Instantaneous Observations Research Articles

A web interface for griding arbitrarily distributed in situ data based on Data-Interpolating Variational Analysis (DIVA)

Abstract. Spatial interpolation of observations on a regular grid is a common task in many oceanographic disciplines (and geosciences in general). It is often used to create climatological maps for physical, biological or chemical parameters representing e.g. monthly or seasonally averaged fields. Since instantaneous observations can not be directly related to a field representing an average, simple spatial interpolation of observations is in general not acceptable. DIVA (Data-Interpolating Variational Analysis) is an analysis tool which takes the error in the observations and the typical spatial scale of the underlying field into account. Barriers due to the coastline and the topography in general and also currents estimates (if available) are used to propagate the information of a given observation spatially. DIVA is a command-line driven application written in Fortran and Shell Scripts. To make DIVA easier to use, a web interface has been developed (http://gher-diva.phys.ulg.ac.be). Installation and compilation of DIVA is therefore not required. The user can directly upload the data in ASCII format and enter several parameters for the analysis. The analyzed field, location of the observations, and the error mask are presented as different layers using the Web Map Service protocol. They are visualized in the browser using the Javascript library OpenLayers allowing the user to interact with layers (for example zooming and panning). Finally, the results can be downloaded as a NetCDF file, Matlab/Octave file and Keyhole Markup Language (KML) file for visualization in applications such as Google Earth.

Calculating the optimal time when albedo approximates its daily average: an example using soil surfaces with various roughnesses at different latitudes

This paper describes how the blue-sky albedo of soil varies during the whole year from midday to sunset under clear-sky conditions. A hemispherical-directional reflectance model was used to calculate albedo variations associated with smooth, moderate and rough soil surfaces, located between the latitude angles of 75° in the Northern and Southern Hemispheres. We calculate the time when the albedo, acquired by an instantaneous observation, best represents its daily averaged value. This optimal time range is assessed in the context of remote-sensing satellite technology.

Seasonal and regional variability of cloud liquid water path in northwestern China derived from MODIS/CERES observations

This article describes the seasonal and regional variability of cloud liquid water path (LWP) in northwestern China. The regions of interest are: the area influenced by the Asian monsoon, the Tianshan Mountains, the Qilian Mountains and the Taklimakan Desert. The results presented here were derived from the instantaneous observations of cloud LWP from National Aeronautics and Space Administration (NASA) Clouds and the Earth's Radiant Energy System (CERES) Single Scanner Footprint (SSF) Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) Edition 1B data from July 2002 to June 2004, and reflect more detailed subregional features than previous results from International Satellite Cloud Climatology Project (ISCCP) D2 monthly mean data. The seasonal and annual variation in cloud LWP is found to be significant in northwestern China, even within the same climate region.

How do temporal stimulus correlations influence the performance of population codes?

Event Abstract Back to Event How do temporal stimulus correlations influence the performance of population codes? Kamiar Rahnama Rad1* and Liam Paninski1 1 Columbia University, United States It has long been argued that many key questions in neuroscience can best be posed in information-theoretic terms; the efficient coding hypothesis discussed by Attneave, Barlow, Atick, et al represents perhaps the best-known example. Answering these questions quantitatively requires us to compute the Shannon information rate of neural channels, whether numerically using experimental data or analytically in mathematical models. The non-linearity and non-Gaussianity of neural responses has complicated these calculations, particularly in the case of stimulus distributions with temporal dynamics and nontrivial correlation structure. In this work we extend a method proposed in [1] that allows us to compute the information rate analytically in some cases. In our approach the stimulus is modeled as a temporally correlated stationary process. Analytical results are available in both the high and low signal-to-noise (SNR) regimes: the former corresponds to the case in which a large population of neurons responds strongly to the stimulus, while the latter implies that the available neurons are only weakly tuned to the stimulus properties, or equivalently that the stimulus magnitude is relatively small. In intermediate SNR regimes, good numerical approximations to the information rate are available using efficient forward-backward decoding methods and Laplace approximations [2,3]. We find that when the number of neurons increases unboundedly, the mutual information for temporarily correlated stimuli has a simple form depending only on the Fisher information, paralleling the classical connection between Fisher and Shannon information for static stimuli [4]. For finite-size populations we are able to calculate the performance difference between a decoder based solely on temporally instantaneous observations and one which integrates temporal observations; interestingly, in both the high- and low-SNR regimes, a simple decoder which only includes temporally local neural responses is able to optimally extract information about the stimuli.

Social dynamics and individual plasticity of infant care behavior in cooperatively breeding cotton‐top tamarins

Individual variation in infant caretaking behavior is prevalent among marmoset and tamarin monkeys. Although most group members participate in infant care, the timing and amount provided differs greatly. In this study, we quantified general trends in infant carrying behavior by using a longitudinal database that included 11 years of instantaneous scan observations following 80 births of cotton-top tamarins. Using detailed focal observations on a subset of the same families (10 births) we identified influences that affected expression of infant care at the group and individual levels. Fathers were the primary carriers and paternal carry time gradually decreased with increasing infant age. Paternal carry time also decreased significantly with an increasing number of older sibling helpers. Most fathers began to carry on the first day postpartum. However, we report circumstances in which fathers delayed carrying until almost a month postpartum. Fathers retrieved infants the most, although adult brothers' rates of retrievals peaked and surpassed fathers' rates during week 4 postpartum. Fathers delayed rejection of infants until week 4, whereas mothers rejected infants immediately and throughout the eight weeks. Nonetheless, infants climbed onto their mothers more than onto any other family member. Mothers showed a high initial investment in carrying during the first two weeks, decreasing quickly thereafter. Maternal contributions to infant carrying remained low and relatively consistent regardless of group size. However, mothers dramatically increased their infant carrying behavior in families in which fathers were absent. Older siblings cared for infants more than did younger siblings, and brothers retrieved and carried infants more than did sisters. Individual expression of infant care changed to accommodate infant needs and changed according to varying social dynamics and circumstances across litters.

Regional estimation of daily to annual regional evapotranspiration with MODIS data in the Yellow River Delta wetland

Abstract. Evapotranspiration (ET) from the wetland of the Yellow River Delta (YRD) is one of the important components in the water cycle, which represents the water consumption by the plants and evaporation from the water and the non-vegetated surfaces. Reliable estimates of the total evapotranspiration from the wetland is useful information both for understanding the hydrological process and for water management to protect this natural environment. Due to the heterogeneity of the vegetation types and canopy density and of soil water content over the wetland (specifically over the natural reserve areas), it is difficult to estimate the regional evapotranspiration extrapolating measurements or calculations usually done locally for a specific land cover type. Remote sensing can provide observations of land surface conditions with high spatial and temporal resolution and coverage. In this study, a model based on the Energy Balance method was used to calculate daily evapotranspiration (ET) using instantaneous observations of land surface reflectance and temperature from MODIS when the data were available on clouds-free days. A time series analysis algorithm was then applied to generate a time series of daily ET over a year period by filling the gaps in the observation series due to clouds. A detailed vegetation classification map was used to help identifying areas of various wetland vegetation types in the YRD wetland. Such information was also used to improve the parameterizations in the energy balance model to improve the accuracy of ET estimates. This study showed that spatial variation of ET was significant over the same vegetation class at a given time and over different vegetation types in different seasons in the YRD wetland.

Analysis of boundary layer separation phenomena by infrared thermography Use of acoustic and/or mechanical devices to avoid or reduce the laminar separation bubble effects

Aerodynamic bodies operating at low Reynolds numbers are normally subjected to local boundary layer separation phenomena; these strongly modify airfoils behavior. The body geometry and the incoming flow angle of attack define the pressure pattern over the surface in a way that there will be sections with a favorable pressure gradient and others with a negative one, the latter causing the flow to slow down and sometimes to separate. A laminar separation, followed by a turbulent transition in the separated shear layer and a subsequent turbulent reattachment, causes the Laminar Separation Bubble (LSB) phenomenon. The LSB presence induces an aerodynamic drag increase and an efficiency decrease; this problem is of interest in many application fields including wind turbine energy production, where a LSB may induce less energy output and occasionally mechanical problems due to pulsating pressure variations (bubble bursting phenomena). This paper illustrates an infrared measurement approach, useful for the instantaneous observation of the boundary layer pattern on an airfoil surface, as well as an analysis of the effects of both an acoustic and a mechanical system on the behavior of the LSB. These latter induce disturbances in the developing boundary layer in order to promote the turbulent transition and contrasting the LSB presence. The first one involves the use of a subwoofer and the analysis is performed on an Eppler 205 airfoil; the second one makes use a Micro Electro Mechanical System (MEMS) and the IR observation is carried out on a WT01 airfoil developed for small wind turbines (about 1 kW). The results show a pronounced effectiveness for both the methodologies particularly when using MEMS.

Tutorial: Pattern recognition in acoustic signal processing.

This tutorial presents a framework for understanding and comparing applications of pattern recognition in acoustic signal processing. Representative examples will be delimited by two binary features: (1) regression versus classification (inferred variables are continuous versus discrete); (2) instantaneous versus dynamic (inference algorithms consider only an instantaneous observation vector versus inference algorithms integrate observations with knowledge of system dynamics). (1. Regression) problems include imaging and sound source tracking using a device with unknown properties and inverse problems, e.g., articulatory estimation from speech audio. (2. Classification) problems include, e.g., classification of animal and human vocalizations and nonspeech audio events. Instantaneous classification and regression are performed using a universal approximator (neural network, Gaussian mixture, classification, and regression tree), regularized, if necessary, to reduce generalization error (resulting in a support vector machine, regularized neural net, pruned classification tree, or AdaBoost). Dynamic classification and regression are done by imposing a prior to characterize system dynamics. Depending on the prior, the resulting model may be called a hidden Markov model, finite state transducer, dynamic Bayesian network, or conditional random field (dynamic classification), or a Kalman filter, extended Kalman filter, or switching Kalman filter (dynamic regression).

A comparison of MODIS-derived cloud amount with visual surface observations

Two main sources for global cloud climatologies are visual surface observations and observations made by spaceborne sensors. Satellite observations compared with surface data show in most cases differences ranging from − 15% up to − 1%, depending on sensor and observation conditions. These differences are partially controlled by sensors' cloud detection capabilities — a higher number of spectral bands and higher spatial resolution are believed to allow discrimination of clouds from land/ocean/snow background. A Moderate-Resolution Imaging Spectroradiometer (MODIS) produces images of the atmosphere in 36 spectral bands with a spatial resolution of 250–1000 m, thus having a capacity for cloud detection far more advanced than other operating sensors. In this study, instantaneous MODIS cloud observations were compared with surface data for Poland for January (winter) and July (summer) 2004. It was found that MODIS observed 4.38% greater cloud amount in summer conditions and 7.28% in winter conditions. Differences were greater at night (7–8%) than in daytime (0.5–7%) and correlations ranged between 0.577 (winter night) and 0.843 (winter day, summer day and night).

Control of quantum dynamics by optimized measurements

Quantum measurements are considered for optimal control of quantum dynamics with instantaneous and continuous observations utilized to manipulate population transfer. With an optimal set of measurements, the highest yield in a two-level system can be obtained. The analytical solution is given for the problem of population transfer by measurement-assisted coherent control in a three-level system with a dynamical symmetry. The anti-Zeno effect is recovered in the controlled processes. The demonstrations in the paper show that suitable observations can be powerful tools in the manipulation of quantum dynamics.

Development of an Atlantic Canadian Coastal Water Level Neural Network Model

Abstract Coastal water-level information is essential for coastal zone management, navigation, and oceanographic research. However, long-term water-level observations are usually only available at a limited number of locations. This study discusses a complementary and simple neural network (NN) approach, to predict water levels at a specified coastal site from the data gathered at other nearby or remote permanent stations. A simple three-layer, feed-forward, back-propagation network and a neural network ensemble, named Atlantic Canadian Coastal Water Level Neural Network (ACCSLENNT) models, was developed to correlate the nonlinear relationship of sea level data among stations by learning from their historical characteristics. Instantaneous hourly observations of water level from five stations along the coast of Atlantic Canada—Argentia, Belledune, Halifax, North Sydney, and St. John’s—are used to formulate and validate the ACCSLENNT models. Qualitative and quantitative comparisons of the network output with target observations showed that despite significant changes in sea level amplitudes and phases in the study area, appropriately trained NN models could provide accurate and robust long-term predictions of both tidal and nontidal (tide subtracted) water levels when only short-term data are available. The robust results indicate that the NN models in conjunction with limited permanent stations are able to supplement long-term historical water-level data along the Atlantic Canadian coast. Because field data collection is usually expensive, the ACCSLENNT models provide a cost-effective alternative to obtain long-term data along Atlantic Canada.

The Effectiveness of an Established Sanctuary Zone for Reducing Human Disturbance to Australian Sea Lions (Neophoca Cinerea) at Carnac Island, Western Australia

This study tested the effectiveness of a recently established sanctuary zone on Carnac Island (Western Australia) in reducing human disturbances to Australian sea lions (Neophoca cinerea). Several methods of recording behaviors were also tested to clarify their adequacy for detecting human disturbances. Observations made between March 2005 and September 2006 (98 observations over 16 days) indicated that a wireless camera was effective for monitoring sea lions unobtrusively, and continuous and instantaneous observations were both generally effective in monitoring levels of human disturbance. The sanctuary zone was ineffective in that sea lions hauled out more often in the adjacent recreational zone, even though the sanctuary was established based on previous observations. This study concluded that sea lions are more likely to haul out where environmental attributes along a beach are suitable. Because environmental conditions are variable over time, a fixed sanctuary zone will only aid in reducing impacts when conditions are suitable in that zone. The authors recommend that future sanctuaries should include entire stretches of useable beach to be effective.

Regional mapping of gross light-use efficiency using MODIS spectral indices

Direct estimation of photosynthetic light-use efficiency (LUE) from space would be of significant benefit to LUE-based models which use inputs from remote sensing to estimate terrestrial productivity. The Photochemical Reflectance Index (PRI) has shown promise in tracking LUE at the leaf- to small canopy levels, but its use at regional to global scales still remains a challenge. In this study, we used different formulations of PRI calculated from the MODIS ocean band centered at 531 nm and a set of alternative reference bands at 488, 551, and 678 nm to explore the relationship between PRI and LUE where LUE was measured at eight eddy covariance flux towers located in the boreal forest of Saskatchewan, Canada. The magnitude and variability of LUE was significantly lower at the times when useful MODIS ocean band images were available (i.e. around midday under clear-sky conditions) relative to the rest of the growing season. PRI 678 (reference band at 678 nm) showed the strongest relationship ( r 2 = 0.70) with LUE 90a (i.e. 90-minute mean LUE calculated using Absorbed Photosynthetically Active Radiation, APAR), but only when all sites were combined. Overall, the relationships between the MODIS PRIs and LUE 90a were always stronger for observations closer to the backscatter direction and there were no significant differences in the strength of the correlations whether LUE was calculated based on incident PAR or on APAR. Predictions of ecosystem photosynthesis at the time of the MODIS overpasses were significantly improved by multiplying either PAR or APAR by MODIS PRI ( r 2 improved from 0.09 to 0.44 and 0.54 depending on the PRI formulation). We used our PRI-LUE model to create a regional LUE 90a map for the three cover types covering 47,500 km 2 around the flux sites. The MODIS PRI-derived LUE 90a map appeared to capture more realistic spatial heterogeneity of LUE across the landscape compared to a daily LUE map derived using the look-up table in the MODIS GPP (MOD17) algorithm. While our LUE map is only a snapshot of minimum regional LUE 90a values, with appropriate gap-filling methods it could be used to improve regional-scale monitoring of GPP. Moreover, the strong relationship between midday and daily LUE on clear days ( r 2 = 0.93) indicates that instantaneous MODIS observations of LUE 90a could be used to estimate daily LUE. Finally, pixel shadow fraction from the 5-Scale geometric-optical model was closely related to both MODIS PRI and tower-derived LUE suggesting that differences in stand leaf area and in diffuse illumination among flux sites play a role in the relationship we observed between LUE and MODIS PRI.

Observation-assisted optimal control of quantum dynamics

This paper explores the utility of instantaneous and continuous observations in the optimal control of quantum dynamics. Simulations of the processes are performed on several multilevel quantum systems with the goal of population transfer. Optimal control fields are shown to be capable of cooperating or fighting with observations to achieve a good yield, and the nature of the observations may be optimized to more effectively control the quantum dynamics. Quantum observations also can break dynamical symmetries to increase the controllability of a quantum system. The quantum Zeno and anti-Zeno effects induced by observations are the key operating principles in these processes. The results indicate that quantum observations can be effective tools in the control of quantum dynamics.

The Frequency of Extreme Rain Events in Satellite Rain-Rate Estimates and an Atmospheric General Circulation Model

Abstract The frequency distributions of surface rain rate are evaluated in the Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave/Imager (SSM/I) satellite observations and the NOAA/GFDL global atmosphere model version 2 (AM2). Instantaneous satellite rain-rate observations averaged over the 2.5° latitude × 2° longitude model grid are shown to be representative of the half-hour rain rate from single time steps simulated by the model. Rain-rate events exceeding 10 mm h−1 are observed by satellites in most regions, with 1 mm h−1 events occurring more than two orders of magnitude more frequently than 10 mm h−1 events. A model simulation using the relaxed Arakawa–Schubert (RAS) formulation of cumulus convection exhibits a strong bias toward many more light rain events compared to the observations and far too few heavy rain events. A simulation using an alternative convection scheme, which includes an explicit representation of mesoscale circulations and an alternative formulation of the closure, exhibits, among other differences, an order of magnitude more tropical rain events above the 5 mm h−1 rate compared to the RAS simulation. This simulation demonstrates that global atmospheric models can be made to produce heavy rain events, in some cases even exceeding the observed frequency of such events. Additional simulations reveal that the frequency distribution of the surface rain rate in the GCM is shaped by a variety of components within the convection parameterization, including the closure, convective triggers, the spectrum of convective and mesoscale clouds, and other parameters whose physical basis is currently only understood to a limited extent. Furthermore, these components interact nonlinearly such that the sensitivity of the rain-rate distribution to the formulation of one component may depend on the formulation of the others. Two simulations using different convection parameterizations are performed using perturbed sea surface temperatures as a surrogate for greenhouse gas–forced climate warming. Changes in the frequency of rain events greater than 2 mm h−1 associated with changing the convection scheme in the model are greater than the changes in the frequency of heavy rain events associated with a 2-K warming using either model. Thus, uncertainty persists with respect to simulating intensity distributions for precipitation and projecting their future changes. Improving the representation of the frequency distribution of rain rates will rely on refinements in the formulation of cumulus closure and the other components of convection schemes, and greater certainty in predictions of future changes in both total rainfall and in rain-rate distributions will require additional refinements in those parameterizations that determine the cloud and water vapor feedbacks.

Effect of environmental enrichment at two stages of development on belly nosing in piglets weaned at fourteen days1

The incidence of belly nosing-related behaviors was studied in 480 piglets weaned at 14 d and provided with environmental enrichment during preweaning, postweaning, or both. Pen enrichment was achieved by providing a foam rubber mat on the pen wall (nose), rubber nipples (suck), a Bite-Rite Tail Chew (bite), a soil-filled tray (root), or no enrichment (control). Instantaneous scan sampling observations, at 5-min intervals, were conducted for 8 h (i.e., 96 scans/observation day) at 3, 10, 19, 26, and 33 d. Observations during the preweaning phase were made to determine the number of piglets lying, standing, nursing, and interacting with environmental enrichment. During the postweaning phase, observations were made to determine the number of piglets belly nosing, belly sucking, other nosing and sucking (other), biting, eating, drinking, and interacting with enrichment. The time-course for belly nosing was confirmed, with the behavior rising by 19 d, peaking by 26 d, and decreasing by 33 d (P < 0.001). Only nosing enrichment was found to reduce the incidence of belly-nosing behavior (3.8%) compared with controls (6.6%; P < 0.001). Pigs provided root enrichment spent more time manipulating their enrichment devices (30.2%) compared with all other enrichment groups (P < 0.001). Providing enrichment relevant to a particular behavioral vice as it commences, or shortly afterward, may have the greatest effect on reducing the incidence of that vice during the nursery period.

Instantaneous cloud overlap statistics in the tropical area revealed by ICESat/GLAS data

This study uses ICESat/GLAS instantaneous observations from 29 September to 18 November 2003 to investigate cloud overlap statistics between 10°S–20°N. The results show that 75.1% of profiles detect clouds: 46.5% are single layer and 28.6% multilayer clouds (cloud layers are separated by 0.5km). Using a definition of cloud type based on cloud heights and laser attenuation information, cloud overlap statistics are derived by analyzing 96.4% of the cloudy profiles. The most frequent overlap occurs between cirrus clouds and boundary layer clouds, which accounts for 31.88% of boundary clouds. 23.8% of deep convection has overlying cirrus clouds. We find that differences exist between the cloud overlap fraction from the GLAS observations and one calculated from the random overlap assumption commonly used by climate models.

Locomotor behavior and long bone morphology in individual free-ranging chimpanzees

We combine structural limb data and behavioral data for free-ranging chimpanzees from Taï (Ivory Coast) and Mahale National Parks (Tanzania) to begin to consider the relationship between individual variation in locomotor activity and morphology. Femoral and humeral cross sections of ten individuals were acquired via computed tomography. Locomotor profiles of seven individuals were constructed from 3387 instantaneous time-point observations (87.4 hours). Within the limited number of suitable chimpanzees, individual variation in locomotor profiles displayed neither clear nor consistent trends with diaphyseal cross-sectional shapes. The percentages of specific locomotor modes did not relate well to diaphyseal shapes since neither infrequent nor frequent locomotor modes varied consistently with shapes. The percentage of arboreal locomotion, rather than estimated body mass, apparently had comparatively greater biological relevance to variation in diaphyseal shape. The mechanical consequences of locomotor modes on femoral and humeral diaphyseal shapes (e.g., orientation of bending strains) may overlap between naturalistic modes more than currently is recognized. Alternatively, diaphyseal shape may be unresponsive to mechanical demands of these specific locomotor modes. More data are needed in order to discern between these possibilities. Increasing the sample to include additional free-ranging chimpanzees, or primates in general, as well as devoting more attention to the mechanics of a greater variety of naturalistic locomotor modes would be fruitful to understanding the behavioral basis of diaphyseal shapes.

Submillimeter-wave and [formula omitted] observations of the event on 28 November, 2001

We present a detailed study of a 1B/M6.9 impulsive flare combining high time resolution (1 ms) and instantaneous emission source localization observations at submillimeter frequencies (212 GHz), obtained with the solar submillimeter telescope (SST), and H α data from the H α solar telescope for argentina (HASTA). The flare, starting at 16:34 UT, occurred in active region (AR) 9715 (NOAA number) on November 28, 2001, and was followed by an H α surge. We complement our data with magnetograms from the Michelson Doppler Imager (SOHO/MDI). SST observed a short impulsive burst at 212 GHz, presenting a weak bulk emission (of about 90 sfu) composed of a few shorter duration ( < 5 s ) structures. The integrated H α and the 212 GHz light curves present a remarkable agreement during the impulsive phase of the event. The delay between both curves stays below 12 s (the time resolution of the H α telescope). The flare as well as the surge are linked to new flux emergence very close to the main AR bipole. Taking into account the AR magnetic field evolution, we infer that magnetic field reconnection, occurring at low coronal levels, could have been at the origin of the flare; while in the case of surge this would happen at the chromospheric level.

Precipitation Distribution in Tropical Cyclones Using the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager: A Global Perspective

TRMM microwave imager rain estimates are used to quantify the spatial distribution of rainfall in tropical cyclones (TCs) over the global oceans. A total of 260 TCs were observed worldwide from 1 January 1998–31 December 2000, providing 2121 instantaneous TC precipitation observations. To examine the relationship between the storm intensity, its geographical location, and the rainfall distribution, the dataset is stratified into three intensity groups and six oceanic basins. The three intensity classes used in this study are tropical storms (TSs) with winds <33 m s−1, category 1–2 hurricane-strength systems (CAT12) with winds from 34–48 m s−1, and category 3–5 systems (CAT35) with winds >49 m s−1. The axisymmetric component of the TC rainfall is represented by the radial distribution of the azimuthal mean rainfall rates (R). The mean rainfall distribution is computed using 10-km annuli from the storm center to a 500-km radius. The azimuthal mean rain rates vary with storm intensity and from basin to basin. The maximum R is about 12 mm h−1 for CAT35, but decreases to 7 mm h−1 for CAT12, and to 3 mm h−1 for TS. The radius from the storm center of the maximum rainfall decreases with increasing storm intensity, from 50 km for TS to 35 km for CAT35 systems. The asymmetric component is determined by the first-order Fourier decomposition in a coordinate system relative to the storm motion. The asymmetry in TC rainfall varies significantly with both storm intensity and geographic locations. For the global average of all TCs, the maximum rainfall is located in the front quadrants. The location of the maximum rainfall shifts from the front-left quadrant for TS to the front-right for CAT35. The amplitude of the asymmetry varies with intensity as well; TS shows a larger asymmetry than CAT12 and CAT35. These global TC rainfall distributions and variability observed in various ocean basins should help to improve TC rainfall forecasting worldwide.