analyzing projected changes and trends of temperature and precipitation in the southern USA from 16 downscaled global climate models

This study aims to examine how future climate, temperature and precipitation specifically, are expected to change under the A2, A1B, and B1 emission scenarios over the six states that make up the Southern Climate Impacts Planning Program (SCIPP): Oklahoma, Texas, Arkansas, Louisiana, Tennessee, and Mississippi. SCIPP is a member of the National Oceanic and Atmospheric Administration-funded Regional Integrated Sciences and Assessments network, a program which aims to better connect climate-related scientific research with in-the-field decision-making processes. The results of the study found that the average temperature over the study area is anticipated to increase by 1.7°C to 2.4°C in the twenty-first century based on the different emission scenarios with a rate of change that is more pronounced during the second half of the century. Summer and fall seasons are projected to have more significant temperature increases, while the northwestern portions of the region are projected to experience more significant increases than the Gulf coast region. Precipitation projections, conversely, do not exhibit a discernible upward or downward trend. Late twenty-first century exhibits slightly more precipitation than the early century, based on the A1B and B1 scenario, and fall and winter are projected to become wetter than the late twentieth century as a whole. Climate changes on the city level show that greater warming will happened in inland cities such as Oklahoma City and El Paso, and heavier precipitation in Nashville. These changes have profound implications for local water resources management as well as broader regional decision making. These results represent an initial phase of a broader study that is being undertaken to assist SCIPP regional and local water planning efforts in an effort to more closely link climate modeling to longer-term water resources management and to continue assessing climate change impacts on regional hazards management in the South.     

Entropy production and coarse graining of the climate fields in a general circulation model

We extend the analysis of the thermodynamics of the climate system by investigating the role played by processes taking place at various spatial and temporal scales through a procedure of coarse graining. We show that the coarser is the graining of the climatic fields, the lower is the resulting estimate of the material entropy production. In other terms, all the spatial and temporal scales of variability of the thermodynamic fields provide a positive contribution to the material entropy production. This may be interpreted also as that, at all scales, the temperature fields and the heating fields resulting from the convergence of turbulent fluxes have a negative correlation, while the opposite holds between the temperature fields and the radiative heating fields. Moreover, we obtain that the latter correlations are stronger, which confirms that radiation acts as primary driver for the climatic processes, while the material fluxes dampen the resulting fluctuations through dissipative processes. We also show, using specific coarse-graining procedures, how one can separate the various contributions to the material entropy production coming from the dissipation of kinetic energy, the vertical sensible and latent heat fluxes, and the large scale horizontal fluxes, without resorting to the full three-dimensional time dependent fields. We find that most of the entropy production is associated to irreversible exchanges occurring along the vertical direction, and that neglecting the horizontal and time variability of the fields has a relatively small impact on the estimate of the material entropy production. The approach presented here seems promising for testing climate models, for assessing the impact of changing their parametrizations and their resolution, as well as for investigating the atmosphere of exoplanets, because it allows for evaluating the error in the estimate of their thermodynamical properties due to the lack of high-resolution data. The findings on the impact of coarse graining on the thermodynamic fields on the estimate of the material entropy production deserve to be explored in a more general context, because they provide a way for understanding the relationship between forced fluctuations and dissipative processes in continuum systems.