Empirical Orthogonal Functions: The Medium is the Message

Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.

Potential functions for hydrogen bond interactions - III. Empirical Potential Function for the Peptide N-H...O=C Hydrogen Bond

A careful comparison of the distribution in the (R, θ)-plane of all NH ... O hydrogen bonds with that for bonds between neutral NH and neutral C=O groups indicated that the latter has a larger mean R and a wider range of θ and that the distribution was also broader than for the average case. Therefore, the potential function developed earlier for an average NH ... O hydrogen bond was modified to suit the peptide case. A three-parameter expression of the form {Mathematical expression}, with △ = R - Rmin, was found to be satisfactory. By comparing the theoretically expected distribution in R and θ with observed data (although limited), the best values were found to be p1 = 25, p3 = - 2 and q1 = 1 × 10-3, with Rmin = 2·95 Å and Vmin = - 4·5 kcal/mole. The procedure for obtaining a smooth transition from Vhb to the non-bonded potential Vnb for large R and θ is described, along with a flow chart useful for programming the formulae. Calculated values of ΔH, the enthalpy of formation of the hydrogen bond, using this function are in reasonable agreement with observation. When the atoms involved in the hydrogen bond occur in a five-membered ring as in the sequence[Figure not available: see fulltext.] a different formula for the potential function is needed, which is of the form Vhb = Vmin +p1△2 +q1x2 where x = θ - 50° for θ ≥ 50°, with p1 = 15, q1 = 0·002, Rmin = 2· Å and Vmin = - 2·5 kcal/mole. © 1971 Indian Academy of Sciences.

Estimation of variables at ungaged locations by empirical orthogonal functions

A technique based on empirical orthogonal functions is used to estimate hydrologic time-series variables at ungaged locations. The technique is applied to estimate daily and monthly rainfall, temperature and runoff values. The accuracy of the method is tested by application to locations where data are available. The second-order characteristics of the estimated data are compared with those of the observed data. The results indicate that the method is quick and accurate.

Variability of the Atlantic thermohaline circulation described by three-dimensional empirical orthogonal functions

We describe the use of bivariate 3d empirical orthogonal functions (EOFs) in characterising low frequency variability of the Atlantic thermohaline circulation (THC) in the Hadley Centre global climate model, HadCM3. We find that the leading two modes are well correlated with an index of the meridional overturning circulation (MOC) on decadal timescales, with the leading mode alone accounting for 54% of the decadal variance. Episodes of coherent oscillations in the sub-space of the leading EOFs are identified; these episodes are of great interest for the predictability of the THC, and could indicate the existence of different regimes of natural variability. The mechanism identified for the multi-decadal variability is an internal ocean mode, dominated by changes in convection in the Nordic Seas, which lead the changes in the MOC by a few years. Variations in salinity transports from the Arctic and from the North Atlantic are the main feedbacks which control the oscillation. This mode has a weak feedback onto the atmosphere and hence a surface climatic influence. Interestingly, some of these climate impacts lead the changes in the overturning. There are also similarities to observed multi-decadal climate variability.

The Empirical Forcing Function as a tool for the diagnosis of large-scale atmospheric anomalies

The time-mean quasi-geostrophic potential vorticity equation of the atmospheric flow on isobaric surfaces can explicitly include an atmospheric (internal) forcing term of the stationary-eddy flow. In fact, neglecting some non-linear terms in this equation, this forcing can be mathematically expressed as a single function, called Empirical Forcing Function (EFF), which is equal to the material derivative of the time-mean potential vorticity. Furthermore, the EFF can be decomposed as a sum of seven components, each one representing a forcing mechanism of different nature. These mechanisms include diabatic components associated with the radiative forcing, latent heat release and frictional dissipation, and components related to transient eddy transports of heat and momentum. All these factors quantify the role of the transient eddies in forcing the atmospheric circulation. In order to assess the relevance of the EFF in diagnosing large-scale anomalies in the atmospheric circulation, the relationship between the EFF and the occurrence of strong North Atlantic ridges over the Eastern North Atlantic is analyzed, which are often precursors of severe droughts over Western Iberia. For such events, the EFF pattern depicts a clear dipolar structure over the North Atlantic; cyclonic (anticyclonic) forcing of potential vorticity is found upstream (downstream) of the anomalously strong ridges. Results also show that the most significant components are related to the diabatic processes. Lastly, these results highlight the relevance of the EFF in diagnosing large-scale anomalies, also providing some insight into their interaction with different physical mechanisms.

Effects of El Niño–Southern Oscillation events on catches of Bigeye Tuna (Thunnus obesus) in the eastern Indian Ocean off Java

The effects of El Niño–Southern Oscillation events on catches of Bigeye Tuna (Thunnus obesus) in the eastern Indian Ocean (EIO) off Java were evaluated through the use of remotely sensed environmental data (sea-surface-height anomaly [SSHA], sea-surface temperature [SST], and chlorophyll a concentration), and Bigeye Tuna catch data. Analyses were conducted for the period of 1997–2000, which included the 1997–98 El Niño and 1999–2000 La Niña events. The empirical orthogonal function (EOF) was applied to examine oceanographic parameters quantitatively. The relationship of those parameters to variations in catch distribution of Bigeye Tuna was explored with a generalized additive model (GAM). The mean hook rate was 0.67 during El Niño and 0.44 during La Niña, and catches were high where SSHA ranged from –21 to 5 cm, SST ranged from 24°C to 27.5°C, and chlorophyll-a concentrations ranged from 0.04 to 0.16 mg m–3. The EOF analysis confirmed that the 1997–98 El Niño affected oceanographic conditions in the EIO off Java. The GAM results indicated that SST was better than the other environmental factors (SSHA and chlorophyll-a concentration) as an oceanographic predictor of Bigeye Tuna catches in the region. According to the GAM predictions, the highest probabilities (70–80%) for Bigeye Tuna catch in 1997–2000 occurred during oceanographic conditions during the 1997–98 El Niño event.

Climate signals in the lower stratosphere and upper troposphere

Empirical orthogonal function (EOF) analysis and regression analysis are used to investigate zonally averaged seasonal temperature anomaly patterns and trends in the lower stratosphere and upper troposphere. The first four EOFs explain 64 percent of the temperature variance and can be related, respectively, to the solar flux (SF) and El Niño/Southern Oscillation (ENSO), to the quasi-biennial oscillation (QBO), to atmospheric carbon dioxide (CO2) and turbidity (TB), and to ENSO. The signal of the fourth EOF is modulated in January to March by the solar flux, with the sense of the modulation determined by the phase of the quasi-biennial oscillation.

ENSO influences on atmospheric circulation and precipitation in the western United States

EXTRACT (SEE PDF FOR FULL ABSTRACT): The influence of ENSO on atmospheric circulation and precipitation over the western United States is presented from two perspectives. First, ENSO-associated circulation patterns over the North Pacific/North America sector were identified using an REOF (rotated empirical orthogonal function) analysis of the 700-mb height field and compositing these for extreme phases of the Southern Oscillation Index. ... Second, we examine the variability of precipitation during the warm and cool phases of ENSO for different locations in the western United States.

Resuspension and advection processes affecting suspended particulate matter concentrations in the central English Channel

Suspended particulate matter (SPM) measurements obtained along a cross-section in the central English Channel (Wight-Cotentin transect) indicate that the area may be differentiated into: (1) an English coastal zone, associated with the highest concentrations; (2) a French coastal zone, with intermediate concentrations; and (3) the offshore waters of the Channel, characterised by a very low suspended-sediment load. The SPM particle-size distribution was modal close to the English coast (main mode 10-12 mu m); the remainder of the area was characterised by flat SPM distributions. Examination of the diatom communities in the SPM suggest:; that material resuspended in the intertidal zone and the estuarine environments was advected towards the offshore waters of the English Channel. Considerable variations in SPM concentrations occurred during a tidal cycle: maximum concentrations were sometimes up to 3 times higher than the minimum concentrations, Empirical orthogonal function (EOF) analysis of the SPM concentration time series indicates that, although the bottom waters were more turbid than the surficial waters, this was not likely to be the result of in situ sediment resuspension. Instead, the observed variations appear to be controlled mainly by advective mechanisms. The limited resuspension was probably caused by: (1) the limited availability of fine-grained material within the bottom sediments, and (2) 'bed-armouring' processes which protect the finer-grained fractions of the seabed material from erosion and entrainment within the overlying flow during the less energetic stages of the tide.

Reconstruction of vertical thermal structure from several subsurface temperatures in the China Seas and adjacent waters

Empirical Orthogonal Function (EOF) analysis is used in this study to generate main eigenvector fields of historical temperature for the China Seas (here referring to Chinese marine territories) and adjacent waters from 1930 to 2002 (510 143 profiles). A good temperature profile is reconstructed based on several subsurface in situ temperature observations and the thermocline was estimated using the model. The results show that: 1) For the study area, the former four principal components can explain 95% of the overall variance, and the vertical distribution of temperature is most stable using the in situ temperature observations near the surface. 2) The model verifications based on the observed CTD data from the East China Sea (ECS), South China Sea (SCS) and the areas around Taiwan Island show that the reconstructed profiles have high correlation with the observed ones with the confidence level > 95%, especially to describe the characteristics of the thermocline well. The average errors between the reconstructed and observed profiles in these three areas are 0.69A degrees C, 0.52A degrees C and 1.18A degrees C respectively. It also shows the model RMS error is less than or close to the climatological error. The statistical model can be used to well estimate the temperature profile vertical structure. 3) Comparing the thermocline characteristics between the reconstructed and observed profiles, the results in the ECS show that the average absolute errors are 1.5m, 1.4 m and 0.17A degrees C/m, and the average relative errors are 24.7%, 8.9% and 22.6% for the upper, lower thermocline boundaries and the gradient, respectively. Although the relative errors are obvious, the absolute error is small. In the SCS, the average absolute errors are 4.1 m, 27.7 m and 0.007A degrees C/m, and the average relative errors are 16.1%, 16.8% and 9.5% for the upper, lower thermocline boundaries and the gradient, respectively. The average relative errors are all < 20%. Although the average absolute error of the lower thermocline boundary is considerable, but contrast to the spatial scale of average depth of the lower thermocline boundary (165 m), the average relative error is small (16.8%). Therefore the model can be used to well estimate the thermocline.

Responses of summertime extreme wave heights to local climate variations in the East China Sea

We detected the responses of summertime extreme wave heights (H-top10, average of the highest 10% of significant wave heights in June, July and August) to local climate variations in the East China Sea by applying an empirical orthogonal function analysis to Htop10 derived from the WAVEWATCH- III wave model driven by 6 hourly sea surface wind fields from ERA-40 reanalysis over the period 1958-2002. Decreases in H-top10 in the northern East China Sea ( Yellow Sea) correspond to attenuation of the East Asian Summer Monsoon, while increases in the south are primarily due to enhancement of tropical cyclone activities in the western North Pacific.