Empirical Orthogonal Function Technique Research Articles

Satellite derived trends and variability of CO2 concentrations in the Middle East during 2014–2023

The Middle East has major sources of anthropogenic carbon dioxide (CO2) emissions, but a dearth of ground-based measurements precludes an investigation of its regional and temporal variability. This is achieved in this work with satellite-derived estimates from the Orbiting Carbon Observatory-2 (OCO-2) and OCO-3 missions from September 2014 to February 2023. The annual maximum and minimum column (XCO2) concentrations are generally reached in spring and autumn, respectively, with a typical seasonal cycle amplitude of 3–8 ± 0.5 ppmv in the Arabian Peninsula rising to 8–10 ± 1 ppmv in the mid-latitudes. A comparison of the seasonal-mean XCO2 values with the CO2 emissions estimated using the divergence method stresses the role played by the sources and transport of CO2 in the spatial distribution of XCO2, with anthropogenic emissions prevailing in arid and semi-arid regions that lack persistent vegetation. In the 8-year period 2015–2022, the XCO2 concentration in the United Arab Emirates (UAE) increased at a rate of about 2.50 ± 0.04 ppmv/year, with the trend empirical orthogonal function technique revealing a hotspot over northeastern UAE and southern Iran in the summer where anthropogenic emissions peak and accumulate aided by low-level wind convergence. A comparison of the satellite-derived CO2 concentration with that used to drive climate change models for different emission scenarios in the 8-year period revealed that the concentrations used in the latter is overestimated, with maximum differences exceeding 10 ppmv by 2022. This excess in the amount of CO2 can lead to an over-prediction of the projected increase in temperature in the region, an aspect that needs to be investigated further. This work stresses the need for a ground-based observational network of greenhouse gas concentrations in the Middle East to better understand its spatial and temporal variability and for the evaluation of remote sensing observations as well as climate models.

A Regional Model of Topside Ionospheric Effective Scale Heights Derived From Ionosonde and GNSS TEC

AbstractIonospheric scale height is critical for the structure of electron density profile in the ionosphere. However, mostly, the effective scale heights (fitted with mathematical functions) instead of topside ionospheric scale heights were used to reconstruct the topside profile. In this study, a new method was proposed to estimate topside ionospheric effective scale heights from ionosonde and Global Navigation Satellite System (GNSS) vertical total electron content (TEC). First, the bottomside electron density profile can be estimated from ionograms. Then, combined the parameters of the F2 layer and effective scale heights, topside electron density profile can be estimated by Epstein Layer. Furthermore, ionosonde TEC can be compared with GNSS vertical TEC by adjusting effective scale heights to obtain best‐fit ionosonde TEC and effective scale heights. In this study, ionosonde and GNSS TEC data recorded at Zhangye station (39.40°N, 100.13°E) were used to test the performance. Results show that diurnal and seasonal characteristics of effective scale heights are consistent with previous studies. Furthermore, the Empirical Orthogonal Function technique was used to build a regional and empirical model of effective scale heights. Results show that the accuracy (between ±2.5 TECU) of ionosonde TEC are about 91.26% by comparing with GNSS TEC. Considered that the traditional methods mostly underestimated TEC, it indicates that the accuracy of ionosonde TEC can be improved significantly by the new model of effective scale heights. Furthermore, results show that the topside electron densities estimated by the proposed method are comparable with in situ observations measured by Swarm B.

Spatial-temporal Variation and Driving Factors of Ozone in China from 2019 to 2021 Based on EOF Technique and KZ Filter

Based on the hourly O3 concentration data of 337 prefectural-level divisions and simultaneous surface meteorological data in China, we applied empirical orthogonal function (EOF) analysis to analyze the main spatial patterns, variation trends, and main meteorological driving factors of O3 concentration in China from March to August in 2019-2021. In this study, a KZ (Kolmogorov-Zurbenko) filter was used to decompose the time series of O3 concentration and simultaneous meteorological factors into corresponding short-term, seasonal, and long-term components in 31 provincial capitals.Then, the stepwise regression was used to establish the relationship between O3 and meteorological factors. Ultimately, the long-term component of O3 concentration after "meteorological adjustment" was reconstructed. The results indicated that the first spatial patterns of O3 concentration showed a convergent change, that is, the volatility of O3 concentration was weakened in the high-value region of variability and enhanced in the low-value region.Before and after the meteorological adjustment, the variation trend of O3 concentration in different cities was different to some extent. The adjusted curve was "flatter" in most cities. Among them, Fuzhou, Haikou, Changsha, Taiyuan, Harbin, and Urumqi were greatly affected by emissions. Shijiazhuang, Jinan, and Guangzhou were greatly affected by meteorological conditions. Beijing, Tianjin, Changchun, and Kunming were greatly affected by emissions and meteorological conditions.

Impacts of the COVID-19 lockdown in China on new particle formation and particle number size distribution in three regional background sites in Asian continental outflow

Despite the curtailment of atmospheric condensing precursor gases during the Coronavirus disease 2019 (COVID-19) lockdown (LD) period, unexpected haze events via the formation of new particles and their subsequent growth have been identified. This study investigated the impact of emission reduction during the Chinese LD period on the new particle formation (NPF) frequency and corresponding particle number size distribution (PNSD) at three regional background atmospheric monitoring sites in the western coastal areas of the Korean Peninsula. During this duration, the number concentrations of the nucleation- (<25 nm) and accumulation-mode (>90 nm) particles significantly decreased in Baengryeong (BRY), showing decreases of 34% and 29%, respectively. Unlike BRY, the PNSD in Anmyeon (AMY), which is influenced by nearby industrial emissions, remained nearly unchanged during the LD period, possibly because the reduction in industrial emissions was not significant during the social distancing period enforced by Korea. Bongseong (BOS) showed a similar variation to that of BRY; however, the magnitude of the reduction was weaker because of its higher altitude compared to other sites. The cyclostationary empirical orthogonal function technique was applied to the measured PNSDs at the three sites to objectively classify NPF events. Because mode 1 of cyclostationary loading vectors commonly represented the typical diurnal variation of PNSD during regional NPF events at three sites, mode 1 of the corresponding principal component time series was used for NPF classification. The NPF frequency decreased by 7%, 1%, and 7% in BRY, AMY, and BOS, respectively, despite favorable meteorological conditions, such as increased temperature and insolation during the LD period. The diurnal variation in the sulfuric acid (H2SO4) proxy implied that the H2SO4 proxy acted as a determining factor for NPF events during the NPF occurrence time (8–12 local hours) in AMY and BOS; however, NPF occurrence in BRY was not connected to the H2SO4 proxy level. This suggests that BRY was more likely to be influenced by the reduction in organic species in the continental upwind regions, while the occurrence of NPF events in AMY and BOS can be suppressed in association with the distinct reduction in inorganic compounds represented by the H2SO4 proxy during the LD period.

Regional model of foF2 for Pakistan using empirical orthogonal function technique

Regional model of foF2 for Pakistan using empirical orthogonal function technique

The leading modes of NH extratropical tropopause variability and their connection with stratosphere-troposphere variability

The leading modes of Northern Hemisphere tropopause variability for November–April (1979/1980–2018/2019) and the associated stratosphere-troposphere variability were analyzed based on the NCEP and ERA interim reanalysis products. For this, cyclostationary empirical orthogonal function technique is employed. The first two modes feature the intraseasonal evolution of tropopause pressure anomalies over the Arctic, which respond directly to stratospheric temperature fluctuations in association with stratospheric polar vortex variations. These two modes reflect the link between stratospheric polar vortex strength and high-latitude tropospheric circulation. The first mode represents a single-phase fluctuation of the stratospheric polar vortex from winter to early spring. The second mode describes a two-phase fluctuation of the stratospheric vortex with opposite signs in winter and in spring. Tropopause pressure anomalies near the mid-latitude tropospheric jet regions exhibit significant zonal variation. In the first mode, in particular, these mid-latitude tropopause anomalies are linked to asymmetric jet variations in the Atlantic and the Pacific regions. In regard to the Northern Annular mode, distinct vertical evolution structures of the two modes are practically related to the varying evolutionary structure of extreme vortex events with relatively long persistence.

Investigation of South Korea Precipitation Variation using Empirical Orthogonal Function (EOF) and Cyclostationary EOF

The monthly precipitation data of 56 stations during 47 years (1973-2019) in South Korea are comprehensively analysed using the EOF technique and CSEOF technique respectively. The main motivation for employing this technique in the present study is to investigate the physical processes associated with the evolution of the precipitation from observation data. The first mode account for 77.07% of the total variance and exhibits annual cycle of corresponding PC time series with traditional spatial pattern, and the second mode spatial patterns account for 8.13% of the total variance and show strong north to south gradient. In CSEOF analysis, two leading modes temporal pattern of PC time series reveals the annual cycle on a monthly time scale and long-term fluctuation, the first mode temporal pattern of PC time series account for 73.55% of the total variance and shows an increasing linear trend which represents that temporal variability of first mode pattern has been strengthened. The spatial distribution corresponding to two leading modes show monthly spatial variation. Compared with the EOF analysis, the CSEOF analysis preferably exhibits the spatial distribution and temporal evolution characteristics and variability of South Korea historical precipitation.

Quantifying Seasonal‐to‐Interannual‐Scale Storm Impacts on Morphology Along a Cuspate Coast With a Hybrid Empirical Orthogonal Function Approach

AbstractThe direct impacts of storms on beaches have been well studied; less well understood are the controls of storms on their seasonal‐interannual evolution. We apply a novel empirical orthogonal function (EOF) analysis to a 5‐year data set of monthly subaerial beach topography at Kennedy Space Center, Florida, to extract dominant spatiotemporal topographic patterns. Our hybrid surface EOF (SEOF) approach applies 1‐D EOF techniques to a data set varying in two dimensions, thereby extracting topographic patterns in the longshore and cross‐shore simultaneously while preserving the analytical simplicity of 1‐D approaches. These topographic patterns are then linked to observations of storm impacts. Our approach comprehensively illustrates that storms influenced local topographic evolution over event‐to‐interannual‐timescales. The first mode of topographic variability captures an interannual‐scale change in behavior triggered by the impact of Hurricane Sandy (2012), whereby a cape feature began and sustained rapid aggradation following the event. This pattern is likely linked to storm‐response processes and pre‐existing morphodynamic feedbacks, illustrating that storm response can dictate poststorm recovery processes. This pattern overwhelmed a spatially uniform, seasonal topographic signal, which we attribute to seasonal variability in water level and storminess forcings. The third mode shows links to local framework geology and suggests that some storms can create and/or destroy subaerial berms at this site, where spatial variability of berm existence in discrete longshore compartments can remain stable until a future event. Our results illustrate mechanisms by which storms can create persistent topographic imprints that remain visible for months‐years following events, potentially influencing response to future storms.

Two Contrasting African Easterly Wave Behaviors

AbstractThe dominant structural variability of African easterly waves (AEWs) is explored using an empirical orthogonal function (EOF) approach. The structure of AEWs is obtained by projecting the wind fields from reanalysis data and satellite-derived brightness temperature Tb onto the principal components associated with EOF patterns of filtered Tb (Tb EOF) and 700-hPa meridional wind (v700 EOF). The wave structure depicted by the Tb EOF has confined convection and circulation mostly south of the African easterly jet. It shares many characteristics with AEWs analyzed and discussed in the literature. In contrast, the v700 EOF exhibits less familiar characteristics and includes interactions with the equatorial and subtropical regions. The convective patterns are characterized by a “checkerboard” pattern of convection that has not been emphasized before. The most striking feature is the broad meridional extent, which depicts interactions with a mixed Rossby–gravity wave (MRG) in the equatorial region and interactions with the basic-state potential vorticity in the subtropics. The southern portion of the wave has a modified MRG structure, and this AEW–MRG hybrid cannot be separated using the EOF technique, indicating the prevalence of such structures. The subtropical interaction at mid- to lower levels establishes a vortex off the coast of Morocco that results in dry-air advection into the tropics in tandem with the northern vortex. At upper levels, a subtropical wave train is induced by the AEW-associated convective inflow and outflow. The contrasting AEW circulations are associated with differences in the precipitation rates and patterns over Africa. These results highlight the variability of AEW structures and their interactions with equatorial and subtropical waves.

Modelling ionospheric vertical drifts over Africa low latitudes using Empirical Orthogonal functions and comparison with climatological model

For the first time, empirical model of daytime vertical E×B drift based on Empirical Orthogonal functions (EOF) decomposition technique is presented. Day-to-day variability of E×B drift inferred from horizontal (H) geomagnetic field data around dip latitude for the period of 2008–2013 is used to both develop and validate the model. Results show that the EOF technique is promising with modelled values and data giving correlation coefficient values of at least 0.90 for geomagnetic conditions of both Kp⩽3 and Kp>3 within 2008–2013. Independent model validation shows that in situ E×B values from ion velocity meter (IVM) instrument on-board C/NOFS satellite are closer to model E×B estimates than the climatological Scherliess-Fejer (SF) model incorporated within the International Reference Ionosphere (IRI).

Using EOF Analysis over a Large Area for Assessing the Climate Impact of Small-Scale Afforestation in a Semiarid Region

AbstractThe authors suggest an approach to analyze the effects of small-scale afforestation on the surrounding climate of a large heterogenic area. While simple statistics have difficulty identifying the effect, here a well-known eigenvector technique is used to overcome several specific challenges that result from a limited research region, complex topography, and multiple atmospheric circulation patterns. This approach is applied to investigate the influence of the isolated Yatir forest, at the north edge of Israel’s Negev Desert. It was found that this forest does influence the daily climate, primarily seen in the main pattern of the empirical orthogonal function (EOF) of temperature and humidity. The EOF explains 93% and 80%, respectively, of the total variance in the data. Although the Yatir forest is small, it is significant in regulating the climate in the nearby surroundings, as it is located in a sharp transition area toward an arid climate. The results are presented as maps of correlation and regression between the normalized principal component time series of each pattern as well as other time series of the raw data and spatially interpolated data stations. Analysis of short-term campaign measurements around the Yatir forest supports the EOF results, and shows the forest’s influence to the south, mainly during nighttime when the forest becomes cooler than its surroundings. Overall, results suggest that in areas of transition to semiarid climates, forests regulate the surrounding surface air temperature and humidity fields. Wind analysis based on a complex EOF technique reveals the pattern of the daily cycle of surface wind over the region.

A Novel Statistical Approach for Ocean Colour Estimation of Inherent Optical Properties and Cyanobacteria Abundance in Optically Complex Waters

Eutrophication is an increasing problem in coastal waters of the Baltic Sea. Moreover, algal blooms, which occur every summer in the Gulf of Gdansk can deleteriously impact human health, the aquatic environment, and economically important fisheries, tourism, and recreation industries. Traditional laboratory-based techniques for water monitoring are expensive and time consuming, which usually results in limited numbers of observations and discontinuity in space and time. The use of hyperspectral radiometers for coastal water observation provides the potential for more detailed remote optical monitoring. A statistical approach to develop local models for the estimation of optically significant components from in situ measured hyperspectral remote sensing reflectance in case 2 waters is presented in this study. The models, which are based on empirical orthogonal function (EOF) analysis and stepwise multilinear regression, allow for the estimation of parameters strongly correlated with phytoplankton (pigment concentration, absorption coefficient) and coloured detrital matter abundance (absorption coefficient) directly from reflectance spectra measured in situ. Chlorophyll a concentration, which is commonly used as a proxy for phytoplankton biomass, was retrieved with low error (median percent difference, MPD = 17%, root mean square error RMSE = 0.14 in log10 space) and showed a high correlation with chlorophyll a measured in situ (R = 0.84). Furthermore, phycocyanin and phycoerythrin, both characteristic pigments for cyanobacteria species, were also retrieved reliably from reflectance with MPD = 23%, RMSE = 0.23, R2 = 0.77 and MPD = 24%, RMSE = 0.15, R2 = 0.74, respectively. The EOF technique proved to be accurate in the derivation of the absorption spectra of phytoplankton and coloured detrital matter (CDM), with R2 (λ) above 0.83 and RMSE around 0.10. The approach was also applied to satellite multispectral remote sensing reflectance data, thus allowing for improved temporal and spatial resolution compared with the in situ measurements. The EOF method tested on simulated Medium Resolution Imaging Spectrometer (MERIS) or Ocean and Land Colour Instrument (OLCI) data resulted in RMSE = 0.16 for chl-a and RMSE = 0.29 for phycocyanin. The presented methods, applied to both in situ and satellite data, provide a powerful tool for coastal monitoring and management.

Impacts of winter NPO on subsequent winter ENSO: sensitivity to the definition of NPO index

This study investigates the linkage between boreal winter North Pacific Oscillation (NPO) and subsequent winter El Nino-Southern Oscillation (ENSO) based on seven different NPO indices. Results show that the influence of winter NPO on the subsequent winter El Nino is sensitive to how the NPO is defined. A significant NPO-El Nino connection is obtained when the NPO-related anomalous cyclone over the subtropical North Pacific extends to near-equatorial regions. The anomalous cyclone induces warm sea surface temperature (SST) anomalies through modulating surface heat fluxes. These warm SST anomalies are able to maintain into the following spring and summer through an air-sea coupled process and in turn induce significant westerly wind anomalies over the tropical western Pacific. In contrast, the NPO-El Nino relationship is unclear when the NPO-related anomalous cyclone over the subtropical North Pacific is confined to off-equatorial regions and cannot induce significant warm SST anomalies over the subtropical North Pacific. The present study suggests that definitions of NPO should be taken into account when using NPO to predict ENSO. In particular, we recommend defining the NPO index based on the empirical orthogonal function technique over appropriate region that does not extend too far north.

Uncertainties in remotely sensed precipitation data over Africa

Quantifying the amount of precipitation and its uncertainty is a challenging task all over the world, particularly over the African continent, where rain gauge (RG) networks are poorly distributed. In recent decades, several satellite remote sensing (SRS)-based precipitation products have become available with reasonable spatial and temporal resolutions to be applied in hydrological and climate studies. However, uncertainties of these products over Africa are largely unknown. In this study, the generalized ‘three-cornered-hat’ (TCH) method is applied to estimate uncertainties of gridded precipitation products over the entire African continent, without being dependent to the choice of a reference dataset. Six widely used SRS-based precipitation products (at monthly scales) were evaluated over the entire continent during the period of 2003–2010. The TCH results are further compared to those of the classical evaluation using the Global Precipitation Climatology Centre (GPCC) over entire Africa, as well as to the RG observations over the Greater Horn of Africa (GHA). Overall, for the study period (2003–2010), the TCH results indicate that the RG-merged products contain smaller error amplitudes compared to the satellite-only products, consistent with the GPCC-based evaluation. A multiple comparison procedure ranking, which was applied based on signal-to-noise ratios (SNRs), indicated that PERSIANN contains the highest SNR and thus suitable over most of Africa, followed by ARCv2, TRMM, CMORPH, TAMSAT, and GSMaP. To extract the main spatio-temporal variability of rainfall over Africa, complex empirical orthogonal function technique was applied, from which the extracted patterns of GPCC, TRMM, PERSIANN, and ARCv2 were found to be similar but different from those of TAMSAT, CMORPH, and GSMaP. Finally, the TCH and RG-based validation methods were found to provide similar evaluations for the SRS-only products (CMORPH and GSMaP) over GHA, with CMORPH emerging to be the most suitable product, consistent with previous studies.

Dominant Large-Scale Atmospheric Circulation Systems for the Extreme Precipitation over the Western Sichuan Basin in Summer 2013

The western Sichuan Basin (WSB) is a rainstorm center influenced by complicated factors such as topography and circulation. Based on multivariable empirical orthogonal function technique for extreme precipitation processes (EPP) in WSB in 2013, this study reveals the dominant circulation patterns. Results indicate that the leading modes are characterized by “Saddle” and “Sandwich” structures, respectively. In one mode, a TC from the South China Sea (SCS) converts into the inverted trough and steers warm moist airflow northward into the WSB. At the same time, WPSH extends westward over the Yangtze River and conveys a southeasterly warm humid flow. In the other case, WPSH is pushed westward by TC in the Western Pacific and then merges with an anomalous anticyclone over SCS. The anomalous anticyclone and WPSH form a conjunction belt and convey the warm moist southwesterly airflow to meet with the cold flow over the WSB. The configurations of WPSH and TC in the tropic and the blocking and trough in the midhigh latitudes play important roles during the EPPs over the WSB. The persistence of EPPs depends on the long-lived large-scale circulation configuration steady over the suitable positions.

Comment on: ‘The quest for a consistent signal in ground and GRACE gravity time-series’, by Michel Van Camp, Olivier de Viron, Laurent Metivier, Bruno Meurers and Olivier Francis

The paper in question by Van Camp and co-authors [MVC] challenges previous work showing that ground gravity data arising from hydrology can provide a consistent signal for the comparison with satellite gravity data. The data sets used are similar to those used previously, that is, the gravity field as measured by the GRACE satellites versus ground-based data from superconducting gravimeters (SGs) over the same continental area, in this case Central Europe. One of the main impediments in this paper is the presentation that is frequently confusing and misleading as to what the data analysis really shows, for example, the irregular treatment of annual components that are first subtracted then reappear in the analysis. More importantly, we disagree on specific points. Two calculations are included in our comment to illustrate where we believe that the processing in [MVC] paper is deficient. The first deals with their erroneous treatment of the global hydrology using a truncated spherical harmonic approach which explains almost a factor 2 error in their computation of the loading. The second shows the effect of making the wrong assumption in the GRACE/hydrology/surface gravity comparison by inverting the whole of the hydrology loading for underground stations. We also challenge their claims that empirical orthogonal function techniques cannot be done in the presence of periodic components, and that SG data cannot be corrected for comparisons with GRACE data. The main conclusion of their paper, that there is little coherence between ground gravity stations and this invalidates GRACE comparisons, is therefore questionable. There is nothing in [MVC] that contradicts any of the previous papers that have shown clearly a strong relation between seasonal signals obtained from both ground gravity and GRACE satellite data.

Quantifying anthropogenic and natural contributions to thermosteric sea level rise

Changes in thermosteric sea level at decadal and longer time scales respond to anthropogenic forcing and natural variability of the climate system. Disentangling these contributions is essential to quantify the impact of human activity in the past and to anticipate thermosteric sea level rise under global warming. Climate models, fed with radiative forcing, display a large spread of outputs with limited correspondence with the observationally based estimates of thermosteric sea level during the last decades of the twentieth century. Here we extract the common signal of climate models from Coupled Model Intercomparison Project Phase 5 using a signal-to-noise maximizing empirical orthogonal function technique for the period 1950–2005. Our results match the observed trends, improving the widely used approach of multimodel ensemble averaging. We then compute the fraction of the observed thermosteric sea level rise of anthropogenic origin and conclude that 87% of the observed trend in the upper 700 m since 1970 is induced by human activity.

Mesoscale and large‐scale variability in high‐latitude ionospheric convection: Dominant modes and spatial/temporal coherence

Empirical orthogonal function (EOF) analysis, a variant of principle component analysis, is applied to 20 months of plasma drift data from the Super Dual Auroral Radar Network radars in the high‐latitude region of the Northern Hemisphere. Dominant modes of ionospheric electric field variability are identified and the spatial and temporal coherence of this variability is quantified. The first three modes of variability, which, together with the mean, account for ∼50% of the observed squared electric field (E2), are characterized by global spatial scales and long time scales (∼1 h). The first and second modes of variability represent the strengthening/weakening of the global convection pattern and the shaping of the convection pattern into asymmetrical round‐ and crescent‐shaped cells. These two modes are correlated with the Bz and By components of the interplanetary magnetic field. The third mode represents the expansion/contraction of the convection pattern and is weakly correlated with the solar wind velocity. For EOFs beyond EOF 3, the power contained in the modes falls off rapidly, the characteristic spatial and temporal scales decrease, and weak correlations with external driving parameters are observed. These higher‐order EOFs likely capture more random behavior of the electric field variability. The notable exception to this trend is EOF 11, which captures midlatitude variations on the duskside and is enhanced during subauroral polarization stream events. The EOF technique described in this paper is applied in a companion paper to characterize the covariance of ionospheric electric fields for use in an assimilative mapping procedure.

A new ensemble-based data assimilation algorithm to improve track prediction of tropical cyclones

This paper proposes a new ensemble-based algorithm that assimilates the vertical rain structure retrieved from microwave radiometer and radar measurements in a regional weather forecast model, by employing a Bayesian framework. The goal of the study is to evaluate the capability of the proposed technique to improve track prediction of tropical cyclones that originate in the North Indian Ocean. For this purpose, the tropical cyclone Jal has been analyzed by the community mesoscale weather model, weather research and forecasting (WRF). The ensembles of prognostic variables such as perturbation potential temperature (θ, k), perturbation geopotential (ϕ, m2/s2), meridional (U) and zonal velocities (V) and water vapor mixing ratio (q v , kg/kg) are generated by the empirical orthogonal function technique. An over pass of the tropical rainfall-measuring mission (TRMM) satellite occurred on 06th NOV 0730 UTC over the system, and the observations from the radiometer and radar on board the satellite(1B11 data products) are inverted using a combined in-home radiometer-radar retrieval technique to estimate the vertical rain structure, namely the cloud liquid water, cloud ice, precipitation water and precipitation ice. Each ensemble is input as a possible set of initial conditions to the WRF model from 00 UTC which was marched in time till 06th NOV 0730 UTC. The above-mentioned hydrometeors from the cloud water and rain water mixing ratios are then estimated for all the ensembles. The Bayesian filter framework technique is then used to determine the conditional probabilities of all the candidates in the ensemble by comparing the retrieved hydrometeors through measured TRMM radiances with the model simulated hydrometeors. Based on the posterior probability density function, the initial conditions at 06 00 UTC are then corrected using a linear weighted average of initial ensembles for the all prognostic variables. With these weighted average initial conditions, the WRF model has been run up to 08th Nov 06 UTC and the predictions are then compared with observations and the control run. An ensemble independence study was conducted on the basis of which, an optimum of 25 ensembles is arrived at. With the optimum ensemble size, the sensitivity of prognostic variables was also analyzed. The model simulated track when compared with that obtained with the corrected set of initial conditions gives better results than the control run. The algorithm can improve track prediction up to 35 % for a 24 h forecast and up to 12 % for a 54 h forecast.

Application of spectral analysis techniques in the intercomparison of aerosol data: 1. An EOF approach to analyze the spatial‐temporal variability of aerosol optical depth using multiple remote sensing data sets

Many remote sensing techniques and passive sensors have been developed to measure global aerosol properties. While instantaneous comparisons between pixel‐level data often reveal quantitative differences, here we use Empirical Orthogonal Function (EOF) analysis, also known as Principal Component Analysis, to demonstrate that satellite‐derived aerosol optical depth (AOD) data sets exhibit essentially the same spatial and temporal variability and are thus suitable for large‐scale studies. Analysis results show that the first four EOF modes of AOD account for the bulk of the variance and agree well across the four data sets used in this study (i.e., Aqua MODIS, Terra MODIS, MISR, and SeaWiFS). Only SeaWiFS data over land have slightly different EOF patterns. Globally, the first two EOF modes show annual cycles and are mainly related to Sahara dust in the northern hemisphere and biomass burning in the southern hemisphere, respectively. After removing the mean seasonal cycle from the data, major aerosol sources, including biomass burning in South America and dust in West Africa, are revealed in the dominant modes due to the different interannual variability of aerosol emissions. The enhancement of biomass burning associated with El Niño over Indonesia and central South America is also captured with the EOF technique.