Empirical Orthogonal Function Components Research Articles

Constructing a Regional Ionospheric TEC Model in China with Empirical Orthogonal Function and Dense GNSS Observation

Using Global Navigation Satellite Systems (GNSS) observation data for developing a high-precision ionospheric Total Electron Content (TEC) model is one of the essential subjects in ionospheric physics research and the application of satellite navigation correction. In this study, we integrate the Empirical Orthogonal Function (EOF) method with the TEC data provided by the Center for Orbit Determination in Europe (CODE), and observed by the dense GNSS receivers operated by the Crustal Movement Observation Network of China (CMONOC) to construct a regional ionospheric TEC model over China. The EOF analysis of CODE TEC in China from 1998 to 2010 shows that the first-order EOF component accounts for 90.3813% of the total variation of the ionospheric TEC in China. Meanwhile, the average value of CODE TEC is consistent with the spatial and temporal distribution characteristics of the first-order EOF base function, which mainly reflects the latitude and diurnal variations of TEC in China. The first-order coefficient after EOF decomposition shows an obvious 11-year period and semi-annual variations. The maximum amplitude of semi-annual variation mainly appears in March and October, which is closely associated with the variation in geographical longitude, the semi-annual change of the low-latitude electric field, and the ionospheric fountain effect. The second-order coefficient has an evident annual variation, the minimum amplitude mainly occurs in March, August, and September, and the amplitude values in the high solar activity years are more significant than those in the low solar activity years. The third-order coefficient mainly shows the characteristics of annual variation, and the fourth-order coefficient shows the noticeable semi-annual and annual variations. The third and fourth-order coefficients are both modulated by the solar activity index F10.7. The ionospheric TEC model in China, driven by CMONOC real-time GNSS observation data, can better reflect the latitude, local time and seasonal variation characteristics of ionospheric TEC over China. In particular, it can clearly show the spring and autumn asymmetry of ionospheric TEC in the low latitudes. The root mean square error of the absolute error between the model and the actual observation is mainly distributed around 2.45 TECU (1 TECU = 1016 electrons/m2). The values of the TEC model constructed in this study are closer to the actual observed values than those of the CODE TEC in China.

Modeling TEC Irregularities in the Arctic Ionosphere Using Empirical Orthogonal Function Method

AbstractWe develop a climatological model for the Arctic ionosphere based on more than one solar cycle of data (2010–2021) of the rate of change of the total electron content index (ROTI) maps from the International GNSS Service (IGS). The IGS ROTI maps are daily averaged in magnetic latitude and local time coordinates. To develop a climatological model, the ROTI maps are decomposed into base functions and coefficients using the empirical orthogonal function (EOF) method. The EOF method converges very quickly, and the first four EOFs reflect the majority (96%) of the total data variability. Furthermore, different EOF components can reflect different drivers of ionospheric irregularities. The first EOF reflects the averaged ROTI activity and the impact of the solar radiation and geomagnetic activity; the second EOF reflects the impact of the interplanetary magnetic field (IMF) Bz and electric field; the third and fourth EOFs reflect the dawn‐dusk asymmetry around the auroral oval and polar cap, and they can be related to the IMF By. To build an empirical model, we fit the EOF coefficients using helio‐geophysical indices from four different categories (solar activity; geomagnetic indices; IMF; the solar wind coupling function). The final EOF model is dependent on seven selected indices (F10.7P, Kp, Dst, Bt, By, Bz, and EKL). The statistical data‐model comparisons show satisfactory results with a good correlation coefficient. However, the model cannot capture the significant expansion of the dayside ROTI activity during strong geomagnetic storms. Future effort is needed to provide corrections to the model during severe storms.

Understanding Water Level Changes in the Great Lakes by an ICA-Based Merging of Multi-Mission Altimetry Measurements

Accurately monitoring spatio-temporal changes in lake water levels is important for studying the impacts of climate change on freshwater resources, and for predicting natural hazards. In this study, we applied multi-mission radar satellite altimetry data from the Laurentian Great Lakes, North America to optimally reconstruct multi-decadal lake-wide spatio-temporal changes of water level. We used the results to study physical processes such as teleconnections of El Niño and southern oscillation (ENSO) episodes over approximately the past three-and-a-half decades (1985–2018). First, we assessed three reconstruction methods, namely the standard empirical orthogonal function (EOF), complex EOF (CEOF), and complex independent component analysis (CICA), to model the lake-wide changes of water level. The performance of these techniques was evaluated using in-situ gauge data, after correcting the Glacial Isostatic Adjustment (GIA) process using a contemporary GIA forward model. While altimeter-measured water level was much less affected by GIA, the averaged gauge-measured water level was found to have increased up to 14 cm over the three decades. Our results indicate that the CICA-reconstructed 35-year lake level was more accurate than the other two techniques. The correlation coefficients between the CICA reconstruction and the in situ water-level data were 0.96, 0.99, 0.97, 0.97, and 0.95, for Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and Lake Ontario, respectively; ~7% higher than the original altimetry data. The root mean squares of errors (RMSE) were 6.07 cm, 4.89 cm, 9.27 cm, 7.71 cm, and 9.88 cm, respectively, for each of the lakes, and ~44% less than differencing with the original altimetry data. Furthermore, the CICA results indicated that the water-level changes in the Great Lakes were significantly correlated with ENSO, with correlation coefficients of 0.5–0.8. The lake levels were ~25 cm higher (~30 cm lower) than normal during EI Niño (La Niña) events.

Characterizing quasi-biweekly variability of the Asian monsoon anticyclone using potential vorticity and large-scale geopotential height field

Abstract. The spatial pattern of subseasonal variability of the Asian monsoon anticyclone is analyzed using long-term reanalysis data, focusing on the large-scale longitudinal movement. The air inside the anticyclone is quantified by a thickness-weighted low-PV (potential vorticity) area on an isentropic surface. It is shown that the longitudinal movement of the air inside the Asian monsoon anticyclone has a timescale of 1 to 2 weeks, which is shorter than the monthly dominant timescale of the variability in the anticyclone intensity. The movement of the anticyclonic air is suggested to be largely controlled by passive advection. The typical time evolution of the variability pattern, explained by two leading empirical orthogonal function (EOF) components of 100 hPa geopotential height, shows large-scale geopotential anomalies moving westward spanning from low to middle latitudes. This corresponds well with the rapid westward movement of low-PV air known as “eddy shedding” and following the eastward retreat of the anticyclonic air. The two EOF components can also explain the bimodal longitudinal distribution of geopotential maximum location.

Modeling the global ionospheric electron densities based on the EOF decomposition of the ionospheric radio occultation observation

An attempt is made to model the three-dimensional global structures and temporal variations of the ionospheric electron density (Ne) using the radio occultation (RO) Ne profile data obtained by the COSMIC/FORMOSAT-3, CHAMP and GRACE missions during the period from July 2006 to June 2017. The modeling technique we adopted is based on the empirical orthogonal function (EOF) analysis of the RO Ne dataset which is binned with grids of 2.5° in geomagnetic latitudes and 1/3 hr in geomagnetic local time (equivalent to 5° in geomagnetic longitudes) and 10 km in height. The EOF analysis decomposed the binned (gridded) Ne dataset into a series of eigen modes or basis functions (E i ) representing the variations with geomagnetic latitude, geomagnetic local time as well as height and the associated EOF amplitude coefficients (A i ) representing the variations with seasons as well as solar cycle activity. Our results showed that the EOF components (E i , A i ) obtained by the EOF decomposition have different three-dimensional spatial structures with distinct features attributable to different factors or processes controlling the variations of the ionosphere: the first EOF component represents mainly the global mean structure of Ne and its temporal variation with seasons and solar cycle activity; the second EOF component represents mainly the seasonal control of the solar zenith angle on the ionosphere; the third EOF component is representative of the uplifting or lowering of the peak height where Ne reaches its maximum value; the fourth and fifth EOF components represent respectively the variations of the thickness of the ionosphere in the southern and northern hemispheres. It is found that the obtained eigen series converges quickly, with the first five EOF components contributing as high as 98% of the variances of the Ne dataset. We then modeled the EOF coefficients A i obtained by the EOF decomposition using the harmonic functions representing the annual and semi-annual variations, with the solar cycle dependences being taken into account by including the changes of the harmonic amplitudes with the solar irradiance flux index F10.7. The Ne model is constructed using the A i thus modeled and E i obtained by the EOF decomposition. Comparison between the Ne model output results and the COSMIC-2 observational data showed that the modeled results capture well the global structures of the observational data and the model output results have very high linear correlation coefficients with the observational ones (R > 0.9), justifying the modeling technique used in our present study.

Global total electron content prediction performance assessment of the IRI-2016 model based on empirical orthogonal function decomposition

Abstract. In this study, the empirical orthogonal function (EOF) decomposition technique was utilized to analyze the similarities and differences of the spatiotemporal characteristics between the total electron content (TEC) of the International GNSS Service global ionospheric map (GIM) and that derived from the International Reference Ionosphere 2016 (IRI-2016) model in 2013. Results showed that the main spatial patterns and time-varying features of the data set have good consistency. The following four main spatiotemporal variation features can be extracted from both data sets through EOF decomposition: the variation with the geomagnetic latitude reflecting the daily averaged solar forcing, the diurnal and semidiurnal periodic changes with longitude due to local time, and the interhemispheric asymmetry caused by the annual variation of the inclination angle of the Earth's orbit. The differences between the spatial patterns represented by the EOF base functions of IRI-2016 and GIM TECs were analyzed by extracting the same time-varying coefficients. The deviations of the interhemispheric asymmetry component between the two data sets showed roughly equal values throughout the Southern or Northern Hemisphere, whereas those of the other spatial modes were mainly concentrated on the equatorial region. The differences of the time-varying characteristics between the IRI-2016 and GIM TECs were also compared by extracting the same EOF base functions. Although the EOF coefficients of the two data sets presented consistent seasonal variations, the magnitude of IRI-2016 TEC changes over time was less than that of GIM TEC. The diurnal variation of the daily averaged solar forcing component and the annual variation of the interhemispheric asymmetry component exhibited relatively large deviations between the two data sets. Considering the variance contribution of the different EOF components and their average relative deviations, both analyses showed that the daily averaged solar forcing and interhemispheric asymmetry components were the main factors for the deviation between the IRI-2016 and GIM TECs.

Long-term trends in the ionospheric response to solar extreme-ultraviolet variations

Abstract. The thermosphere–ionosphere system shows high complexity due to its interaction with the continuously varying solar radiation flux. We investigate the temporal and spatial response of the ionosphere to solar activity using 18 years (1999–2017) of total electron content (TEC) maps provided by the international global navigation satellite systems service and 12 solar proxies (F10.7, F1.8, F3.2, F8, F15, F30, He II, Mg II index, Ly-α, Ca II K, daily sunspot area (SSA), and sunspot number (SSN)). Cross-wavelet and Lomb–Scargle periodogram (LSP) analyses are used to evaluate the different solar proxies with respect to their impact on the global mean TEC (GTEC), which is important for improved ionosphere modeling and forecasts. A 16 to 32 d periodicity in all the solar proxies and GTEC has been identified. The maximum correlation at this timescale is observed between the He II, Mg II, and F30 indices and GTEC, with an effective time delay of about 1 d. The LSP analysis shows that the most dominant period is 27 d, which is owing to the mean solar rotation, followed by a 45 d periodicity. In addition, a semi-annual and an annual variation were observed in GTEC, with the strongest correlation near the equatorial region where a time delay of about 1–2 d exists. The wavelet variance estimation method is used to find the variance of GTEC and F10.7 during the maxima of the solar cycles SC 23 and SC 24. Wavelet variance estimation suggests that the GTEC variance is highest for the seasonal timescale (32 to 64 d period) followed by the 16 to 32 d period, similar to the F10.7 index. The variance during SC 23 is larger than during SC 24. The most suitable proxy to represent solar activity at the timescales of 16 to 32 d and 32 to 64 d is He II. The Mg II index, Ly-α, and F30 may be placed second as these indices show the strongest correlation with GTEC, but there are some differences in correlation during solar maximum and minimum years, as the behavior of proxies is not always the same. The indices F1.8 and daily SSA are of limited use to represent the solar impact on GTEC. The empirical orthogonal function (EOF) analysis of the TEC data shows that the first EOF component captures more than 86 % of the variance, and the first three EOF components explain 99 % of the total variance. EOF analysis suggests that the first component is associated with the solar flux and the third EOF component captures the geomagnetic activity as well as the remaining part of EOF1. The EOF2 captures 11 % of the total variability and demonstrates the hemispheric asymmetry.

Climatic changes of thermal condition in the Kara sea at last 40 years

The paper discusses air (Ta) and sea surface temperature (SST) year-to-year variability due to warming of the Kara Sea, using the data from regular observations at the meteorological stations Roshydromet (GMS) in 1978–2017, NOAA optimum interpolation and reanalysis data. We use the methods of cluster, correlation analysis and Empirical Orthogonal Functions (EOF). We investigate possible cause and effect relationships of these changes with the variations of the wind field components, climatic indices and the sea ice concentration field. The cluster analysis of the three main EOF components has allowed us to identify four areas on the basis of the nature of changes of the water temperature anomalies field. The climatic changes in these areas, in the coastal and island zones of the Kara Sea have manifested themselves in the steady increase of the annual air temperature at GMS from 0,47–0,77 °C/10 years on the southwest coast to 1,33–1,49 °C/10 years in the north of the sea. This is equivalent to warming from 1,9 to 6,0 °C in the last 40 years. For the open sea the value of the Ta trend is about 1,22 °C/10 years, which corresponds to an increase in the average Ta by 4,9 °C in the last 40 years. This value is approximately 3 times greater than that for all the Northern hemisphere for the same period.Annualy, the maximal trend was observed in November and April mainly and exceeded 2–3 °C/10 years at some of the stations. We identify anomalously warm (2016 and 2012) and anomalously cold (1978, 1979, 1992 and 1998) years: the warmest year was 2012, the coldest — 1979. Positive SST trends were observed over all the sea area during the warm period of year (to 1 °C/10 years). SST increased to 2,4 °C, which is approximately 1,5 times greater than the corresponding SST values for the Northern hemisphere. The maximum SST trend (0,4 °C/10 years) was observed in the northwest and southwest parts of the sea. From June to August the trends of SST exceed the annual ones 1,5–2 times. Interannual SST and Ta variations are characterized by close correlation links. Until approximately 1998–2004 the warming was rather insignificant, and after that the growth rate of Ta and SST increased many fold. Apparently it indicates changes in the mode and the large-scale atmospheric circulation in the early 2000s. We also observed a trend of strengthening of the southern wind during the cold period of the year and the northern one — in the warm period (0,5–0,6 m/s in 40 years). It is shown that there is a close correlation between the Ta increase and the changes in the meridional component of the wind speed during the cold period of the year for all the sea areas. For the warm period it is statistically insignificant both for Ta and SST. For the cold season we observed a contribution of the large-scale mode of atmospheric circulation into the variability of V component of the wind speed. The conribution was expressed through the indeces NAO, SCAND, Pol/EUR, AZOR, ISL and the differences of ISLSIB. For the warm season this contribution is expressed through the NAO, SCAND and AO only. For the warm period we showed statistically significant correlation between the increase in SST, Ta and the processes parametrized by the AMO, EA/WR and AZOR indeces. For the cold period the indeces are AMO, Pol/Eur, SIB and ISL SIB. The interannual variations of the sea ice concentration field are characterized by close correlation with Ta changes both in the annual cycle and during the periods of ice cover formation and evolution (R = –0,7... –0,9). For these periods we showed statistically significant relationships between the first EOF mode fluctuations and two climatic indeces — AMO (R = 0,5) and Pol/Eur (R = 0,4). The relationships between the temporary variability of the sea ice concentration and the wind field characteristics are weaker and statistically significant only for the meridional component of the wind speed (R = –0,4).

The influence of ENSO, PDO and PNA on secular rainfall variations in Hawai‘i

Over the last century, significant declines in rainfall across the state of Hawai‘i have been observed, and it is unknown whether these declines are due to natural variations in climate, or manifestations of human-induced climate change. Here, a statistical analysis of the observed rainfall variability was applied as first step towards better understanding causes for these long-term trends. Gridded seasonal rainfall from 1920 to 2012 is used to perform an empirical orthogonal function (EOF) analysis. The leading EOF components are correlated with three indices of natural climate variations (El Nino-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and Pacific North American (PNA)), and multiple linear regression (MLR) is used to model the leading components with climate indices. PNA is the dominant mode of wet season (November–April) variability, while ENSO is most significant in the dry season (May–October). To assess whether there is an anthropogenic influence on rainfall, two methods are used: a linear trend term is included in the MLR, and pattern correlation coefficients (PCC) are calculated between recent rainfall trends and future changes in rainfall projected by downscaling methods. PCC results indicate that recent observed rainfall trends in the wet season are positively correlated with future expected changes in rainfall, while dry season PCC results do not show a clear pattern. The MLR results, however, show that the trend term adds significantly to model skill only in the dry season. Overall, MLR and PCC results give weak and inconclusive evidence for detection of anthropogenic signals in the observed rainfall trends.

Two anomalous convective systems in the tropical western Pacific and their influences on the East Asian summer monsoon

AbstractBy decomposing outgoing longwave radiation through empirical orthogonal function (EOF) analysis, the authors identify two anomalous convective systems in the tropical western Pacific. Besides the classical convective system near the Philippines (PC), there is another convective system near the Federated States of Micronesia (MC). As the first EOF component in this region, the variance explained by MC is higher than that by PC. Both MC and PC are regulated by the tropical sea surface temperature (SST) anomalies. While PC is associated with an El Nino event, MC is correlated with SST anomalies in the central and eastern Pacific during summer. It is also found that the East Asian summer monsoon (EASM) is influenced by these two convective systems. In general, enhanced (suppressed) convection corresponds to an eastwards (westwards) western Pacific subtropical high with weak (strong) intensity. Besides, the summer monsoon rainfall from the Yangtze River basin to Japan tends to increase (decrease) when ...

Discharge variability in Romania using Palmer indices and a simple atmospheric index of large-scale circulation

ABSTRACTThe aim of this study is to analyse the seasonal characteristics of four Palmer indices calculated on the basis of data from 27 meteorological stations in Romania, and the impact of these indices on river discharges in the period 1931–1998. Our research also tests the influence of large-scale atmospheric circulation on these indices and on discharge. For each season, developments in the empirical orthogonal functions (EOF) and multivariate EOF (MEOF) are achieved. The MEOF representation highlights the overall characteristics of the four Palmer indices. It maximizes specific information for each season compared with individual information of each Palmer index. We then identify geographical areas with homogeneous distribution, taking into account both the discharge distribution and the rotated EOF components of each Palmer index. Finally, we analysed the impact of large-scale atmospheric circulation on hydro-climatic events in Romania by means of the Greenland-Balkan Oscillation Index (GBOI), which is shown to have a greater influence on southeastern Europe than the North Atlantic Oscillation Index (NAOI).

Spatial and temporal analysis of the total electron content over China during 2011–2014

In the present work we investigate variations of ionospheric total electron content (TEC) with empirical orthogonal function (EOF) analysis, the four-year TEC data are derived from ∼250GPS observations of the crustal movement observation network of China (CMONOC) over East Asian area (30–55°N, 70–140°E) during the period from 2011, January to 2014, December. The first two EOF components together account for ∼93.78% of total variance of the original TEC data set, and it is found that the first EOF component represents a spatial variability of semi-annual variation and the second EOF component exhibits pronounced east–west longitudinal difference with respect to zero valued geomagnetic declination line. In addition, climatology of the vertical plasma drift velocity vdz induced by HWM zonal wind field (∼300km) are studied in the paper. Results shows vdz displays significant east–west longitudinal difference at 10:00LT and 20:00LT, and its daytime temporal variation is consistent with the second EOF principal component, which suggests that the east–west longitudinal variability is partly caused by the thermospheric zonal wind and geomagnetic declination. It is expected that with this dense GPS network, local ionospheric variability can be described more accurately and a more realistic ionospheric model can be constructed and used for the satellite navigation and radio propagation.

Predicting coastal morphological changes with empirical orthogonal function method

In order to improve the accuracy of prediction when using the empirical orthogonal function (EOF) method, this paper describes a novel approach for two-dimensional (2D) EOF analysis based on extrapolating both the spatial and temporal EOF components for long-term prediction of coastal morphological changes. The approach was investigated with data obtained from a process-based numerical model, COAST2D, which was applied to an idealized study site with a group of shore-parallel breakwaters. The progressive behavior of the spatial and temporal EOF components, related to bathymetric changes over a training period, was demonstrated, and EOF components were extrapolated with combined linear and exponential functions for long-term prediction. The extrapolated EOF components were then used to reconstruct bathymetric changes. The comparison of the reconstructed bathymetric changes with the modeled results from the COAST2D model illustrates that the presented approach can be effective for long-term prediction of coastal morphological changes, and extrapolating both the spatial and temporal EOF components yields better results than extrapolating only the temporal EOF component.

Using moving North Pacific index to improve rainy season rainfall forecast over the Yangtze River basin by analog error correction

A new analog error correction (AEC) scheme based on the moving North Pacific index (MNPI) is designed in this study. This scheme shows obvious improvement in the prediction skill of the operational coupled general circulation model (CGCM) of the National Climate Center of China for the rainy season rainfall (RSR) anomaly pattern correlation coefficient (ACC) over the mid-to-lower reaches of the Yangtze River (MLRYR). A comparative analysis indicates that the effectiveness of the new scheme using the MNPI is better than the system error correction scheme using the North Pacific index (NPI). A Euclidean distanceweighted mean rather than a traditional arithmetic mean, is applied to the integration of the analog year’s prediction error fields. By using the MNPI AEC scheme, independent sample hindcasts of RSR during the period 2003–2009 are then evaluated. The results show that the new scheme exhibited a higher forecast skill during 2003–2009, with an average ACC of 0.47; while the ACC for the NPI case was only 0.19. Furthermore, the forecast skill of the RSR over the MLRYR is examined. In the MNPI case, empirical orthogonal function (EOF) was used in the degree compression of the prediction error fields from the CGCM, whereas the AEC scheme was applied only to its first several EOF components for which the accumulative explained variance accounted for 80% of the total variance. This further improved the ACC of the independent sample hindcasts to 0.55 during the 7-yr period.

MODELLING LONG-TERM COASTAL MORPHOLOGY USING EOF METHOD

Coastline is constantly changing due to the action of wind, waves, tides and sea level variations. Coastal erosion and coastal flooding become increasingly concerned for coastal engineers and coastal zone managers. With global warming due to the climate change which leads to the sea level rise, the frequency and severity of storms are increasing, so that coastal defence becomes even more challenging. In the past decades, various coastal defence structures have been built worldwide to protect our coasts and coastal environment. These structures include sea wall, breakwaters, groynes, and other forms, which often are the combinations of those mentioned, in addition to the soft engineering approaches, such as beach nourishment. To ensure the coastal defence structures to be effectively functional for their design life, it requires the designers to fully understand the effects of the structures on the hydrodynamics and morphodynamics in the surrounding areas, and the response of the coastline in long term. In recent years, the data-driven models have been widely used for long-term modelling of shoreline changes, as such Empirical Orthogonal Functions (EOF) method or one-line model, but require extensively the field data. This paper is to present the details of the EOF analysis using the results obtained from a process-based model COAST2D and the parameterisation procedure for predicting longer term morphological changes from the extrapolated spatial and temporal EOF components. The results presented in this paper illustrate the novelty and effectiveness of the approach as a practical tool for long-term morphological predictions.

Empirical orthogonal function analysis and modeling of the ionospheric peak height during the years 2002–2011

AbstractThe ionospheric peak electron density height (hm) is one of the most important ionospheric parameters characterizing high‐frequency radio wave propagation conditions. In this paper, a global hm model based on the empirical orthogonal function (EOF) analysis method is constructed by using Global Navigation Satellite Systems ionospheric radio occultation measurements from COSMIC and CHAMP as well as global ionosonde data during the years 2002–2011. The variability of hm can be well represented by the several EOF base functions Ek and the corresponding coefficients Pk. The rapid convergence of EOF decomposition makes it possible to use only the first four EOFs components, which express 99.133% of total variance in this study, to construct the empirical model. The variations of hm with respect to the magnetic latitude, local time, season, and solar cycle have been studied, and the EOF‐based hm model has been validated through comparisons with the International Reference Ionosphere (IRI) model and other observation. The evaluations indicate that the EOF and IRI model give better hmF2 at middle and high latitudes than those at low latitudes. Since the limited data were used in the EOF model during high solar activity years, its accuracy degrades to some extent. During nighttime of spring, summer, and winter in the auroral zone, the hm derived from the EOF model may range from 90 to 150 km because of the reduction of hm, which is due to particle precipitation, whereas the IRI model does not include this reduction. During the periods of low solar activity, the F2 peak heights (hmF2) from the EOF model are in good agreement with the observed data, while the IRI model tends to overestimate the hmF2 in the middle and high latitudes.

Analysis of stable components for extended-range (10–30 days) weather forecast: A case study of continuous overcast-rainy process in early 2009 over the mid-lower reaches of the Yangtze River

A continuous overcast-rainy weather (CORW) process occurred over the mid-lower reaches of the Yangtze River (MLRYR) in China from February 14 to March 9 in 2009, with a large stretch and long duration that was rarely seen in historical records. Using the empirical orthogonal function (EOF), we analyzed the geopotential height anomaly field of the NCEP-DOE Reanalysis II in the same period, and defined the stable components of extended-range (10–30 days) weather forecast (ERWF). Furthermore, we defined anomalous and climatic stable components based on the variation characteristics of the variance contribution ratio of EOF components. The climatic stable components were able to explain the impact of climatically averaged information on the ERWF, and the anomalous stable components revealed the abnormal characteristics of the continuous overcast-rainy days. Our results show that the stable components, especially the anomalous stable components, can maintain the stability for a longer time (more than 10 days) and manifest as monthly scale low-frequency variation and ultra-long-wave activities. They also behave as ultra-long waves of planetary scale with a stable and vertically coherent structure, reflect the variation of general circulation in mid-high latitudes, display the cycle of the zonal circulation and the movement and adjustment of the ultra-long waves, and are closely linked to the surface CORW process.

Principal component analysis of background and sunspot magnetic field variations during solar cycles 21-23

The aim of this paper is to derive the principal components (PCs) in variations of (i) the solar background magnetic field (SBMF), measured by the Wilcox Solar Observatory with low spatial resolution for solar cycles 21–23, and (ii) the sunspot magnetic field (SMF) in cycle 23, obtained by SOHO/MDI. For reduction of the component dimensions, principal component analysis (PCA) is carried out to identify global patterns in the data and to detect pairs of PCs and corresponding empirical orthogonal functions (EOFs). PCA reveals two main temporal PCs in the SBMF of opposite polarities originating in opposite hemispheres and running noticeably off-phase (with a delay of about 2.5 yr), with their maxima overlapping in the most active hemisphere for a given cycle. Their maximum magnitudes are reduced by a factor of 3 from cycle 21 to 23, and overlap in the Northern hemisphere for cycle 21, in the Southern one in cycle 22 and in the Northern one again in cycle 23. The reduction of magnitudes and slopes of the maxima of the SBMF waves from cycle 21 to cycle 23 leads us to expect lower magnitudes of the SBMF wave in cycle 24. In addition, PCA allowed us to detect four pairs of EOFs in the SBMF latitudinal components: the two main latitudinal EOFs attributed to symmetric types and another three pairs of EOFs assigned to asymmetric types of meridional flows. The results allow us to postulate the existence of dipole and quadruple (or triple-dipole) magnetic structures in the SBMF, which vary from cycle to cycle and take the form of two waves travelling off-phase, with a phase shift of one-quarter of the 11 yr period. Similar PC and EOF components were found in temporal and latitudinal distributions of the SMF for cycle 23, revealing polarities opposite to the SBMF polarities, and a double maximum in time or maxima in latitude corresponding to the maxima of the SBMF PC residuals or minima in the SBMF EOFs, respectively. This suggests that the SBMF waves modulate the occurrence and magnitude of the SMF in time and latitude.

Comparison of long-, medium- and short-term variations of beach profiles with and without submerged geological control

Abstract Victoria Beach (Cadiz, Spain) comprises a rocky flat outcrop in its northern zone and a sand-rich southern zone. These natural features allowed for a 5-year monitoring period and subsequent analysis of two different profiles (one in each zone) based on differences in bottom contours. Topo-bathymetric data were analysed using empirical orthogonal functions (EOFs) to determine changes over the short-, medium- and long-term. Several morphologic phenomena were identified (generalised erosion, seasonal or summer–winter tilting of the profile around different hinge points, berm development and its posterior destruction, etc.) in terms of their importance in explaining the variability of the collected data for both profiles. It is worth mentioning that both profiles undergo parallel regression in the medium-term. Thus, the 1st eigenfunction enabled us to identify the true regression of the beach shoreline, independent of seasonal or summer–winter slope changes. Reconstruction of profiles using EOF components demonstrated that though accretion periods in the medium-term were similar for both types of profiles, the accretion speed was much faster in the sand-rich profile than in the reef-protected profile (1.01 m 3 /day versus 0.33 m 3 /day). Moreover, the seasonal erosion rate and the subsequent shoreline retreat for the sand-rich profile were much larger than for the reef-protected profile (121 m 3 /year versus 29 m 3 /year). Analysis in the short-term (changes induced by a single day's storm) showed an instantaneous tilting of the profile, with the mobilised sand volume being much greater for the sand-rich than for the reef-protected profile (68 m 3 /m versus 12 m 3 /m). In brief, we can assume that the wave energy attenuation provoked by the existence of a reef flat acted as a geological control for profile evolution, which is essentially different for both profiles. Among the most important differences, special attention should be given to the larger slope, smaller mobilised sand volume and slower accretion rate of the reef-flat profile versus the non-protected profile.

Polynomial chaos expansions for coupled mode amplitude and phase uncertainty in the presence of oceanographic uncertainty

Polynomial chaos (PC) techniques have recently been introduced to the field of underwater acoustics for modeling the nonlinear transfer of probabilistic measures of the propagation environment into measures of acoustic propagation uncertainty [Finette, J. Acoust. Soc. Am. 117, 997–1000 (2005)]. Recently we have proposed and implemented a PC method for modeling this process for coupled mode propagation through internal waves (IWs) [LePage, J. Acoust. Soc. Am. 118, 1903–1904 (2005)]. While showing promise, the approach was implemented for a single empirical orthogonal function (EOF) component of the IW field only and was derived for small PC coefficients. In this paper the restriction of small coefficients is removed for the first two terms of the PC expansion, and results for uncertainty caused by more than one uncorrelated EOF component are also presented. [Work supported by ONR.]