A multi-sensor climatological view of double ITCZs over the Indian Ocean

We characterize the climatological features of the double inter-tropical convergence zones (DITCZs) over the western Indian Ocean during November–December by a synergistic analysis of the Hamburg Ocean Atmosphere Parameters and Fluxes from Satellite (HOAPS III) data (1988–2005) and the National Aeronautics and Space Administration's (NASA's) A-Train data (2002–2009). We investigate rainfall, freshwater flux and cloud liquid water, cloud fraction and relative humidity over the DITCZs. In addition, the daily rainfall data from the Global Precipitation Climatology Project (GPCP) are used to document the DITCZs during the El Niño southern oscillation (ENSO) events. An analysis of the GPCP data shows that the DITCZs are clearly discernible during strong ENSO events (1997, 2002 and 2006), in sharp contrast to the DITCZs in the eastern Pacific Ocean, where they are absent during ENSOs. Further, these convergence zones on either side of the equator are of short duration, approximately 3–6 pentads during November and December. All satellite sensor data sets consistently capture the major features of DITCZs. As an accurate simulation of DITCZs in coupled global climate models remains a challenge, the results from the present study would provide a platform for evaluating these models.     

A comparative assessment of IRS-P4 (MSMR)-derived sea surface temperature and sea surface wind speed over the north Indian Ocean

Indian Remote Sensing Satellite (IRS-P4) multi-frequency scanning microwave radiometer (MSMR) provides geophysical parameters like sea surface temperature (SST), sea surface wind speed (SSWS), integrated water vapour (IWV) and cloud liquid water (CLW). The retrieval procedure of these parameters given by Gohil et al. (2000 Gohil, B.S., Mathur, A.K. and Varma, A.K. Geophysical parameter retrieval over global oceans from IRS-P4 (MSMR). Preprints, Fifth Pacific Ocean Remote Sensing Conference. December5–82000, Goa. pp.207–211. Goa, , India: National Institute of Oceanography.  [Google Scholar], Geophysical parameter retrieval over global oceans from IRS-P4 (MSMR). In Preprints, Fifth Pacific Ocean Remote Sensing Conference, 5–8 December 2000, Goa, India (Goa: National Institute of Oceanography), pp. 207–211) was summarized by Sharma et al. (2002 Sharma, R., Babu, K.N., Mathur, A.K. and Ali, M.M. 2002. Identification of large scale atmospheric and oceanic features from IRS-P4 multifrequency scanning microwave radiometer: preliminary results. Journal of Atmospheric and Oceanic Technology, 19: 1127–1134. [Crossref], [Web of Science ®] , [Google Scholar], Identification of large scale atmospheric and oceanic features from IRS-P4 multifrequency scanning microwave radiometer: preliminary results. Journal of Atmospheric and Oceanic Technology, 19, pp. 1127–1134) and Jena (2007 Jena, B. 2007. Studies on the retrieval, validation and applications of geophysical parameters from IRS-P4 (MSMR) data, Orissa: PhD thesis, Berhampur University.  [Google Scholar], Studies on the retrieval, validation and applications of geophysical parameters from IRS-P4 (MSMR) data. PhD thesis, Berhampur University, Orissa). Demonstration of self-consistency of these parameters has primary scientific importance. This article deals with the validation of MSMR geophysical parameters such as SST and SSWS with in situ observations (buoy data) over the north Indian Ocean during 2000. Result shows that the MSMR-derived SST and SSWS can be utilized for several applications because of their reasonable accuracy and coverage even under cloudy condition.     

A parallel computing engine for a class of time critical processes

This paper focuses on the efficient parallel implementation of systems of numerically intensive nature over loosely coupled multiprocessor architectures. These analytical models are of significant importance to many real-time systems that have to meet severe time constants. A parallel computing engine (PCE) has been developed in this work for the efficient simplification and the near optimal scheduling of numerical models over the different cooperating processors of the parallel computer. First, the analytical system is efficiently coded in its general form. The model is then simplified by using any available information (e.g., constant parameters). A task graph representing the interconnections among the different components (or equations) is generated. The graph can then be compressed to control the computation/communication requirements. The task scheduler employs a graph-based iterative scheme, based on the simulated annealing algorithm, to map the vertices of the task graph onto a Multiple-Instruction-stream Multiple-Data-stream (MIMD) type of architecture. The algorithm uses a nonanalytical cost function that properly considers the computation capability of the processors, the network topology, the communication time, and congestion possibilities. Moreover, the proposed technique is simple, flexible, and computationally viable. The efficiency of the algorithm is demonstrated by two case studies with good results.     

Analysis of freshwater flux climatology over the Indian Ocean using the HOAPS data

Estimation of freshwater flux over a certain region is very difficult, as it needs both accurate evaporation and precipitation rates over the study area. Over the Indian Ocean (IO), the precipitation estimates are totally lacking or unknown due to the lack of in-situ measurements. In the present study, we examine the climatology and the annual cycle of the freshwater flux over the IO using the newly available Hamburg Ocean Atmosphere Parameters and Fluxes from Satellite data (HOAPS). This data set has been derived from passive microwave and infrared satellite data utilising the data from the Special Sensor Microwave/Imager (SSM/I) and the Advanced Very High Resolution Radiometer (AVHRR). We have compared the freshwater flux estimates from HOAPS data set with the earlier estimates to see how they differ from the older estimates. The evaporation rates from HOAPS are significantly different from the earlier estimates. The annual cycle of freshwater flux shows that the Bay of Bengal (BB) is a moisture convergence region most of the year as compared to the Arabian Sea (AS), which is a moisture flux divergence region. Further, the build-up of moisture in the southern Indian Ocean (SIO) is also clearly seen from March to June, indicating its major role in the summer monsoon activity over the Indian subcontinent. An analysis of monthly mean freshwater flux indicates that a small part of the southwest coast of India and southern parts of the BB region receives freshwater in April almost 2 months ahead of the onset of the summer monsoon.     

On some aspects of precipitation over the tropical Indian Ocean using satellite data

The annual and inter‐annual variability of precipitation over the tropical Indian Ocean is studied for the period 1979–1997, using satellite data from a variety of sensors. The Climate Prediction Center Merged Analysis Precipitation (CMAP), Microwave Sounding Unit (MSU) estimates of rainfall had better correlation with the island rainfall data than the National Centers for Environmental Prediction/National Center for Atmospheric Research Reanalysis (NRA) estimates. A comparison of the mean annual rainfall by different estimates (CMAP, MSU, NRA and GPCP (Global Precipitation Climatology Programme)) showed significant differences with the CMAP, GPCP and MSU estimates depicting maximum off the Indonesian Islands whilst the NRA exhibited maximum in the southern part of the Bay of Bengal and equatorial Indian Ocean. A study of the inter‐annual variability of the monsoon rainfall using the monthly CMAP data over the tropical Indian Ocean for different study areas, namely, Arabian Sea (AS), Bay of Bengal (BB), south Indian Ocean (SIO) and Indian Ocean (IO) showed significant differences during deficit years (1979, 1982, 1986 and 1987), excess monsoon years (1983 and 1988) and also during El Nino Southern Oscillation (ENSO) years (1982, 1987, 1992 and 1997). An analysis of the rainfall anomalies showed positive and negative anomalies in the north‐eastern Bay of Bengal during the summer season of deficit (1986) and excess (1988) monsoon years respectively, whilst the eastern equatorial Indian Ocean showed large positive and negative rainfall anomalies during the autumn season of El Niño years, 1987 (deficit monsoon) and 1997 (normal monsoon) respectively.     

Characteristic patterns of QuikScat-based wind stress and turbulent heat flux in the tropical Indian Ocean

Using QuikScat-based vector wind data for 1999-2003, surface wind stress and turbulent heat (Q) have been mapped for the tropical Indian Ocean (IO) to understand their seasonal variability. During July wind stress is enhanced by ∼ 70% in the Arabian Sea compared to that during January. The Arabian Sea experiences a large Q loss (150-200 W/m²) during the summer and winter monsoons, which is nearly 1.3 times of that in the Bay of Bengal. The southeasterlies are strengthened during the southern hemisphere winter. Empirical Orthogonal Function analysis captures different phases of monsoon-induced variability in wind stress and Q, ranging from seasonal to high-frequency perturbations. Coherency between time coefficients of EOF-1 for wind stress and Q suggests that former leads the latter with a temporal lag of 20-40 days for period > 322 days. At high frequencies (< 21 days) Q leads wind stress with a temporal lag of 2 days. Possible explanation for wind stress leading Q over an annual time scale is offered based on the marine atmospheric boundary layer physics and pre-conditioned ocean surface, while on shorter time scales (21 days) ocean thermodynamics through mixed layer processes cause Q to lead wind stress.     

On computing the transitive closure of a relation

Summary An algorithm is presented for computing the transitive closure of an arbitrary relation which is based upon Tarjan's algorithm [7] for finding the strongly connected components of a directed graph. A new formulation, justifying a somewhat simplified statement of the latter, characterises weaker restrictions on the form of the graph traversal than Tarjan's depth first conditions and reveals aspects of the behaviour of this algorithm which have been obscure hitherto. If V is the number of vertices in the directed graph representing the relation then the worst case behaviour, O(V ³) is inferior to existing algorithms [1, 2] which require O(V ³/log V) and operations respectively. The best case performance, O(V ²) operations, is better. Viewed in this way, it is similar to other algorithms [5, 6, 8] but it combines the improved efficiency in the presence of strongly connected components which characterises the algorithms in [5, 6] with the advantages of Warshall's algorithm [8], namely, succinctness, a single traversal of the directed graph and ability to exploit the availability of Boolean vector operations. This research was begun while the authors were visiting Stanford University and was supported in part by National Science Foundation grant DCR72-03752 A02 and by the Office of Naval Research contract NR 044-402     

Algorithms for computing the optimal transitive approximation of a proximity relation

Three ways for generating the optimal transitive approximations or a suboptimal transitive approximation are given in this paper. The first one can obtain all the optimal transitive approximations for any proximity relation. However, trying to find all the optimal transitive approximations can be very expensive. The second one gives a method to obtain a suboptimal transitive approximation which can frequently generate an optimal transitive approximation. Furthermore, starting from the transitive closure the third method is proposed which can obtain a locally optimal transitive approximation. Finally, numerical experiments are carried out to show the abilities of these algorithms and compare them to other existing approximation algorithms.     

A delineability-based method for computing critical sets of algebraic surfaces

In this paper, we address the problem of determining a real finite set of z$z$-values where the topology type of the level curves of a (maybe singular) algebraic surface may change. We use as a fundamental and crucial tool McCallum’s theorem on analytic delineability of polynomials (see [McCallum, S., 1998. An improved projection operation for cylindrical algebraic decomposition. In: Caviness, B.F., Johnson, J.R. (Eds.), Quantifier Elimination and Cylindrical Algebraic Decomposition. Springer Verlag, pp. 242–268]). Our results allow to algorithmically compute this finite set by analyzing the real roots of a univariate polynomial; namely, the double discriminant of the implicit equation of the surface. As a consequence, an application to offsets is shown.     

An assessment of satellite-based agricultural water productivity over the Indian region

The preliminary analysis of agricultural water productivity (AWP) over India using satellite data were investigated through productivity mapping, water use (actual evapotranspiration (ET_a)/effective rainfall (R_eff) mapping and water productivity mapping. Moderate Resolution Imaging Spectroradiometer data was used for generating agricultural land cover (MCD12Q1 at 500 m), gross primary productivity (GPP; MOD17A2 at 1 km), and ET_a (MOD16A2 at 1 km). R_eff was estimated at 10 km using the United States Department of Agriculture soil conservation service method from daily National Oceanic and Atmospheric Administration Climate Prediction Center rainfall data. Six years’ (2007–2012) data were analysed from June to October. The seasonal AWP and rainwater productivity (RWP) were estimated using the ratios of seasonal GPP (kg C m^?2) and water use (mm) maps. The average AWP and RWP ranges from 1.10–1.30 kg Cm^?3 and 0.94–1.0 kg C m^?3, respectively, with no significant annual variability but a wide spatial variability over India. The highest AWP was observed in northern India (1.22–1.80 kg C m^?3) and lowest in western India (0.81–1.0 kg C m^?3). Large variations in AWP (0.69–1.80 kg C m^?3) were observed in Himachal Pradesh, Jammu and Kashmir, northeastern states (except Assam), Kerala, and Uttaranchal. The low GPP of these areas (0.0013–0.13 kg C m^?2) with low seasonal total ET_a (<101 mm) and R_eff (<72 mm) making the AWP high that do not correspond to high productivity but possible water stress. Gujarat, Rajasthan, Maharashtra, Madhya Pradesh, Jharkhand, and Karnataka showed low AWP (0.73–1.13 kg C m^?3) despite having high ET_a (261–558 mm) and high R_eff (287–469 mm), indicating significant scope for improving productivity. The highest RWP was observed in northern parts and Indo-Gangetic plains (0.80–1.6 kg C m^?3). The 6 years’ analysis reveals the status of AWP, leading to appropriate interventions to better manage land and water resources, which have great importance in global food security analysis.     

Spatio-temporal variability of surface chlorophyll-a in the Halmahera Sea and its relation to ENSO and the Indian Ocean Dipole

ABSTRACT

Long-term satellite data are used to investigate the variability of ocean surface chlorophyll-a (chl-a) concentration in the Halmahera Sea (HS) under influence of the Australian-Indonesian Monsoon (AIM), the El Niño-Southern Oscillation (ENSO), and the Indian Ocean Dipole (IOD). In this study, we first analysed the seasonal variability of chl-a, and then examine the relationship between surface chl-a, sea surface temperature (SST), and sea surface wind stress in the area. Our results suggest that prevailing southeasterly winds play a fundamental role in generating chl-a blooms in the HS. Particularly on a seasonal timescale, through the mechanism of Ekman mass transport, strengthening of southeasterly wind stress during the Southeast Monsoon season (June – August) produces enhanced chl-a concentrations associated with ocean surface cooling in the area of study. On the other hand, the chl-a bloom completely diminishes during the Northwest Monsoon season (December – February) due to weakening of wind stress and Ekman transport. On an interannual timescale, sea level pressure and wind stress are coherent with ENSO and IOD phases. During El Niño and positive IOD events (La Niña and negative IOD events), both sea level pressure and wind stress greatly increase (decrease) over the HS. These conditions cause an anomaly in southerly (northerly) wind stress, which is favourable to an enhancement (reduction) of the chl-a concentration in the region. This study demonstrates that sea level pressure and wind stress are the critical factors in determining the magnitude of chl-a bloom in the HS.     

Interannual variability of vegetation over the Indian sub-continent and its relation to the different meteorological parameters

The dynamic nature of climate over Indian sub-continent is well known which influences Indian monsoon. Such dynamic variability of climate factors can also have significant implications for the vegetation and agricultural productivity of this region. Using empirical orthogonal function (EOF) and wavelet decomposition techniques, normalized difference vegetation index (NDVI) monthly data over Indian sub-continent for 18 years from 1982 to 2000 have been used to study the variability of vegetation. The present study shows that the monsoon precipitation and land surface temperature over the Indian sub-continent landmass have significant impact on the distribution of vegetation. Tropospheric aerosols exert a strong influence too, albeit secondary to monsoon precipitation and prove to be a powerful governing factor. Local climate anomaly is seen to be more effective in determining the vegetation change than any global teleconnection effects. The study documents the dominating influence of monsoon precipitation and highlights the importance of aerosols on the vegetation and necessitates the need for remedial measures. The present study and an earlier one point towards a possible global teleconnection pattern of ENSO as it is seen to affect a particular mode of vegetation worldwide.     

Comparison of the performance of latent heat flux products over southern hemisphere forest ecosystems: estimating latent heat flux error structure using in situ measurements and the triple collocation method

ABSTRACT

In this study, we compared different remote-sensing (RS)-based land surface models (LSM) and reanalysis latent heat flux (LE) products over different forest ecosystems. We analysed the performance of three RS products, the MOD16A2, the Breathing Earth System Simulator (BESS) model, and a combined optical-microwave model (COM) in their ability to replicate eddy covariance (EC) flux observations of LE at eight southern hemisphere forest ecosystems and compared their results to simulated LE from the offline LSM (GLDAS/NOAH) and a reanalysis LE dataset (MERRA). To determine spatial uncertainties, we used the triple collocation (TC) method, which does not require a priori knowledge of the true LE value, at selected Australian EC locations and over an area without in situ measurement (the Dry Chaco Forest (DCF), Argentina). The spatial pattern of the TC results was commensurable with uncertainties calculated using EC observations, indicating that the TC method is a robust technique to estimate spatial uncertainties. As global products have been validated with EC measurement from Ozflux stations, we hypothesized and found, using the TC model, that LE products achieve a better performance over areas with EC from networks than over sites without ground-based measurements and may reflect over-calibration of models or a need for a more diverse representation of ecosystems at flux tower networks.     

A grid computing based approach for the power system dynamic security assessment

This paper addresses the problem of parallel dynamic security assessment applications from static homogeneous cluster environment to dynamic heterogeneous grid environment. Functional parallelism and data parallelism are supported by each of the message passing interface model and TCP/IP model. To consider the differences in heterogeneous computing resources and complexity of large-scale power system communities, a kernel-based multilevel algorithm is proposed for network partitioning. Since the bottleneck in distributed computation is low speed network communication, a bi-level latency exploitation technique is introduced for numerically solving system differential equations. The proposed grid-based implementation includes the core simulation engine, grid computing middleware, a Python interface and Python front-end utilities. Tests for a 39-bus network, a 4000-bus network and a 10,000-bus network are reported, and the results of these experiments demonstrate that the proposed scheme is able to execute the distributed simulations on computational grid infrastructure and provide efficient parallelism.     

A mathematical model for nanoparticle melting with size-dependent latent heat and melt temperature

In this paper, we study the melting of a spherical nanoparticle. The model differs from previous ones in that a number of features have been incorporated to match experimental observations. These include the size dependence of the latent heat and a cooling condition at the boundary (as opposed to the fixed temperature condition used in previous studies). Melt temperature variation and density change are also included. The density variation drives the flow of the outer fluid layer. The latent heat variation is modelled by a new relation, which matches experimental data better than previous models. A novel form of Stefan condition is used to determine the position of the melt front. This condition takes into account the latent heat variation, the energy required to create new surface and the kinetic energy of the displaced fluid layer. Results show that melting times can be significantly faster than predicted by previous theoretical models; for smaller particles, this can be around a factor 3. This is primarily due to the latent heat variation. The previously used fixed temperature boundary condition had two opposing effects on melt times: the implied infinite heat transfer led to faster melting but also artificially magnified the effect of kinetic energy, which slowed down the process. We conclude that any future models of nanoparticle melting must be based on the new Stefan condition and account for latent heat variation.     

On the variation of the tropospheric ozone over Indian region in relation to the meteorological parameters

Using monthly mean satellite measurements of TOMS/SBUV tropospheric ozone residual (TOR) data and meteorological parameters (tropopause height (TPH), 200 hPa geopotential height (GPH) and outgoing longwave radiation (OLR)) during 1979–2001, seasonal variability of TOR data and their association with meteorological parameters are outlined over the Indian region. Prominent higher values of TOR (44–48 DU, which is higher than the globally averaged 31.5 DU) are observed over the northern parts of the country during the summer monsoon season (June–September). Similar to the TOR variation, meteorological parameters (tropopause height, 200 hPa geopotential height and outgoing longwave radiation) also show higher values during the summer monsoon season, suggesting an in phase relationship and strong association between them because of deep convection present during summer monsoon time. The monthly trends in TOR values are found to be positive over the region. TOR has significant positive correlations (5% level) with GPH, and negative correlations with OLR and TPH for the month of September. The oxidation chains initiated by CH₄ and CO show the enhanced photochemical production of ozone that would certainly become hazardous to the ecological system. Interestingly, greenhouse gases (GHG) emissions were found to have continuously increased over the Indian region during the period 1990–2000, indicating more anthropogenic production of ozone precursor gases causing higher level of tropospheric ozone during this period.     

Bimodal variation of SST and related physical processes over the North Indian Ocean: special emphasis on satellite observations

Using sea surface temperature (SST) and wind speed retrieved by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), for the period of 1998–2003, we have studied the annual cycle of SST and confirmed the bimodal distribution of SST over the north Indian Ocean. Detailed analysis of SST revealed that the summer monsoon cooling (winter cooling) over the eastern Arabian Sea (Bay of Bengal) is more prominent than winter cooling (summer monsoon cooling). A sudden drop in surface short wave radiation by 57 W m^?2 (74 W m^?2) and rise in kinetic energy per unit mass by 24 J kg^?1 (26 J kg^?1) over the eastern Arabian Sea (Bay of Bengal) is observed in summer monsoon cooling period. The subsurface profiles of temperature and density for the spring warming and summer monsoon cooling phases are studied using the Arabian Sea Monsoon Experiment (ARMEX) data. These data indicate a shallow mixed layer during the spring warming and a deeper mixed layer during the summer monsoon cooling. Deepening of the mixed layer by 30 to 40 m with corresponding cooling of 2°C is found from warming to summer monsoon cooling in the eastern Arabian Sea. The depth of the 28°C isotherm in the eastern Arabian Sea during the spring warming is 80 m and during summer monsoon cooling it is about 60 m, while over the Bay of Bengal the 28°C isotherm is very shallow (35 m), even during the summer monsoon cooling. The time series of the isothermal layer depth and mixed layer depth during the warming phase revealed that the formation of the barrier layer in the spring warming phase and the absence of such layers during the summer cooling over the Arabian Sea. However, the barrier layer does exist over the Bay of Bengal with significant magnitude (20–25 m). The drop in the heat content with in first 50 m of the ocean from warming to the cooling phase is about 2.15 × 10⁸ J m^?2 over the Arabian Sea.     

A parametrization of all the unfalsified plant models for MIMOsystems

The results of the parametrization of all the unfalsified models for single-input/single-output systems are extended to multi-input/multi-output (MIMO) systems. In this parametrization, the assumed a priori plant and noise information are upper bounds of the H _∞-norm of the plant matrix-valued transfer function and the noise magnitude. The parametrization is on the basis of several series of plant time-domain identification experiment data. It is shown that for MIMO systems, all the unfalsified plant matrix-valued transfer functions can still be expressed by the linear fractional transformation of a fixed matrix-valued transfer function and an H_∞-norm bounded structure fixed, but uncertain matrix-valued transfer function. However, the high dimensions of the matrix-valued transfer functions involved in the parametrization hamper the direct application of these results to robust controller design. To overcome these difficulties, further efforts are needed     

Climatic oscillations in aerosol optical depth over tropical oceanic regions pertaining to genesis of the Indian Ocean Dipole

Data on aerosol optical depth (AOD) derived from the ocean colour sensor of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) from September 1997 to December 2010 over the western tropical Indian Ocean (WTIO) (10° S to 10° N; 50° E to 70° E) and southeastern tropical Indian Ocean (SETIO) (10° S to equator; 90° E to 110° E) were analysed with a view to understanding its response to climatic oscillations in regard to the El Niño–Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD). This study demonstrates the existence of a bimodal distribution pattern of AOD in the atmosphere over both WTIO and SETIO, with the highest values being around 1.1 during the period of primary maximum during August over the WTIO and during October over the SETIO. A secondary maximum (～0.9) appeared during March over both areas. In addition, the existence of a see-saw oscillation in the distribution of AOD between the atmospheric columns over the study regions was revealed, with higher values during August–December over the SETIO. AOD data over the SETIO captured very well the influence of these atmospheric modes, whereas the influence was not as significant over the WTIO. Stronger El Niño (Niño index > 0.80) events produced a significantly positive (more than +0.03) anomaly in AOD values over the SETIO during October, whereas the lone mode of IOD events and La Niña were not sufficient to induce any significant change in the aerosol distribution over the area. The mode of El Niño co-occurring with a positive IOD (PIOD) strengthens this anomalous behaviour. A significantly negative anomaly (≤0.03) in AOD was observed with concurrent La Niña (Niño index < ?1.1) and negative IOD (NIOD) (dipole mode index ≤ 1.1) events. The Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model and National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) winds were utilized to verify these observations.     

A lagrange parametrization for the design of variable stiffness laminates

A Lagrange parameterization of lamination parameters which are used for optimization of variable stiffness laminates is presented. The advantages of the approach are: a) the design variables become independent of the finite element mesh and, b) the smoothness of the solution is inherently guaranteed. Due to independency of design variables of the finite element mesh, the reduction in the number of design variables is drastic, once variable stiffness laminates usually demand a fine mesh. The lamination parameters formulation allows a more precise and concise approach to laminate design, removing difficulties related to fiber direction and stacking sequence, increasing the chances to find a global optimal solution. In this paper, the Lagrange parameterization is used for the maximization of the buckling load of a variable stiffness composite plate.