Dominant Empirical Orthogonal Functions Research Articles

Computational Modeling for High-Fidelity Coarsening of Shallow Water Equations Based on Subgrid Data

Small-scale features of shallow water flow obtained from direct numerical simulation (DNS) with two different computational codes for the shallow water equations are gathered offline and subsequently employed with the aim of constructing a reduced-order correction. This is used to facilitate high-fidelity online flow predictions at much reduced costs on coarse meshes. The resolved small-scale features at high resolution represent subgrid properties for the coarse representation. Measurements of the subgrid dynamics are obtained as the difference between the evolution of a coarse grid solution and the corresponding DNS result. The measurements are sensitive to the particular numerical methods used for the simulation on coarse computational grids and can be used to approximately correct the associated discretization errors. The subgrid features are decomposed into empirical orthogonal functions (EOFs), after which a corresponding correction term is constructed. By increasing the number of EOFs in the approximation of the measured values the correction term can in principle be made arbitrarily accurate. Both computational methods investigated here show a significant decrease in the simulation error already when applying the correction based on the dominant EOFs only. The error reduction accounts for the particular discretization errors that incur and are hence specific to the particular simulation method that is adopted. This improvement is also observed for very coarse grids which may be used for computational model reduction in geophysical and turbulent flow problems.

Spatio-temporal and trend analysis of rain days having different intensity from 1901 – 2020 at regional scale in Haryana, India

Our study has investigated spatio-temporal distribution of rainfall and rain day trends during different seasons for all districts of Haryana, India. Gridded rainfall dataset of 120 years (1901 to 2020) from India Meteorological Department (IMD) was analysed using mean rainfall, rainfall deviation, seasonal rainfall ratio (SRR), coefficient of variation (CV), number of rain days, rainfall intensity, trends of rain days, Empirical Orthogonal Functions (EOF) and Principal Component (PC) analysis. Districts lying in eastern Haryana have experienced more rainfall (less variability) than the ones lying in western Haryana during each season. SRR and CV analysis depicted most consistent rainfall during monsoon and maximum variability during post-monsoon season. Highest number of rain days was observed during monsoon season followed by pre-monsoon, winter and post-monsoon season in Haryana. Innovative trend analysis method (ITAM) shows a declining trend in number of rain days during winter and post-monsoon season while an increasing trend was observed during pre-monsoon season. Overall, monsoon season has shown a falling trend in moderate while rising trend was observed in both light and heavy rainfall intensity categories in most of districts. Dominant EOF explained maximum variability during post-monsoon season followed by winter, pre-monsoon, and monsoon season, respectively. PC analysis captured inter-annual variability in rainfall during each season. Our findings highlight qualitative and quantitative aspects of seasonal rainfall dynamics at districts level. This study is beneficial in understanding impact of climate change and climate variability on rainfall dynamics in Haryana which may guide policymakers and beneficiaries in optimizing use of hydrological resources.

Influence of Sea Level Pressure on Inter-Annual Rainfall Variability in Northern Senegal in the Context of Climate Change

This study examines the inter-annual variability of rainfall and Mean Sea Level Pressure (MSLP) over west Africa based on analysis of the Global Precipitation Climatology Project (GPCP) and National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) Reanalysis respectively. An interconnection is found in this region, between Mean Sea Level Pressure (MSLP) anomaly (over Azores and St. Helena High) and monthly mean precipitation during summer (June to September: JJAS). We also found that over northern Senegal (15°N - 17°N; 17°W - 13°W) the SLP to the north is strong; the wind converges at 200 hPa corresponding to the position of the African Easterly Jet (AEJ) the rotational wind 700 hPa (corresponding to the position of the African Easterly Jet (AEJ) coming from the north-east is negative. In this region, the precipitation is related to the SLP to the north with the opposite sign. The Empirical Orthogonal Functions (EOF) of SLP is also presented, including the mean spectrum of precipitation and pressures to the north (15°N - 40°N and 50°W - 25°W) and south (40°S - 10°S and 40°W - 0°E). The dominant EOF of Sea Level Pressures north and south of the Atlantic Ocean for GPCP represents about 62.2% and 69.4% of the variance, respectively. The second and third EOFs of the pressure to the north account for 24.0% and 6.5% respectively. The second and third EOFs of the pressure to the south represent 12.5% and 8.9% respectively. Wet years in the north of Senegal were associated with anomalous low-pressure areas over the north Atlantic Ocean as opposed to the dry years which exhibited an anomalous high-pressure area in the same region. On the other hand, over the South Atlantic, an opposition is noted. The wavelet analysis method is applied to the SLP showings to the north, south and precipitation in our study area. The indices prove to be very consistent, especially during intervals of high variance.

Intraseasonal Oscillation Indices from Complex EOFs

AbstractIndices of oscillatory behavior are conveniently obtained by projecting the fields in question into a phase space of a few (mostly just two) dimensions; empirical orthogonal functions (EOFs) or other, more dynamical, modes are typically used for the projection. If sufficiently coherent and in quadrature, the projected variables simply describe a rotating vector in the phase space, which then serves as the basis for predictions. Using the boreal summer intraseasonal oscillation (BSISO) as a test case, an alternative procedure is introduced: it augments the original fields with their Hilbert transform (HT) to form a complex series and projects it onto its (single) dominant EOF. The real and imaginary parts of the corresponding complex pattern and index are compared with those of the original (real) EOF. The new index explains slightly less variance of the physical fields than the original, but it is much more coherent, partly from its use of future information by the HT. Because the latter is in the way of real-time monitoring, the index can only be used in cases with predicted physical fields, for which it promises to be superior. By developing a causal approximation of the HT, a real-time variant of the index is obtained whose coherency is comparable to the noncausal version, but with smaller explained variance of the physical fields. In test cases the new index compares well to other indices of BSISO. The potential for using both indices as an alternative is discussed.

Testing the validity of regional detail in global analyses of sea surface temperature – the case of Chinese coastal waters

Abstract. We have designed a method for testing the quality of multidecadal analyses of sea surface temperature (SST) in regional seas by using a set of high-quality local SST observations. In recognizing that local data may reflect local effects, we focus on the dominant empirical orthogonal functions (EOFs) of the local data and of the localized data of the gridded SST analyses. We examine the patterns, variability, and trends of the principal components. This method is applied to examine three different SST analyses, i.e., HadISST1, ERSST, and COBE SST. They have been assessed using a newly constructed high-quality dataset of SST at 26 coastal stations along the Chinese coast in 1960–2015, which underwent careful examination with respect to quality and a number of corrections for inhomogeneities. The three gridded analyses perform generally well from 1960 to 2015, in particular since 1980. However, for the pre-satellite period prior to the 1980s, the analyses differ among each other and show some inconsistencies with the local data, such as artificial break points, periods of bias, and differences in trends. We conclude that gridded SST analyses need improvement in the pre-satellite period (prior to the 1980s) by reexamining in detail archives of local quality-controlled SST data in many data-sparse regions of the world.

Global Mean Climate and Main Patterns of Variability in the CMCC‐CM2 Coupled Model

AbstractEuro‐Mediterranean Centre on Climate Change coupled climate model (CMCC‐CM2) represents the new family of the global coupled climate models developed and used at CMCC. It is based on the atmospheric, land and sea ice components from the Community Earth System Model coupled with the global ocean model Nucleus for European Modeling of the Ocean. This study documents the model components, the coupling strategy, particularly for the oceanic, atmospheric, and sea ice components, and the overall model ability in reproducing the observed mean climate and main patterns of interannual variability. As a first step toward a more comprehensive, process‐oriented, validation of the model, this work analyzes a 200‐year simulation performed under constant forcing corresponding to present‐day climate conditions. In terms of mean climate, the model is able to realistically reproduce the main patterns of temperature, precipitation, and winds. Specifically, we report improvements in the representation of the sea surface temperature with respect to the previous version of the model. In terms of mean atmospheric circulation features, we notice a realistic simulation of upper tropospheric winds and midtroposphere geopotential eddies. The oceanic heat transport and the Atlantic meridional overturning circulation satisfactorily compare with present‐day observations and estimates from global ocean reanalyses. The sea ice patterns and associated seasonal variations are realistically reproduced in both hemispheres, with a better skill in winter. Main weaknesses of the simulated climate are related with the precipitation patterns, specifically in the tropical regions with large dry biases over the Amazon basin. Similarly, the seasonal precipitation associated with the monsoons, mostly over Asia, is weaker than observed. The main patterns of interannual variability in terms of dominant empirical orthogonal functions are faithfully reproduced, mostly in the Northern Hemisphere winter. In the tropics the main teleconnection patterns associated with El Niño–Southern Oscillation and with the Indian Ocean Dipole are also in good agreement with observations.

Compressive ocean acoustic sound speed profile estimation in shallow water

The estimation of ocean acoustic sound speed profiles (SSPs) requires the inversion of an acoustic transmission model using limited observations. Provided the parameters of the inverse model are sparse, Compressive Sensing (CS) can help solve such underdetermined problems accurately, efficiently, and with enhanced resolution. Here, CS is used to estimate range-independent acoustic SSPs in shallow water ocean environments using a normal-mode representation of the acoustic field. Two sparse parameterizations of the SSPs are considered. The first parameterization assumes that change in the sound speed with depth is sparse and that the SSP can be constructed from a limited number of dominant changes in sound speed. The second case assumes a priori information about the ocean SSP variability in terms of Empirical Orthogonal Functions (EOFs), estimating the dominant EOFs describing the current SSP. For both cases, both real and synthetic acoustic data are processed. It is shown that in the CS framework, both of the optimizations can be solved with increased resolution and robustness over traditional methods.

Hyperresolution hydrologic modeling in a regional watershed and its interpretation using empirical orthogonal functions

Hyperresolution (<1 km) hydrologic modeling of regional watersheds is expected to support a broad range of terrestrial water cycle studies, but its feasibility is still challenging due to process, data and computational constraints, as well as difficulties in interpreting the high-dimensional dataset of spatiotemporal model forcings and outputs. We address some of these modeling challenges by extending the application of a physically-based, distributed hydrologic model to the Río San Miguel watershed (3796 km2) in Mexico based on prior efforts that demonstrated the process fidelity at smaller spatiotemporal scales. Long-term (7 year) simulations are conducted at a hyperresolution (∼78 m) over the large domain using parallel simulation capabilities. To address data sparseness, we develop strategies to integrate ground, remotely-sensed and reanalysis data for setting up, forcing and parameterizing the model. Complementary tests with observations at individual stations and remotely-sensed spatial patterns reveal a robust model performance. After building confidence in the model, we interpret the spatiotemporal model forcings and outputs using empirical orthogonal functions (EOFs) analyses. For all model outputs, a large portion (58–80%) of the spatiotemporal variability can be explained by two dominant EOFs, which are related to model forcings and basin properties. Terrain controls on soil water accumulation have a marked impact on the spatial distribution of most hydrologic variables during the wet season. In addition, soil properties affect soil moisture patterns, while vegetation and elevation distributions influence evapotranspiration and runoff fields. Given the large outputs from long-term hyperresolution simulations, EOF analyses provide a promising avenue for extracting meaningful hydrologic information within complex, regional watersheds.

Interannual variability of Black Sea's hydrodynamics and connection to atmospheric patterns

The long term variability (1962–2000) of the Black Sea physical processes (e.g. temperature, main circulation, cold intermediate layer, sea level) and its relation to atmospheric conditions and large scale climate patterns are investigated using an eddy-resolving tridimensional model in combination with statistical tools (e.g. Empirical Orthogonal Functions, Self Organizing Maps). First, the ability of the model to represent the interannual dynamics of the system is assessed by comparing the modeled and satellite sea surface temperature (SST) and sea level anomaly (SLA) decomposed into their dominant Empirical Orthogonal Functions (EOFs). The correlation between the spatial and temporal EOFs modes derived from model and satellite data is usually satisfactory and this gives some confidence in using the model as a tool to investigate not only the SST and SLA dynamics but also the dynamics of connected variables.Then, the long term variability (1962–2000) of the Black Sea hydrodynamics is assessed by decomposing into their dominant EOFs modeled SST, SLA and selected key hydrodynamical variables associated to the main circulation and vertical structure of the water column. Significant correlations between the EOFs associated to these variables are investigated in order to link the variability of surface fields and the internal dynamics of the system.In particular, the intensity of the general cyclonic circulation (the Rim Current) is shown to impact strongly (1) the mean sea level, (2) the SST response to air temperature (AT), (3) the formation of the cold intermediate layer, (4) the meridional repartition of the SST anomaly and (5) the exchanges of heat between the north-western shelf and the open basin.In order to appraise the variability of atmospheric conditions over the Black Sea during 1962–2000 and their role in driving the hydrodynamics, a self-organizing maps technique is used to identify spatial recurrent patterns of atmospheric fields (i.e., AT, wind stress and curl).The impact on these patterns of large scale climatic variability over the north Atlantic, Eurasia and the Pacific Ocean (estimated by respectively the north Atlantic oscillation (NAO), the east Atlantic/west Russia oscillation (EA/WR) and the El Niño southern oscillation (ENSO) indexes) is assessed. Distinct time scales of influence of the large scale teleconnection patterns on the AT are identified: EA/WR drives the short scale (1–5 years) variations of SST, while the long term (>5 years) trends of the NAO drive the long term SST trends.The drastic changes that have occurred in the Black Sea deep sea ecosystem at the end of the 80s are connected to an intensification of the general circulation that has promoted an export of riverine materials from the eutrophicated north-western shelf to the deep sea.Finally, in the last two decades, we find an increased duration of persistent atmospheric anomalies regime that has the potential to drive the system away from its average state as occurred in the late 80s. If persistent in the future, such long lasting atmospheric anomalies may have a significant impact on the ecosystem functioning.

A pre-operational three Dimensional variational data assimilation system in the North/Baltic Sea

Abstract. This paper describes the implementation and evaluation of a pre-operational three dimensional variational (3DVAR) data assimilation system for the North/Baltic Sea. Univariate analysis for both temperature and salinity is applied in a 3DVAR scheme in which the horizontal component of the background error covariance is modeled by an isotropic recursive filter (IRF) and the vertical component is represented by dominant Empirical Orthogonal Functions (EOFs). Observations of temperature and salinity (T/S) profiles in the North/Baltic Sea are assimilated in the year of 2005. Effect of the 3DVAR scheme is assessed by a comparison between data assimilation run and control run. The statistical analysis indicates that the model simulation is significantly improved with the 3DVAR scheme. On average, the root mean square errors (RMSE) of temperature and salinity are reduced by 0.2 °C and 0.25 psu in the North/Baltic Sea. In addition, the bias of temperature and salinity is also decreased by 0.1 °C and 0.2 psu, respectively. Starting from an analyzed initial state, one month simulation without assimilation is carried out with the aim of examining the persistence of the initial impact. It is shown that the assimilated initial state can impact the model simulation for nearly two weeks. The influence on salinity is more pronounced than temperature.

A Model-Based Assessment and Design of a Tropical Indian Ocean Mooring Array

Abstract A series of observing system simulation experiments (OSSEs) are performed for the tropical Indian Ocean (±15° from the equator) using a simple analysis system. The analysis system projects an array of observations onto the dominant empirical orthogonal functions (EOFs) derived from an intermediate-resolution (2° × 0.5°) ocean circulation model. This system produces maps of the depth of the 20°C isotherm (D20), representing interannual variability, and the high-pass-filtered mixed layer depth (MLD), representing intraseasonal variability. The OSSEs are designed to assess the suitability of the proposed Indian Ocean surface mooring array for resolving intraseasonal to interannual variability. While the proposed array does a reasonable job of resolving the interannual time scales, it may not adequately resolve the intraseasonal time scales. A procedure is developed to rank the importance of observation locations by determining the observation array that best projects onto the EOFs used in the analysis system. OSSEs using an optimal array clearly outperform the OSSEs using the proposed array. The configuration of the optimal array is sensitive to the number of EOFs considered. The optimal array is also different for D20 and MLD, and depends on whether fixed observations are included that represent an idealized Argo array. Therefore, a relative frequency map of observation locations identified in 24 different OSSEs is compiled and a single, albeit less optimal, array that is referred to as a consolidated array is objectively determined. The consolidated array reflects the general features of the individual optimal arrays derived from all OSSEs. It is found that, in general, observations south of 8°S and off of the Indonesian coast are most important for resolving the interannual variability, while observations a few degrees south of the equator, and west of 75°E, and a few degrees north of the equator, and east of 75°E, are important for resolving the intraseasonal variability. In a series of OSSEs, the consolidated array is shown to outperform the proposed array for all configurations of the analysis system for both D20 and MLD.

Multigrid state vector for data assimilation in a two-way nested model of the Ligurian Sea

A system of two nested models composed by a coarse resolution model of the Mediterranean Sea, an intermediate resolution model of the Provençal Basin and a high resolution model of the Ligurian Sea is coupled with a Kalman-filter based assimilation method. The state vector for the data assimilation is composed by the temperature, salinity and elevation of the three models. The forecast error is estimated by an ensemble run of 200 members by perturbing initial condition and atmospheric forcings. The 50 dominant empirical orthogonal functions (EOF) are taken as the error covariance of the model forecast. This error covariance is assumed to be constant in time. Sea surface temperature (SST) and sea surface height (SSH) are assimilated in this system.

Can principal component analysis be used to predict the dynamics of a strongly non-linear marine biogeochemical model?

Abstarct In the framework of model complexity reduction, we investigate the ability of the principal component analysis technique to represent in a compact form the dynamics of a coupled physical-ecosystem model. The biogeochemical model describes the evolution in time and depth of the partly decoupled nitrogen and carbon cycles of the pelagic food web in the Ligurian Sea (North Western Mediterranean Sea) through 19 biogeochemical state variables. The GHER hydrodynamic model (1D version) is used to represent the physical forcings. The coupled model presents a high variability in time and space that can be decomposed in modes by principal component analysis. To investigate the possibility of being represented in a compact form, the model is constrained to evolve in a reduced space spanned by its most dominant modes of variability that are the empirical orthogonal functions (EOFs). Different orthogonal bases (formed by 1D and 0D EOFs) are used to investigate the performance and realism of the method. 1D vertical EOFs show a tendency to impose a spatial structure to model results according to the most dominant EOFs. In the case of 0D EOFs, results of the reduced model can be very close to the original one, but it requires a large number of modes.

A Test for Annular Modes

The use of empirical orthogonal functions (EOFs) has grown popular as a tool to determine underlying variability from the rapidly increasing volume of climate data. It has been noted that the dominant or first EOF of geopotential heights, in each hemisphere at levels from the surface through the troposphere and into the midstratosphere, appears to be zonally symmetric. It has also been suggested that all of the first EOFs, throughout the atmospheric column are barotropically coupled and annular. Moreover, such modes of variability in both hemispheres are thought to be analogous to each other. To define annularity more objectively and to facilitate comparisons both temporally and spatially, a framework has been formulated within which modes of variability may be tested for their degree of zonal symmetry or annularity. Motivated by previous choices, pressure–height fields in each hemisphere are tested for annularity, one near the surface and the other in the midstratosphere. Periods chosen coincide with times when the troposphere and stratosphere are actively coupled. According to the test for annularity on the first mode of variability, these fields can be ranked in order of degree of annularity: the first EOF of Northern Hemisphere (NH) December–January–February (DJF) 50-hPa geopotential height is annular; the first EOF of Southern Hemisphere November 50-hPa geopotential height is weakly annular; the first EOF of Southern Hemisphere November 850-hPa geopotential height is weakly nonannular; and the first EOF of NH DJF sea level pressure is nonannular.

Isopycnal empirical orthogonal functions (EOFs) in the North and tropical Atlantic and their use in estimation problems

We investigated the vertical variability of the thermal/dynamical structure of the North and tropical Atlantic ocean from a set of historical hydrographic data [Reynaud et al., 1998]. The analysis was performed in 10° geographic bins in terms of vertical empirical orthogonal functions (EOFs) in isopycnal coordinates as first proposed by Gavart and De Mey [1997] (hereinafter referred to as GDM97). In the isopycnal coordinate system the state vector is made up of isopycnal displacements (η) and the compensated potential temperature along isopycnals (θ). GDM97 showed that in the Azores‐Madeira region the isopycnal EOFs consistently help to better separate physical processes in the water column and to better project the dynamic height anomaly downward in comparison with the classical EOF analysis in depth coordinates. In the present study, we extended their work geographically and the connection with state estimation and data assimilation was more formalized. From our results, smooth spatial variations of isopycnal EOFs were found in the North Atlantic and confirmed the large‐scale relevance of isopycnal EOFs in the ocean. North of 20°N the dominant isopycnal EOF was associated with a quasihomogeneous vertical displacement of the isopycnal surfaces (η ≈ 1) with a quasiconservation of compensated potential temperature on those surfaces (θ ≈ 0). That mode was strongly modified by thermocline‐intensified baroclinic effects along the path of the Gulf Stream up to 40°W. Some physical interpretations of the vertical EOFs were also suggested in several areas as far as the isopycnal formulation was concerned (e.g., some thermal fronts, the Mediterranean outflow, water lenses, or “meddies”). This work confirmed the validity of the ideas of GDM97 over the entire North Atlantic ocean. The potential use of the isopycnal EOFs in state estimation problems was discussed. They are possible candidates to reduce the order of state estimation problems provided that they have good observability properties. These observability properties were studied in the case of satellite altimetry; that is, we examined how the dominant isopycnal EOFs were connected to sea‐level anomalies. In most bins it was found that the order of an estimation problem could be truncated to one (primarily north of 20°N) or two modes. The dominant EOF was found to account for most of the surface dynamic height variability with a rather normally distributed error of only a few centimeters. Dynamically more robust results were also presented, performing a univariate isopycnal analysis in η, leaving coherent thermal effects out. As a result, the dominant character of mode 1 was further enhanced everywhere. These univariate isopycnal EOFs can be used for purely dynamical state estimation. More generally, we believe that our results can be used to set up reduced‐order data assimilation schemes in the North Atlantic or in other regions with good historical data.

Simulation of ENSO-Related Surface Winds in the Tropical Pacific by an Atmospheric General Circulation Model Forced by Observed Sea Surface Temperatures

The authors present the simulation of the tropical Pacific surface wind variability by a low-resolution (R15 horizontal resolution and 18 vertical levels) version of the Center for Ocean-Land-Atmosphere Interactions, Maryland, general circulation model (GCM) when forced by observed global sea surface temperature. The authors have examined the monthly mean surface winds and precipitation simulated by the model that was integrated from January 1979 to March 1992. Analyses of the climatological annual cycle and interannual variability over the Pacific are presented. The annual means of the simulated zonal and meridional winds agree well with observations. The only appreciable difference is in the region of strong trade winds where the simulated zonal winds are about 15%–20% weaker than observed. The amplitude of the annual harmonics are weaker than observed over the intertropical convergence zone and the South Pacific convergence zone regions. The amplitudes of the interannual variation of the simulated zonal and meridional winds are close to those of the observed variation. The first few dominant empirical orthogonal functions (EOF) of the simulated, as well as the observed, monthly mean winds are found to contain a large amount of high-frequency intraseasonal variations. While the statistical properties of the high-frequency modes, such as their amplitude and geographical locations, agree with observations, their detailed time evolution does not. When the data are subjected to a 5-month running-mean filter, the first two dominant EOFs of the simulated winds representing the low-frequency E1 Niño-Southern Oscillation fluctuations compare quite well with observations. However, the location of the center of the westerly anomalies associated with the warm episodes is simulated about 15° west of the observed locations. The model simulates well the progress of the westerly anomalies toward the eastern Pacific during the evolution of a warm event. The simulated equatorial wind anomalies are comparable in magnitude to the observed anomalies. An intercomparison of the simulation of the interannual variability by a few other GCMs with comparable resolution is also presented. The success in simulation of the large-scale low-frequency part of the tropical surface winds by the atmospheric GCM seems to be related to the model's ability to simulate the large-scale low-frequency part of the precipitation. Good correspondence between the simulated precipitation and the highly reflective cloud anomalies is seen in the first two EOFs of the 5-month running means. Moreover, the strong correlation found between the simulated precipitation and the simulated winds in the first two principal components indicates the primary role of model precipitation in driving the surface winds. The surface winds simulated by a linear model forced by the GCM-simulated precipitation show good resemblance to the GCM-simulated winds in the equatorial region. This result supports the recent findings that the large-scale part of the tropical surface winds is primarily linear.

Signal-to-noise analysis of time-dependent greenhouse warming experiments Part 1: pattern analysis

Results from a control integration and time-dependent greenhouse warming experiments performed with a coupled ocean-atmosphere model are analysed in terms of their signal-to-noise properties. The aim is to illustrate techniques for efficient description of the space-time evolution of signals and noise and to identify potentially useful components of a multivariate greenhouse-gas “fingerprint”. The three 100-year experiments analysed here simulate the response of the climate system to a step-function doubling of CO2 and to the time-dependent greenhouse-gas increases specified in Scenarios A (“Business as Usual”) and D (“Draconian Measures”) of the Intergovernmental Panel on Climate Change (IPCC). If signal and noise patterns are highly similar, the separation of the signal from the natural variability noise is difficult. We use the pattern correlation between the dominant Empirical Orthogonal Functions (EOFs) of the control run and the Scenario A experiment as a measure of the similarity of signal and noise patterns. The EOF 1 patterns of signal and noise are least similar for near-surface temperature and the vertical structure of zonal winds, and are most similar for sea level pressure (SLP). The dominant signal and noise modes of precipitable water and stratospheric/tropospheric temperature contrasts show considerable pattern similarity. Despite the differences in forcing history, a highly similar EOF 1 surface temperature response pattern is found in all three greenhouse warming experiments. A large part of this similarity is due to a common land-sea contrast component of the signal. To determine the degree to which the signal is contaminated by the natural variability (and/or drift) of the control run, we project the Scenario A data onto EOFs 1 and 2 of the control. Signal contamination by the EOF 1 and 2 modes of the noise is lowest for near-surface temperature, a situation favorable for detection. The signals for precipitable water, SLP, and the vertical structure of zonal temperature and zonal winds are significantly contaminated by the dominant noise modes. We use cumulative explained spatial variance, principal component time series, and projections onto EOFs in order to investigate the time evolution of the dominant signal and noise modes. In the case of near-surface temperature, a single pattern emerges as the dominant signal component in the second half of the Scenario A experiment. The projections onto EOFs 1 and 2 of the control run indicate that Scenario D has a large common variability and/or drift component with the control run. This common component is also apparent between years 30 and 50 of the Scenario A experiment, but is small in the 2 × CO2 integration. The trajectories of the dominant Scenario A and control run modes evolve differently, regardless of the basis vectors chosen for projection, thus making it feasible to separate signal and noise within the first two decades of the experiments. For Scenario D it may not be possible to discriminate between the dominant signal and noise modes until the final 2–3 decades of the 100-year integration.

Signal-to-noise analysis of time-dependent greenhouse warming experiments

Results from a control integration and time-dependent greenhouse warming experiments performed with a coupled ocean-atmosphere model are analysed in terms of their signal-to-noise properties. The aim is to illustrate techniques for efficient description of the space-time evolution of signals and noise and to identify potentially useful components of a multivariate greenhouse-gas “fingerprint”. The three 100-year experiments analysed here simulate the response of the climate system to a step-function doubling of CO2 and to the time-dependent greenhouse-gas increases specified in Scenarios A (“Business as Usual”) and D (“Draconian Measures”) of the Intergovernmental Panel on Climate Change (IPCC). If signal and noise patterns are highly similar, the separation of the signal from the natural variability noise is difficult. We use the pattern correlation between the dominant Empirical Orthogonal Functions (EOFs) of the control run and the Scenario A experiment as a measure of the similarity of signal and noise patterns. The EOF 1 patterns of signal and noise are least similar for near-surface temperature and the vertical structure of zonal winds, and are most similar for sea level pressure (SLP). The dominant signal and noise modes of precipitable water and stratospheric/tropospheric temperature contrasts show considerable pattern similarity. Despite the differences in forcing history, a highly similar EOF 1 surface temperature response pattern is found in all three greenhouse warming experiments. A large part of this similarity is due to a common land-sea contrast component of the signal. To determine the degree to which the signal is contaminated by the natural variability (and/or drift) of the control run, we project the Scenario A data onto EOFs 1 and 2 of the control. Signal contamination by the EOF 1 and 2 modes of the noise is lowest for near-surface temperature, a situation favorable for detection. The signals for precipitable water, SLP, and the vertical structure of zonal temperature and zonal winds are significantly contaminated by the dominant noise modes. We use cumulative explained spatial variance, principal component time series, and projections onto EOFs in order to investigate the time evolution of the dominant signal and noise modes. In the case of near-surface temperature, a single pattern emerges as the dominant signal component in the second half of the Scenario A experiment. The projections onto EOFs 1 and 2 of the control run indicate that Scenario D has a large common variability and/or drift component with the control run. This common component is also apparent between years 30 and 50 of the Scenario A experiment, but is small in the 2 × CO2 integration. The trajectories of the dominant Scenario A and control run modes evolve differently, regardless of the basis vectors chosen for projection, thus making it feasible to separate signal and noise within the first two decades of the experiments. For Scenario D it may not be possible to discriminate between the dominant signal and noise modes until the final 2–3 decades of the 100-year integration.

Classification of summer monsoon rainfall patterns over India

AbstractSeasonal (June through September) percentage departure from normal rainfall patterns over India have been classified by objective methods utilizing data for a 120‐year period (1871–1990). The methods used are the map‐to‐map correlation method and the k‐means clustering method. Empirical orthogonal functions (EOFs) are also presented.It is seen that 75 per cent of the charts can be classified into six distinct types by the map‐to‐map method. Six distinct types also are obtained by the k‐means method. The first four dominant EOFs explain 52 per cent of the variance.Intercorrelations and contingency tables among the types obtained by these methods and visual examination suggests that the dominant patterns are similar, irrespective of the method used. It is also seen that the monsoon rainfall for the country as a whole and the spatial patterns may have no relationship. Even during normal monsoon years, the spatial patterns may be different.The advantages and disadvantages of the methods used are discussed.

Atmospheric conditions during the spring and fall transitions in the coastal ocean off western United States

We examine large‐scale atmospheric behavior around the time of the spring and fall transitions in the coastal ocean off the west coast of North America. Records of adjusted sea level (ASL), coastal wind stress, sea level atmospheric pressure (SLP), and 500‐mbar heights for the years 1971–1975 and 1980–1983 are analyzed. The records cover periods of 91 days, centered on the dates of the spring and fall transitions as determined from coastal adjusted sea level data. Empirical orthogonal functions are obtained from the ASL, coastal wind stress, and SLP records. The two dominant modes of the ASL and coastal wind stress are similar around the times of both the spring and fall transitions, and the time series for these modes are highly correlated with one another. Transitionlike behavior is evident in the time series of the first modes in both spring and fall, but the spring transition is more pronounced. Principal estimator patterns, formed from the dominant empirical orthogonal functions show the spatial patterns of SLP which force the ASL and coastal wind stress during the transitions. The SLP pattern which coincides with the spring transition is the formation of a high‐pressure system centered at 45°N and 140°W along with the development of a low‐pressure cell over the southwest continental United States. Inspection of the 500‐mbar height composites for 91 days surrounding the spring transition for the 9 years reveals the formation of a ridging pattern and diffluent flow over the western United States at the time of the transition; following the transition, the ridging relaxes but the diffluent flow over the continent remains for the duration of the 45 days examined here. The fall transition is characterized by a rise in ASL, particularly north of 40°N, and a change from southward to northward wind stress. The SLP pattern which coincides with the fall transition involves the appearance of a low‐pressure system off western North America centered at 50°N and 140°W, representing the passage of synoptic storms through the region. Prior to the fall transition, the 500‐mbar heights are somewhat diffluent and show a trough over the southwestern United States; after the transition the 500‐mbar flow over the northeast Pacific and North America is nearly zonal.