Empirical Orthogonal Function Approach Research Articles

A Comparison of Multiple Approaches to Study the Modulation of Ocean Waves Due To Climate Variability

AbstractUsing multiple approaches, the modulation of climate variability on global ocean waves from 1981 to 2020 is investigated based on a wave hindcast model forced by ERA5 winds. These climate variabilities include El Niño–Southern Oscillation (ENSO), Antarctic Oscillation (AAO), Arctic Oscillation (AO), Pacific Decadal Oscillation (PDO), Atlantic Multidecadal Oscillation (AMO), and Indian Ocean Dipole. Linear regression and composite analysis results indicate that El Niño‐induced low‐pressure systems in December–February (DJF) generate energetic waves in the Pacific Ocean. Positive AAO events are associated with the southward movement of westerlies in the Southern Hemisphere and thus produce long‐period Southern Ocean swell that impacts the South Pacific Ocean. In the Northern Hemisphere, positive AO is associated with strengthening winds which generate larger waves around the Icelandic region. An empirical orthogonal function approach was further undertaken to study interannual variability of significant wave height (Hs) anomalies. In DJF, mode 1 marks the impacts of ENSO and PDO in the Pacific Ocean and AO in the North Atlantic Ocean. Mode 2 is controlled by AO, which is characterized by a dipole pattern in the North Atlantic Ocean. Mode 3 describes the AAO footprints in the Southern Ocean and the eastern Pacific Ocean. In June–August, the leading mode is influenced by AAO and AMO. Mode 2 indicates the importance of ENSO and PDO which exhibit opposite patterns in the Pacific Ocean sector of the Southern Ocean. Finally, a wavelet coherence analysis is conducted on the principal components and climate indexes, which shows their respective evolutions over the time–frequency domain.

Long term temporal trends in synoptic-scale weather conditions favoring significant tornado occurrence over the central United States.

We perform a statistical climatological study of the synoptic- to meso-scale weather conditions favoring significant tornado occurrence to empirically investigate the existence of long term temporal trends. To identify environments that favor tornadoes, we apply an empirical orthogonal function (EOF) analysis to temperature, relative humidity, and winds from the Modern-Era Retrospective analysis for Research and Applications Version 2 (MERRA-2) dataset. We consider MERRA-2 data and tornado data from 1980 to 2017 over four adjacent study regions that span the Central, Midwestern, and Southeastern United States. To identify which EOFs are related to significant tornado occurrence, we fit two separate groups of logistic regression models. The first group (LEOF models) estimates the probability of occurrence of a significant tornado day (EF2-EF5) within each region. The second group (IEOF models) classifies the intensity of tornadic days either as strong (EF3-EF5) or weak (EF1-EF2). When compared to approaches using proxies such as convective available potential energy, our EOF approach is advantageous for two main reasons: first, the EOF approach allows for the discovery of important synoptic- to mesoscale variables previously not considered in the tornado science literature; second, proxy-based analyses may not capture important aspects of three-dimensional atmospheric conditions represented by the EOFs. Indeed, one of our main novel findings is the importance of a stratospheric forcing mode on occurrence of significant tornadoes. Other important novel findings are the existence of long-term temporal trends in the stratospheric forcing mode, in a dry line mode, and in an ageostrophic circulation mode related to the jet stream configuration. A relative risk analysis also indicates that changes in stratospheric forcings are partially or completely offsetting increased tornado risk associated with the dry line mode, except in the eastern Midwest region where tornado risk is increasing.

Benchmarking performance changes in the simulation of extratropical modes of variability across CMIP generations

AbstractWe evaluate extratropical modes of variability in the three most recent phases of the Coupled Model Intercomparison Project (CMIP3, 5, and 6) to gauge improvement of climate models over time. A suite of high-level metrics is employed to objectively evaluate how well climate models simulate the qobserved Northern Annular Mode (NAM), North Atlantic Oscillation (NAO), Pacific North America pattern (PNA), Southern Annular Mode (SAM), Pacific Decadal Oscillation (PDO), North Pacific Oscillation (NPO), and North Pacific Gyre Oscillation (NPGO). We apply a Common Basis Function (CBF) approach that projects model anomalies onto observed empirical orthogonal functions (EOFs), together with the traditional EOF approach, to CMIP Historical and AMIP models. We find simulated spatial patterns of those modes have been significantly improved in the newer models, although the skill improvement is sensitive to the mode and season considered. We identify some potential contributions to the pattern improvement of certain modes (e.g., the Southern Hemisphere jet and High-top vertical coordinate), however the performance changes are likely attributed to gradual improvement of the base climate and multiple relevant processes. Less performance improvement is evident in the mode amplitude of these modes and systematic overestimation of the mode amplitude in spring remains in the newer climate models. We find that the post-dominant season amplitude errors in atmospheric modes are not limited to coupled runs but are often already evident in AMIP simulations. This suggests that rectifying the egregious post-dominant season amplitude errors found in many models can be addressed in an atmospheric-only framework making it more tractable to address in the model development process.

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.

The role of topography, soil, and remotely sensed vegetation condition towards predicting crop yield

Foreknowledge of the spatiotemporal drivers of crop yield would provide a valuable source of information to optimize on-farm inputs and maximize profitability. In recent years, an abundance of spatial data providing information on soils, topography, and vegetation condition have become available from both proximal and remote sensing platforms. Given the wide range of data costs (between USD $0−50/ha), it is important to understand where often limited financial resources should be directed to optimize field production. Two key questions arise. First, will these data actually aid in better fine-resolution yield prediction to help optimize crop management and farm economics? Second, what level of priority should stakeholders commit to in order to obtain these data? Before fully addressing these questions a remaining challenge is the complex nature of spatiotemporal yield variation. Here, a methodological framework is presented to separate the spatial and temporal components of crop yield variation at the subfield level. The framework can also be used to quantify the benefits of different data types on the predicted crop yield as well to better understand the connection of that data to underlying mechanisms controlling yield. Here, fine-resolution (10 m) datasets were assembled for eight 64 ha field sites, spanning a range of climatic, topographic, and soil conditions across Nebraska. Using Empirical Orthogonal Function (EOF) analysis, we found the first axis of variation contained 60–85 % of the explained variance from any particular field, thus greatly reducing the dimensionality of the problem. Using Multiple Linear Regression (MLR) and Random Forest (RF) approaches, we quantified that location within the field had the largest relative importance for modeling crop yield patterns. Secondary factors included a combination of vegetation condition, soil water content, and topography. With respect to predicting spatiotemporal crop yield patterns, we found the RF approach (prediction RMSE of 0.2−0.4 Mg/ha for maize) was superior to MLR (0.3−0.8 Mg/ha). While not directly comparable to MLR and RF the EOF approach had relatively low error (0.5–1.7 Mg/ha) and is intriguing as it requires few calibration parameters (2–6 used here) and utilizes the climate-based aridity index, allowing for pragmatic long-term predictions of subfield crop yield.

Assessing the Potential Benefits of the Geostationary Vantage Point for Generating Daily Chlorophyll-a Maps in the Baltic Sea

Currently, observations from low-Earth orbit (LEO) ocean color sensors represent one of the most used tools to study surface optical and biogeochemical properties of the ocean. LEO observations are available at daily temporal resolution, and are often combined into weekly, monthly, seasonal, and annual averages in order to obtain sufficient spatial coverage. Indeed, daily satellite maps of the main oceanic variables (e.g., surface phytoplankton chlorophyll-a) generally have many data gaps, mainly due to clouds, which can be filled using either Optimal Interpolation or the Empirical Orthogonal Functions approach. Such interpolations, however, may introduce large uncertainties in the final product. Here, our goal is to quantify the potential benefits of having high-temporal resolution observations from a geostationary (GEO) ocean color sensor to reduce interpolation errors in the reconstructed hourly and daily chlorophyll-a products. To this aim, we used modeled chlorophyll-a fields from the Copernicus Marine Environment Monitoring Service’s (CMEMS) Baltic Monitoring and Forecasting Centre (BAL MFC) and satellite cloud observations from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor (on board the geostationary satellite METEOSAT). The sampling of a GEO was thus simulated by combining the hourly chlorophyll fields and clouds masks, then hourly and daily chlorophyll-a products were generated after interpolation from neighboring valid data using the Multi-Channel Singular Spectral Analysis (M-SSA). Two cases are discussed: (i) A reconstruction based on the typical sampling of a LEO and, (ii) a simulation of a GEO sampling with hourly observations. The results show that the root mean square and interpolation bias errors are significantly reduced using hourly observations.

Surface impacts of the Quasi Biennial Oscillation

Abstract. Teleconnections between the Quasi Biennial Oscillation (QBO) and the Northern Hemisphere zonally averaged zonal winds, mean sea level pressure (mslp) and tropical precipitation are explored. The standard approach that defines the QBO using the equatorial zonal winds at a single pressure level is compared with the empirical orthogonal function approach that characterizes the vertical profile of the equatorial winds. Results are interpreted in terms of three potential routes of influence, referred to as the tropical, subtropical and polar routes. A novel technique is introduced to separate responses via the polar route that are associated with the stratospheric polar vortex, from the other two routes. A previously reported mslp response in January, with a pattern that resembles the positive phase of the North Atlantic Oscillation under QBO westerly conditions, is confirmed and found to be primarily associated with a QBO modulation of the stratospheric polar vortex. This mid-winter response is relatively insensitive to the exact height of the maximum QBO westerlies and a maximum positive response occurs with westerlies over a relatively deep range between 10 and 70 hPa. Two additional mslp responses are reported, in early winter (December) and late winter (February/March). In contrast to the January response the early and late winter responses show maximum sensitivity to the QBO winds at ∼ 20 and ∼ 70 hPa respectively, but are relatively insensitive to the QBO winds in between (∼ 50 hPa). The late winter response is centred over the North Pacific and is associated with QBO influence from the lowermost stratosphere at tropical/subtropical latitudes in the Pacific sector. The early winter response consists of anomalies over both the North Pacific and Europe, but the mechanism for this response is unclear. Increased precipitation occurs over the tropical western Pacific under westerly QBO conditions, particularly during boreal summer, with maximum sensitivity to the QBO winds at 70 hPa. The band of precipitation across the Pacific associated with the Inter-tropical Convergence Zone (ITCZ) shifts southward under QBO westerly conditions. The empirical orthogonal function (EOF)-based analysis suggests that this ITCZ precipitation response may be particularly sensitive to the vertical wind shear in the vicinity of 70 hPa and hence the tropical tropopause temperatures.

Millennial-scale variability in south-east Australian hydroclimate between 30,000 and 10,000 years ago

Global climate variability during the late Quaternary is commonly investigated within the framework of the ‘bipolar seesaw’ pattern of asynchronous temperature variations in the northern and southern polar latitudes. The terrestrial hydrological response to this pattern in south-eastern Australia is not fully understood, as continuous, high-resolution, well-dated proxy records for the hydrological cycle in the region are sparse. Here we present a well-dated, highly resolved record of moisture balance spanning 30000–10000 calendar years before present (30–10 ka BP), based on x-ray fluorescence and organic carbon isotope (δ13COM) measurements of a sedimentary sequence from Lake Surprise in south-eastern Australia. The data provide a locally coherent record of the hydrological cycle. Elevated Si (reflecting windblown quartz and clays), and relatively high δ13COM, indicate an extended period of relative aridity between 28 and 18.5 ka BP, interrupted by millennial-scale episodes of decreased Si and δ13COM, suggesting increased moisture balance. This was followed by a rapid deglacial shift to low Si and δ13COM at 18.5 ka BP, indicative of wetter conditions. We find that these changes are coeval with other records from south-eastern Australia and New Zealand, and use a Monte Carlo Empirical Orthogonal Function approach to extract a common trend from three high-resolution records. Our analyses suggest that drivers of the regional hydrological cycle have varied on multi-millennial time scales, in response to major shifts in global atmosphere-ocean dynamics during the last glacial-interglacial transition. Southern Ocean processes were the dominant control on hydroclimate during glacial times, via a strong influence of cold sea surface temperatures on moisture uptake and delivery onshore. Following the last deglaciation (around 18 ka BP), the southward migration of cold Southern Ocean fronts likely resulted in the establishment of conditions more like those of the present day. Millennial-scale variability in records from the region is dominated by a persistent ca. 2300-year periodicity, consistent with other records across the Southern Hemisphere mid-latitudes; however, this pervasive periodicity is not obviously linked to the ‘bipolar seesaw’ and the mechanism remains equivocal.

Chlorophyll-a Concentration Retrieval in the Optically Complex Waters of the St. Lawrence Estuary and Gulf Using Principal Component Analysis

Empirical methods based on band ratios to infer chlorophyll-a concentration by satellite do not perform well over the optically complex waters of the St. Lawrence Estuary and Gulf. Using a dataset of 93 match-ups, we explore an alternative method relying on empirical orthogonal functions (EOF) to develop an algorithm that relates the satellite-derived remote sensing reflectances to in situ chlorophyll-a concentration for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS). Results show that an accuracy of 41% at retrieving chlorophyll-a concentration can be reached using the EOF method compared to 140% for the widely-used Ocean Chlorophyll 4 (OC4v4) empirical algorithm, 53% for the Garver-Siegel-Maritorena (GSM01) and 54% for the Generalized Inherent Optical Property (GIOP) semi-analytical algorithms. This result is possible because the EOF approach is able to extract region-specific radiometric features from the satellite remote sensing reflectances that are related to absorption properties of optical components (water, coloured dissolved organic matter and chlorophyll-a) using the visible SeaWiFS channels. The method could easily be used with other ocean-colour satellite sensors (e.g., MODIS, MERIS, VIIRS, OLCI) to extend the time series for the St. Lawrence Estuary and Gulf waters.

Conditioned empirical orthogonal functions for interpolation of runoff time series along rivers: Application to reconstruction of missing monthly records

Reconstruction of missing runoff data is of important significance to solve contradictions between the common situation of gaps and the fundamental necessity of complete time series for reliable hydrological research. The conventional empirical orthogonal functions (EOF) approach has been documented to be useful for interpolating hydrological series based upon spatiotemporal decomposition of runoff variation patterns, without additional measurements (e.g., precipitation, land cover). This study develops a new EOF-based approach (abbreviated as CEOF) that conditions EOF expansion on the oscillations at outlet (or any other reference station) of a target basin and creates a set of residual series by removing the dependence on this reference series, in order to redefine the amplitude functions (components). This development allows a transparent hydrological interpretation of the dimensionless components and thereby strengthens their capacities to explain various runoff regimes in a basin. The two approaches are demonstrated on an application of discharge observations from the Ganjiang basin, China. Two alternatives for determining amplitude functions based on centred and standardised series, respectively, are tested. The convergence in the reconstruction of observations at different sites as a function of the number of components and its relation to the characteristics of the site are analysed. Results indicate that the CEOF approach offers an efficient way to restore runoff records with only one to four components; it shows more superiority in nested large basins than at headwater sites and often performs better than the EOF approach when using standardised series, especially in improving infilling accuracy for low flows. Comparisons against other interpolation methods (i.e., nearest neighbour, linear regression, inverse distance weighting) further confirm the advantage of the EOF-based approaches in avoiding spatial and temporal inconsistencies in estimated series.

Reconstructing Regional Ionospheric Electron Density: A Combined Spherical Slepian Function and Empirical Orthogonal Function Approach

The computerized ionospheric tomography is a method for imaging the Earth’s ionosphere using a sounding technique and computing the slant total electron content (STEC) values from data of the global positioning system (GPS). The most common approach for ionospheric tomography is the voxel-based model, in which (1) the ionosphere is divided into voxels, (2) the STEC is then measured along (many) satellite signal paths, and finally (3) an inversion procedure is applied to reconstruct the electron density distribution of the ionosphere. In this study, a computationally efficient approach is introduced, which improves the inversion procedure of step 3. Our proposed method combines the empirical orthogonal function and the spherical Slepian base functions to describe the vertical and horizontal distribution of electron density, respectively. Thus, it can be applied on regional and global case studies. Numerical application is demonstrated using the ground-based GPS data over South America. Our results are validated against ionospheric tomography obtained from the constellation observing system for meteorology, ionosphere, and climate (COSMIC) observations and the global ionosphere map estimated by international centers, as well as by comparison with STEC derived from independent GPS stations. Using the proposed approach, we find that while using 30 GPS measurements in South America, one can achieve comparable accuracy with those from COSMIC data within the reported accuracy (1 × 1011 el/cm3) of the product. Comparisons with real observations of two GPS stations indicate an absolute difference is less than 2 TECU (where 1 total electron content unit, TECU, is 1016 electrons/m2).

A Hybrid EOF Algorithm to Improve MODIS Cyanobacteria Phycocyanin Data Quality in a Highly Turbid Lake: Bloom and Nonbloom Condition

Extensive monitoring of cyanobacterial blooms in lakes and reservoirs can provide important protection for drinking water sources. In most inland waterbodies, phycocyanin (PC) concentrations are the best indicator of cyanobacteria distribution. PC has a characteristic absorption peak near 620 nm; however, reflectance at this wavelength is only available from MEdium Resolution Imaging Spectrometer (MERIS) and Ocean and Land Colour Instrument (OLCI) sensors. MERIS stopped providing data after 2012 and OLCI was only recently launched (February 2016). The Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua is currently the only satellite instrument that can provide well-calibrated top-of-atmosphere radiance data over an extended number of years to the present. In this study, we develop and validate a new approach based on empirical orthogonal function (EOF) to quantify PC concentrations in a turbid inland lake (Lake Chaohu, China). Based on Rayleigh-corrected reflectance data ( $R_{{\rm{rc}}}$ ) at 469, 555, 645, and 859 nm, the concentrations of PC were estimated by regression of 87 concurrent MODIS-field measurements for bloom and nonbloom conditions. The validation ( N = 93) showed R 2 = 0.40 and unbiased RMS = 60.86%. Application of the algorithm from 2000 and 2014 showed spatial distribution patterns and seasonal changes that confirmed in situ and MERIS-based studies of floating algae mats. The spatial information on PC concentrations in Lake Chaohu had a reduced sensitivity to perturbations from thin aerosols and high sediments. This EOF approach allows us for new insights in the long-term dynamics of shallow lakes and reservoirs where having a better understanding of cyanobacterial blooms is important.

Sea ice algae chlorophyll a concentrations derived from under-ice spectral radiation profiling platforms

Multiscale sea ice algae observations are fundamentally important for projecting changes to sea ice ecosystems, as the physical environment continues to change. In this study, we developed upon previously established methodologies for deriving sea ice-algal chlorophyll a concentrations (chl a) from spectral radiation measurements, and applied these to larger-scale spectral surveys. We conducted four different under-ice spectral measurements: irradiance, radiance, transmittance, and transflectance, and applied three statistical approaches: Empirical Orthogonal Functions (EOF), Normalized Difference Indices (NDI), and multi-NDI. We developed models based on ice core chl a and coincident spectral irradiance/transmittance (N = 49) and radiance/transflectance (N = 50) measurements conducted during two cruises to the central Arctic Ocean in 2011 and 2012. These reference models were ranked based on two criteria: mean robustness R2 and true prediction error estimates. For estimating the biomass of a large-scale data set, the EOF approach performed better than the NDI, due to its ability to account for the high variability of environmental properties experienced over large areas. Based on robustness and true prediction error, the three most reliable models, EOF-transmittance, EOF-transflectance, and NDI-transmittance, were applied to two remotely operated vehicle (ROV) and two Surface and Under-Ice Trawl (SUIT) spectral radiation surveys. In these larger-scale chl a estimates, EOF-transmittance showed the best fit to ice core chl a. Application of our most reliable model, EOF-transmittance, to an 85 m horizontal ROV transect revealed large differences compared to published biomass estimates from the same site with important implications for projections of Arctic-wide ice-algal biomass and primary production.

A New Method for Identifying the Pacific–South American Pattern and Its Influence on Regional Climate Variability

Abstract The Pacific–South American (PSA) pattern is an important mode of climate variability in the mid-to-high southern latitudes. It is widely recognized as the primary mechanism by which El Niño–Southern Oscillation (ENSO) influences the southeast Pacific and southwest Atlantic and in recent years has also been suggested as a mechanism by which longer-term tropical sea surface temperature trends can influence the Antarctic climate. This study presents a novel methodology for objectively identifying the PSA pattern. By rotating the global coordinate system such that the equator (a great circle) traces the approximate path of the pattern, the identification algorithm utilizes Fourier analysis as opposed to a traditional empirical orthogonal function approach. The climatology arising from the application of this method to ERA-Interim reanalysis data reveals that the PSA pattern has a strong influence on temperature and precipitation variability over West Antarctica and the Antarctic Peninsula and on sea ice variability in the adjacent Amundsen, Bellingshausen, and Weddell Seas. Identified seasonal trends toward the negative phase of the PSA pattern are consistent with warming observed over the Antarctic Peninsula during autumn, but are inconsistent with observed winter warming over West Antarctica. Only a weak relationship is identified between the PSA pattern and ENSO, which suggests that the pattern might be better conceptualized as a preferred regional atmospheric response to various external (and internal) forcings.

The Relationship between Equatorial Mixed Rossby–Gravity and Eastward Inertio-Gravity Waves. Part I

Abstract The relationship between n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) from Matsuno’s shallow-water theory on an equatorial beta plane is studied using statistics of satellite brightness temperature Tb and dynamical fields from ERA-Interim data. Unlike other observed convectively coupled equatorial waves, which have spectral signals well separated into eastward and westward modes, there is a continuum of MRG–EIG power standing above the background that peaks near wavenumber 0. This continuum is also present in the signals of dry stratospheric MRGs. While hundreds of papers have been written on MRGs, very little work on EIGs has appeared in the literature to date. The authors attribute this to the fact that EIG circulations are much weaker than those of MRGs for a given amount of divergence, making them more difficult to observe even though they strongly modulate convection. Empirical orthogonal function (EOF) and cross-spectral analysis of 2–6-day-filtered Tb isolate zonally standing modes of synoptic-scale convection originally identified by Wallace in 1971. These display antisymmetric Tb signals about the equator that propagate poleward with a period of around 4 days, along with westward-propagating MRG-like circulations that move through the Tb patterns. Further analysis here and in Part II shows that these signatures are not artifacts of the EOF approach but result from a mixture of MRG or EIG modes occurring either in isolation or at the same time.

Identifying coherent patterns of environmental change between multiple, multivariate records: an application to four 1000-year diatom records from Victoria, Australia

Empirical orthogonal functions (EOFs) of indirect archives of environmental change are increasingly used to identify coherent trends between palaeoclimate records, to separate externally forced patterns from locally driven idiosyncrasies. Lake sediments are particularly suited to such syntheses: they are abundant in most landscapes and record a wide array of information, yet local complexities often conceal or confuse the climate signal recorded at individual sites. Lake sediment parameters usually exhibit non-linear, multivariate and indirect responses to climate, therefore identifying coherent patterns between two or more lake records presents a complex challenge. Ideally, the selection of representative variables should be non-subjective and inclusive of as many different variables as possible, allowing for unexpected correlations between sites. In order to meet such demands, we propose a two-tier ordination procedure whereby site-specific (local) ordinations, obtained using Detrended Correspondence Analysis (DCA), are nested within a second, regional EOF. Using the local DCAs as representative variables allows the retention of a larger fraction of variance from each site, removes any subjectivity from variable selection and retains the potential for observing multiple, coherent signals from within and between each dataset. We explore this potential using four decadally resolved diatom records from volcanic lakes in Western Victoria, Australia. The records span the 1000 years prior to European settlement in CE 1803. Our analyses reveal at least two coherent patterns of ecological change that are manifest in each of the four datasets, patterns which may have been overlooked by a single-variable, empirical orthogonal function approach. This intra-site coherency provides a valuable step towards understanding multi-decadal hydroclimate variability in southeastern Australia.

An EOF-Based Algorithm to Estimate Chlorophyll a Concentrations in Taihu Lake from MODIS Land-Band Measurements: Implications for Near Real-Time Applications and Forecasting Models

For near real-time water applications, the Moderate Resolution Imaging Spectroradiometers (MODIS) on Terra and Aqua are currently the only satellite instruments that can provide well-calibrated top-of-atmosphere (TOA) radiance data over the global aquatic environments. However, TOA radiance data in the MODIS ocean bands over turbid atmosphere in east China often saturate, leaving only four land bands to use. In this study, an approach based on Empirical Orthogonal Function (EOF) analysis has been developed and validated to estimate chlorophyll a concentrations (Chla, μg/L) in surface waters of Taihu Lake, the third largest freshwater lake in China. The EOF approach analyzed the spectral variance of normalized Rayleigh-corrected reflectance (Rrc) data at 469, 555, 645, and 859 nm, and subsequently related that variance to Chla using 28 concurrent MODIS and field measurements. This empirical algorithm was then validated using another 30 independent concurrent MODIS and field measurements. Image analysis and radiative transfer simulations indicated that the algorithm appeared to be tolerant to aerosol perturbations, with unbiased RMS uncertainties of <80% for Chla ranging between 3 and 100 μg/L. Application of the algorithm to a total of 853 MODIS images between 2000 and 2013 under cloud-free conditions revealed spatial distribution patterns and seasonal changes that are consistent to previous findings based on floating algae mats. The current study can provide additional quantitative estimates of Chla that can be assimilated in an existing forecast model, which showed improved performance over the use of a previous Chla algorithm. However, the empirical nature, relatively large uncertainties, and limited number of spectral bands all point to the need of further improvement in data availability and accuracy with future satellite sensors.

An Empirical Orthogonal Function Iteration Approach for Obtaining Homogeneous Radiative Fluxes from Satellite Observations

Abstract Conventional observations of climate parameters are sparse in space and/or time, and the representativeness of such information needs to be optimized. Observations from satellites provide improved spatial coverage over point observations; however, they pose new challenges for obtaining homogeneous coverage. Surface radiative fluxes, the forcing functions of the hydrologic cycle and biogeophysical processes, are now becoming available from global-scale satellite observations. They are derived from independent satellite platforms and sensors that differ in temporal and spatial resolution and in the size of the footprint from which information is derived. Data gaps, degraded spatial resolution near boundaries of geostationary satellites, and different viewing geometries in areas of satellite overlap could result in biased estimates of radiative fluxes. In this study will be discussed issues related to the sources of inhomogeneity in surface radiative fluxes as derived from satellites, development of an approach to obtain homogeneous datasets, and application of the method to the widely used International Satellite Cloud Climatology Project data that currently serve as a source of information for deriving estimates of surface and top-of-the-atmosphere radiative fluxes. Introduced is an empirical orthogonal function (EOF) iteration scheme for homogenizing the fluxes. The scheme is evaluated in several ways, including comparison of the inferred radiative fluxes with ground observations, both before and after the EOF approach is applied. On the average, the latter reduces the RMS error by about 2–3 W m−2.

Analysis and estimation of soil moisture at the catchment scale using EOFs

Soil moisture patterns and dynamics are important for numerous applications such as flood forecasting, climate modeling, and management of agricultural lands. Unfortunately, widespread observations of soil moisture are not currently available at the spatial scale of most of these applications. Given these data limitations and the complexity of soil moisture dynamics, there is a need to gain a better understanding of soil moisture patterns and to develop methods that can efficiently estimate these patterns from limited observations. In this paper, we use Empirical Orthogonal Function (EOF) analysis to study the Tarrawarra soil moisture dataset from Australia. EOF analysis partitions the observed variation into a series of time-invariant spatial patterns (EOFs) that can be multiplied by temporal varying (but spatially constant) coefficients and summed to reconstruct observed soil moisture patterns. Using this approach, we identify two spatial patterns underlying soil moisture variability at Tarrawarra, which supports previous contentions that the spatial patterns are controlled by local soil properties in wet and dry conditions and topographic characteristics during intermediate conditions. We also use the EOF analysis to identify points whose variability is most representative of each of the underlying spatial patterns and thus can be used to monitor these distinct modes of variability. Finally, we show that the EOF approach can be used to estimate soil moisture patterns for unobserved times if a field campaign has collected detailed soil moisture observations for a limited time period in the past.

Using meteorological data for reconstruction of annual runoff series over an ungauged area: Empirical orthogonal function approach to Moldova–Southwest Ukraine region

The water-management transformation of runoff and the prospective change of global climate necessitate studying the climate forcing associated with runoff processes. This paper presents some quantitative estimations for the role of climatic factors in this process on an example of the Moldova–Southwest Ukraine region. Using empirical orthogonal functions, we establish the contribution of the annual evaporation, annual precipitation, and warm- and cold-season precipitation to the annual runoff for arid-zone rivers. An efficient approach for the reconstruction of natural annual runoff time series is developed and tested. The problems relating to (i) the estimation of annual runoff for rivers with lacking or deficient observational data, (ii) the definition of climate forcing for natural runoff parameters, and (iii) the modelling of annual runoff time series are solved.