Empirical Orthogonal Function Analysis Method Research Articles

Study on the Thermospheric Density Distribution Pattern during Geomagnetic Activity

The atmospheric density of the thermosphere is a fundamental parameter for spacecraft launch and orbit control. Under magnetic storm conditions, the thermospheric atmospheric density experiences significant fluctuations, which have a negative impact on spacecraft control. Exploring thermospheric density during geomagnetic storms can help to mitigate the effects of such events. Research on the inversion of accelerometer measurements for different satellites and the variations of atmospheric density under extreme conditions is still in its infancy. In this paper, the distribution of atmospheric density during three geomagnetic storms is investigated from the inversion results of the Swarm-C accelerometer. Three major geomagnetic storms and their recovery phases are selected as case studies. The thermospheric density obtained by Swarm-C is separated into day and night regions. The empirical orthogonal function analysis method is used to study the spatiotemporal distribution of thermospheric density during geomagnetic storms. The results indicate that storms have a more significant impact on nighttime thermospheric density. The impact of magnetic storms on the temporal distribution of thermospheric density is considerable. The first-order empirical orthogonal function (EOF) time coefficient value on the day after the storm is the largest, reaching 2–3 times that before the magnetic storm. The impact of magnetic storms on atmospheric density is mainly reflected in the time distribution. The spatial distribution of atmospheric density is less affected by magnetic storms and is relatively stable in the short term. The impact of magnetic storms on the spatial distribution of nighttime thermospheric density is more significant than that of daytime regions, and the response of daytime regions to magnetic storms is slower.

Investigations into Synoptic Spatiotemporal Characteristics of Coastal Upper Ocean Circulation Using High Frequency Radar Data and Model Output

Numerical models and remote sensing observation systems such as radars are useful for providing information on surface flows for coastal areas. Evaluation of their performance and extracting synoptic characteristics are challenging and important tasks. This research aims to investigate synoptic characteristics of surface flow fields through undertaking a detailed analysis of model results and high frequency radar (HFR) data using self-organizing map (SOM) and empirical orthogonal function (EOF) analysis. A dataset of surface flow fields over thirteen days from these two sources was used. A SOM topology map of size 4 × 3 was developed to explore spatial patterns of surface flows. Additionally, comparisons of surface flow patterns between SOM and EOF analysis were carried out. Results illustrate that both SOM and EOF analysis methods are valuable tools for extracting characteristic surface current patterns. Comparisons indicated that the SOM technique displays synoptic characteristics of surface flow fields in a more detailed way than EOF analysis. Extracted synoptic surface current patterns are useful in a variety of applications, such as oil spill treatment and search and rescue. This research provides an approach to using powerful tools to diagnose ocean processes from different aspects. Moreover, it is of great significance to assess SOM as a potential forecasting tool for coastal surface currents.

Research on Short-term Ionospheric Prediction Combining with EOF and ARIMA Model Over Guangxi Area

Abstract. According to the empirical orthogonal function (EOF), the non-stationary time series data are decomposed into time function and space function, so this mathematical method can simplify the non-stationary time series and eliminate redundant information, thus it performs well in non-stationary time series analysis. The ionospheric Vertical Total Electron Content (VTEC) is a non-stationary time series, which has non-stationary and seasonal variation and the activity of VTEC is more active in low latitudes. Guangxi is located in the middle and low latitudes of the Northern Hemisphere with abundant sunshine in summer and autumn. The energy released by solar radiation makes the ionospheric activity in this region more complex than that in the high latitudes. However, no expert or scholar has used EOF analysis method to conduct a comprehensive study of the low latitudes. The International GNSS Service (IGS) provided by high precision Global Ionospheric Maps (GIM) center in Guangxi are used in the modeling data, the GIM data of the first 10 days of different seasons are decomposed by EOF, and then the time function is predicted by ARIMA model. VTEC values for the next five days are obtained through reconstruction, and relative accuracy and standard deviation are used as accuracy evaluation criteria. The results of EOF-ARIMA model are compared with those of ARIMA model, and the prediction accuracy of EOF-ARIMA model at the equatorial anomaly is analyzed in order to explore the reliability of the model in the more complex region of ionospheric activity. The results show that the average relative precision of EOF-ARIMA model is 84.0, the average standard deviation is 7.45TECu, the average relative precision of ARIMA model is 81.5, the average standard deviation is 8.29TECu, and the precision of EOF-ARIMA model is higher than that of ARIMA model.; There is no significant seasonal difference in the prediction accuracy of EOF-ARIMA model, and the prediction accuracy of ARIMA model in autumn is lower than that of other seasons, which indicates that the prediction results of EOF-ARIMA model are more reliable; The prediction accuracy of the EOF-ARIMA model at the equatorial anomaly is not affected, and it is consistent with the accuracy of the high latitude area in Guangxi. It is shown that the EOF-ARIMA model has high accuracy and stability in the short-term ionospheric prediction in Guangxi at low latitudes of China, and provides a new and reliable method for ionospheric prediction at low latitudes.

An Ionosphere Specification Technique Based on Data Ingestion Algorithm and Empirical Orthogonal Function Analysis Method

AbstractA data ingestion method in reproducing ionospheric electron density and total electron content (TEC) was developed to incorporate TEC products from the Madrigal Database into the NeQuick 2 model. The method is based on retrieving an appropriate global distribution of effective ionization parameter (Az) to drive the NeQuick 2 model, which can be implemented through minimizing the difference between the measured and modeled TEC at each grid in the local time‐modified dip latitude coordinates. The performance of this Madrigal TEC‐driven‐NeQuick 2 result is validated through the comparison with various International Global Navigation Satellite Systems Services global ionospheric maps and ionosonde data. The validation results show that a general accuracy improvement of 30–50% can be achieved after data ingestion. In addition, the empirical orthogonal function (EOF) analysis technique is used to construct a parameterized time‐varying global Az model. The quick convergence of EOF decomposition makes it possible to use the first six EOF series to represent over 90% of the total variances. The intrinsic diurnal variation and spatial distribution in the original data set can be well reflected by the constructed EOF base functions. The associated EOF coefficients can be expressed as a set of linear functions of F10.7 and Ap indices, combined with a series of trigonometric functions with annual/seasonal variation components. The NeQuick TEC driven by EOF‐modeled Az shows 10–15% improvement in accuracy over the standard ionosphere correction algorithm in the Galileo navigation system. These preliminary results demonstrate the effectiveness of the combined data ingestion and EOF modeling technique in improving the specifications of ionospheric density variations.

Predictability of the Loop Current Variation and Eddy Shedding Process in the Gulf of Mexico Using an Artificial Neural Network Approach

AbstractA novel approach based on an artificial neural network was used to forecast sea surface height (SSH) in the Gulf of Mexico (GoM) in order to predict Loop Current variation and its eddy shedding process. The empirical orthogonal function analysis method was applied to decompose long-term satellite-observed SSH into spatial patterns (EOFs) and time-dependent principal components (PCs). The nonlinear autoregressive network was then developed to predict major PCs of the GoM SSH in the future. The prediction of SSH in the GoM was constructed by multiplying the EOFs and predicted PCs. Model sensitivity experiments were conducted to determine the optimal number of PCs. Validations against independent satellite observations indicate that the neural network–based model can reliably predict Loop Current variations and its eddy shedding process for a 4-week period. In some cases, an accurate forecast for 5–6 weeks is possible.

Revisiting the trend of the tropical and subtropical Pacific surface latent heat flux during 1977–2006

[1] Using the Objectively Analyzed Air-Sea Fluxes data provided by the Woods Hole Oceanographic Institution and the trend empirical orthogonal function analysis method, we have investigated the trend of ocean surface latent heat flux (LHF) over the tropical and subtropical Pacific (100°E–70°W, 35°S–35°N) during the period 1977–2006. The present study suggests that the ocean surface LHF presents a large-scale upward trend pattern, and the identified positive surface LHF trend is closely associated with both the sea surface temperature (SST) warming and the surface wind speed strengthening. The SST increasing is the primary direct/local cause of the surface LHF trend, while the large-scale surface wind speed strengthening, ascribed to its contribution to the observed SST trend pattern, is an important indirect/nonlocal factor of the surface LHF trend. The present work also suggests that the coherent upward trends in surface LHF, surface wind speed, and SST should be in essence closely linked to the global warming forcing. To some extent, these results unify the two seemingly contradictory conclusions proposed previously by other researchers and attempt to help obtain a new insight into the causes of the positive basin-scale surface LHF trend.

Variability study of the crest-to-trough TEC ratio of the equatorial ionization anomaly around 120°E longitude

In this paper, latitudinal profiles of the vertical total electron content (TEC) deduced from the dual-frequency GPS measurements obtained at ground stations around 120°E longitude were used to study the variability of the equatorial ionization anomaly (EIA). The present study mainly focuses on the analysis of the crest-to-trough TEC ratio (TEC-CTR) which is an important parameter representing the strength of EIA. Data used for the present study covered the time period from 01 January, 1998 to 31 December, 2004. An empirical orthogonal function analysis method is used to obtain the main features of the TEC-CTR’s diurnal and seasonal variations as well as its solar activity level dependency. Our results showed that: (1) The diurnal variation pattern of the TEC-CTR at 120°E longitude is characterized by two remarkable peaks, one occurring in the post-noon hours around 13–14 LT, and the other occurring in the post-sunset hours around 20–21 LT, and the post-sunset peak has a much higher value than the post-noon one. (2) Both for the north and south crests, the TEC-CTR at 120°E longitude showed a semi-annual variation with maximum peak values occurring in the equinoctial months. (3) TEC-CTR for the north crest has lower values in summer than in winter, whereas TEC-CTR for the south crest does not show this ‘winter anomaly’ effect. In other words, TEC-CTR for both the north and south crests has higher values in the northern hemispheric winter than in the northern hemispheric summer. (4) TEC-CTR in the daytime post-noon hours (12–14 LT) does not vary much with the solar activity, however, TEC-CTR in the post-sunset hours (19–21 LT) shows a clear dependence on the solar activity, its values increasing with solar activity.

Modeling M(3000)F2 based on empirical orthogonal function analysis method

An empirical orthogonal function (EOF) analysis, combined with a regression analysis, is conducted to construct an empirical model for the ionospheric propagation factor M(3000)F2. First, a single station model is constructed using monthly median hourly values of M(3000)F2 data observed at Wuhan Ionospheric Observatory (geographic 114.4°E, 30.6°N; 45.2°dip) during the years of 1957–1991 for demonstrating the modeling technique based on EOF expansion and regression analysis of the EOF coefficients. The constructed climatological model incorporates the diurnal, seasonal as well as solar‐cycle variations of M(3000)F2. A comparison between the observational results and the modeled ones showed good agreement. Then, an attempt is made to model global M(3000)F2 data using data from stations distributed around the world. Our preliminary result showed that the modeling technique based on EOF expansion, which is combined with regression analysis of the EOF coefficients as described in this paper, is very promising when used in global modeling and is worthwhile to investigate further.

Rainfall variations of Sri Lanka Part 1: Spatial and temporal patterns

In order to study the spatial and temporal patterns in Sri Lanka, monthly rainfall data at 29 stations for the period 1881–1980 were analysed in this study. First, Empirical Orthogonal Function analysis method was applied for the monthly rainfall anomalies. The result indicated clear dominant spatial patterns. The first eigenvector accounts for 40.2% and the second for 11.1% of the total variance explain the most apparently existing patterns with orographic influences. In particular, the former is explained by the rainfall patterns in the period between October and February (northeast monsoon), and the later by that in May to September (southwest monsoon) period. Power spectra of first eigenvector's time coefficients revealed cycles at 40, 24 and 14–15 months, while the second eigenvector's time coefficients indicated at 120 and 40 months. Lastly, a regional division by rainfall fluctuations is presented for Sri Lanka based on the space coefficients of first two eigenvectors.