Intraseasonal variability of Indian Ocean sea surface temperature during boreal winter: Madden-Julian Oscillation versus submonthly forcing and processes

[ 1] Intraseasonal variability of Indian Ocean sea surface temperature (SST) during boreal winter is investigated by analyzing available data and a suite of solutions to an ocean general circulation model for 1998 - 2004. This period covers the QuikSCAT and Tropical Rainfall Measuring Mission (TRMM) observations. Impacts of the 30 - 90 day and 10 - 30 day atmospheric intraseasonal oscillations (ISOs) are examined separately, with the former dominated by the Madden-Julian Oscillation (MJO) and the latter dominated by convectively coupled Rossby and Kelvin waves. The maximum variation of intraseasonal SST occurs at 10 degrees S - 2 degrees S in the wintertime Intertropical Convergence Zone (ITCZ), where the mixed layer is thin and intraseasonal wind speed reaches its maximum. The observed maximum warming ( cooling) averaged over ( 60 degrees E - 85 degrees E, 10 degrees S - 3 degrees S) is 1.13 degrees C ( - 0.97 degrees C) for the period of interest, with a standard deviation of 0.39 degrees C in winter. This SST change is forced predominantly by the MJO. While the MJO causes a basin-wide cooling ( warming) in the ITCZ region, submonthly ISOs cause a more complex SST structure that propagates southwestward in the western-central basin and southeastward in the eastern ocean. On both the MJO and submonthly timescales, winds are the deterministic factor for the SST variability. Short-wave radiation generally plays a secondary role, and effects of precipitation are negligible. The dominant role of winds results roughly equally from wind speed and stress forcing. Wind speed affects SST by altering turbulent heat fluxes and entrainment cooling. Wind stress affects SST via several local and remote oceanic processes.

内蒙古温带草原生态系统过程对气候变化响应的实验研究

羊草草原、大针茅草原和草甸草原是内蒙古温带典型草原地区的三种主要植被类型，本文以此为研究对象，应用时空替代、温室、网室、自然降水接移、养分添加等多种方法模拟未来可能发生的气候变化，研究了这些变化对上述草原植物群落和生态系统过程的直接和间接影响。主要研究结果如下： 1. 气候变暖及其诱导的土壤养分释放速率增加对植物群落有明显的影响，表现在种种植物群落在高度、盖度、密度和生物量等都有不同程度的变化。说明我国温带草原生态系统对气候变化反应敏感。 2. 在群落说平上，气候变暖直接或间接使地上生物量提高17%～90%，但在种群水平，不同种群对模拟气候变化的响应具有很强的个性，而不具普遍性，不同种群反应的大小、方向不同。因此由在不同群落进行研究得出的推论只有部分是可能的，并且即使观测到相类似的反应，它们内在的机制也很可能是不同的。 3. 气候变化显著地影响着凋落物的分解特征。但不同的气候变化情景下，凋落物分解过程的响应不同。在温度升高降水变化不大或升高的情景下，凋落物的分解速率将加快;在气温上升，降水明显下降的情景下，凋落物的分解速率将降低。 4. 草甸草原土壤碳素释放过程和氮素矿化过程对气候变暖有明显的响应。气候变暖将促进土壤有机碳的释放，使草甸草原土壤成为碳源，同时加速氮素矿化速率，在一定程度上提高土壤有效养分的浓度。 5. 在中小尺度上，海拔样带所是应用时空替代原理，研究陆地生态系统与气候变化的理想平台，生物量是综合反应气候变化对土壤-植物系统影响的敏感指标。 6. 草原土壤有机碳和氮在2m～3m的小尺度上存在空间自相关性，其空间自相关尺度受人类活动的影响。

土壤微生物和酶对大气CO2浓度与温度升高的响应

土壤微生物(Soil microbes)是生态系统的重要组成部分，它参与土壤中复杂有机物质的分解和再合成，也参与C、N、S、P等的循环。土壤酶(Soil enzyme)是土壤中具有生物活性的蛋白质，它与微生物一起推动着土壤的生物化学过程，并在树木营养物质的转化中起着重要的作用。鉴于土壤微生物和土壤酶对环境变化的敏感性，它们在CO2浓度和温度升高时的反应将在很大程度上影响森林生态系统的结构和功能。因此，要全面评价大气CO2浓度和温度升高对整个生态系统的影响，有必要对CO2浓度和温度升高条件下的土壤微生物的反应进行深入的研究与探讨。本文应用自控、封闭、独立的生长室系统，研究了川西亚高山岷江冷杉（Abies faxoniana）根际、非根际土壤微生物数量，红桦（Betula albosinensis）根际微生物数量以及根际、非根际土壤酶活性对大气CO2浓度(环境CO2浓度+350±25μmol·mol-1，EC)和温度(环境温度+2.0±0.5℃，ET)升高及两者同时升高(ECT)的响应。结果表明： 1) EC和ET显著增加岷江冷杉根际微生物数量，但不同微生物种类对EC和ET的反应有所差异。6、8和10月，岷江冷杉根际微生物数量与对照(CK)相比，EC处理的根际细菌数量分别增加了35%、164%和312%，ET处理增加了30%、115%和209%；EC和ET处理对根际放线菌和根际真菌数量影响不显著。ECT处理的根际放线菌数量分别增加了49%、50%和96%，根际真菌数量增加了151%、57%和48%；而ECT对根际细菌数量影响不显著。EC、ET和ECT处理对岷江冷杉土壤微生物总数的根际效应明显，其R/S值分别为1.93、1.37和1.46(CK的R/S值为0.81)。 2) 红桦根际微生物数量对EC、ET和ECT的响应不同。生长季节(5~10月)，高密度的红桦根际细菌数量与CK 相比，EC的根际细菌数量分别增加28%、33%、423%、65%、43%和79%，而低密度的红桦根际细菌数量增加不显著。ET能显著增加根际细菌数量(7~10月)，其中高密度的根际细菌数量分别增加了377%、107%、35%、22%，而低密度的根际细菌数量分别增加了27%、27%、64%、48%；ECT对两个密度水平下根际细菌数量均未产生有显著的影响。高、低密度的红桦根际放线菌和根际真菌数量与 CK 相比，EC显著增加了低密度的红桦根际放线菌数量，而对高密度的根际放线菌数量无显著影响；ET和ECT对高低密度的红桦根际放线菌数量均未产生显著影响。EC和ET对高低密度的根际真菌数量也无显著影响，而ECT却显著增加了高低密度的根际真菌数量。 3) EC、ET和ECT处理的低密度红桦根际微生物(细菌、放线菌和真菌)数量没有显著高于或低于高密度根际微生物数量，表明短期内密度对红桦根际微生物数量不产生影响。 4) 不同种类的氧化还原酶对EC、ET和ECT的响应不同。5~10月，EC的红桦根际过氧化氢酶活性是CK 的1.44、1.06、1.11、1.10、1.12和1.24倍，差异显著(6月除外)；ET和ECT处理根际过氧化氢酶活性无显著增加。EC的红桦根际多酚氧化酶活性比CK显著增加；ET的根际多酚氧化酶活性显著高于CK(8月除外)。ECT的根际多酚氧化酶活性高于CK，差异不显著。EC的根际脱氢酶活性分别增加了46%、40%、133%、48%、17%和26%，差异显著。5~7月，ET和ECT的根际脱氢酶活性高于CK的脱氢酶活性，而8~9月则相反，差异性均不显著。 5) EC、ET和ECT对不同种类的水解酶的影响不同。EC能显著增加红桦根际脲酶活性，5~10月分别增加了29%、42%，、70%、67%、59%和57%。ET和ECT 对根际脲酶活性未产生显著影响。EC显著提高根际转化酶活性，5、6和9月EC的根际转化酶活性分别比CK高51%、42%和40%。5和10月，ET的根际转化酶活性低于CK，而其余月份却高于CK，但均具有显著性差异。ECT的根际转化酶活性与CK的根际转化酶活性有显著性差异(9月除外)，5、6和7月的根际转化酶活性分别提高了94%、198%和67%。 6) 与CK相比，EC、ET和ECT的非根际土壤微生物数量以及非根际土壤酶活性均无显著提高。EC、ET和ECT的过氧化氢酶、脲酶的根际效应明显，而多酚氧化酶和脱氢酶根际效应不明显。EC和ECT的转化酶根际效应明显，而ET的转化酶根际效应不明显。 It is well known that atmospheric CO2 concentration and temperature are increasing as a consequence of human activities. In past decades, considerable efforts had been put into investigating the effects of climate change on processes of forest ecological system. In general, studies had been mainly focused on the effects of elevated atmospheric CO2 on plant physiology and development, litter quality, and soil microorganisms. Studies showed that there was variation in the responses of root development and below-ground processes to climate between different plant communities. Since the concentration of CO2 in soil was much higher (10~50 times) than in the atmosphere, increasing levels of atmospheric CO2 may not directly in fluence below ground processes. Betula albosinensis and Abies faxoniana, as the dominated tree species of subalpine dark coniferous forest in the western Sichuan province, which play an important role in the structure and function of this kind of forest ecosystem. In our study, effects of elevated atmospheric CO2 concentration (350±25μmol·mol-1), increased temperature (2.0±0.5℃) and both of the two on the number of rhizospheric microbe and rhizospheric enzyme activity were studied by the independent and enclosed-top chamber’ system under high-frigid conditions. Responses of rhizospheric bacteria, actinomycetes and fungi number of Betula albosinensis and Abies faxoniana under different densities(high density with 84 stems·m-2, low density with 28 stems·m-2 ), and rhizospheric enzyme activity of Betula albo-sinensis to elevated CO2 concentration and increased temperature were analyzed and discussed. The results are as the following, 1) In comparion with the control, the numbers of rhizospheric bacteria of Abies faxoniana were increased by 35%, 164% and 312% significantly in June, August and October respectively of EC, and were increased by 30%, 115% and 209% respectively of ET.However the effect of EC and ET on rhizospheric actinomycetes and fungi was not significant. The number of rhizospheric actinomycetes of ECT were increased significantly by 49%, 50% and 96% respectively, and the increment of rhizospheric fungi were 151%, 57% and 48% respectively .The effect of ECT on rhizospheric bacteria was not significant. Rhizospheric effect of soil microbe for all treatments was significant, with the R/S of 1.93, 1.27 and 1.46 for EC, ET and ECT, respectively. 2) Treatment EC improved the number of rhizospheric bacteria of Betula albosinensis under high density significantly in comparison with the control, over the growing season, the greatest increment of rhizospheric bacteria was from July. However, EC had no effect on the number of rhizospheric bacteria under low density. Except May and June, treatment ET improved the number of rhizospheric signifcantly. The effect of treatment ECT on the number of rhizospheric bacteria under different densities was not significant. Of treatment EC, the number of rhizospheric actinomycetes of Betula albosinensis under low density were increased significantly, however, treatment EC did not stimulate the number of rhizospheric actinomycetes under high density. Simultaneously, treatment ET and ECT did not stimulate the number of rhizospheric actinomycetes. Finally, in treatment ECT, the number of rhizospheric fungi under high density were increased significantly, however treatment EC and ET did not stimulate the number of rhizospheric fungi under different densities. 3) Of treatment EC, ET and ECT, the number of rhizospheric microbe of Betula albosinensis under low density were not more or fewer than that of microbe under hign density along the growing season, which showed that plant density had no effect on the nmber of microbe. 4) From May to October, 2004，rhizospheric catalase activity of Betula albosinensis of treatment EC was 1.44, 1.06, 1.11, 1.10, 1.12 and 1.24 times as treatment CK respectively, and the difference was statistically significant(except June). Treatment ET and ECT did not increase rhizospheric catalase activity significantly. In treatment EC, the rhizospheric pohyphenol oxidase activity was higher than treatment CK significantly. The rhizospheric pohyphenol oxidase activity of treatment ET was higher than CK significantly (except August). The rhizospheric pohyphenol oxidase activity of treatment ECT was higher than CK, but the difference was not statistically significant. Over the growing period, the rhizospheric dehydrogenase activity were increased 46%, 40%, 133%, 48%, 17% and 26% respectively by treatment EC, and the difference was statistically significant. From May to July, the rhizospheric dehydrogenase activity in treatment ET and ECT was higher than CK, but from August to October, the rhizospheric dehydrogenase activity was lower than CK, the difference was not significant. 5) Treatment EC increased rhizospheric urease activity significantly, from May to October, rhizospheric urease activity were increased 29%, 42%, 70%, 67%, 59% and 57% respectively by EC. Treatment ET and ECT had no effect on rhizospheric urease activity. Treatment EC improved rhizospheric invertase activity significantly, in May, June and September, the rhizospheric invertase activity of treatment EC were increased 51%, 42% and 40% in comparison with the control. Except May and October, the rhizospheric invertase activity of treatment ET was markly higher than CK. The rhizospheric invertase activity of treatment ECT was significantly different from CK (except September), in May, June and July treatment ECT increased rhizospheric invertase activity by 94%, 198% and 67% respectively. 6) In comparison with the control, treatment EC, ET, and ECT had no effect on the number of non-rhizospheric microbe and non-rhizospheric enzyme activity. Rhizospheric effect of catalase and urease for all treatments was significant, but rhizospheric effect of pohyphenol oxidase and dehydrogenase was not significant. Rhizospheric effect of invertase of EC and ECT was significant, but rhizospheric effect of invertase of ET was not significant.

Electron emission induced by the interaction of highly charged ions Pb-207(q+) (24 <= q <= 36) with solid surface of Si(110)

The electron emission induced by highly charged ions Pb-207(q+) (24 <= q <= 36) interacting with Si(110) surface is reported. The result shows that the electron emission yield Y has a strong dependence on the projectile charge state q, incidence angle psi and impact energy E. In fitting the experimental data we found a nearly 1/tan psi dependence of Y. Theoretical analysis shows that these processes are closely related to the process of potential electron emission based on the classical over-the-barrier model.

红豆草与土壤氮含量对大气二氧化碳浓度升高的响应

在封闭的植物培养箱中,通过盆栽实验,研究了红豆草和土壤氮含量对CO2浓度增加的响应.结果表明,与正常CO2浓度(355~370μmol·mol-1)相比,CO2浓度升高(700μmol·mol-1),植物生物量增加25·1%(P<0·01),但植物体氮浓度降低25·3%(P<0·001),植物全氮没有显著的变化.经3个月盆栽实验后,与原始土壤相比,两种CO2浓度处理土壤全N、NO3--N和NH4+-N都有所降低,而土壤微生物氮则显著增加,这可能与植物生长有关.不同CO2浓度处理土壤NH4+-N浓度基本一致,但在高CO2浓度下,土壤NO3--N浓度显著降低,而微生物生物氮显著增加.对整个土壤-植物系统而言,盆栽实验后,整个系统全氮有少量增加,但变化不显著,特别是在高CO2浓度条件下,土壤-植物系统全氮最大,这可能与培养材料红豆草为豆科植物,而且在高CO2浓度下生物量增加,导致氮的固定量增加有关.

渭南地区末次冰期以来的蜗牛化石记录及古气候古环境研究

In this study, 172 mollusk assemblages from the Weinan loess section in the southeast of Loess Plateau, China, were identified quantitatively at relative high resolution. The results show: 1) the history and processes of paleoclimatic and paleoenvironmental changes in Weinan since the last 70 ka; 2) the characteristics of climatic changes during the period of the last glacial maximum (LGM); 3) the spatial pattern of paleoclimate variations at the south and middle parts of the Loess Plateau during the LGM period; 4) the timing of the last deglaciation and the return event of rapid climate change during the last deglaciation. The main conclusions are as follows: 1) 172 mollusk samples taken from the uppermost 9 m deposits cover the past 70 ka, which were sampled at the internals of 5 cm for S_0, 3 cm for L_(1-1) and L_(1-2), and 10 cm for L_(1-3), L_(1-4) and L_(1-5). Author analyzed quantitatively all individuals including broken pieces of snail shells, percentages of 15 species identified from 172 samples. Three main groups were determined according to the ecological requirement of each taxon. Based on the variations of three ecological groups and typical ecological species, The author intended to reconstruct the history of and processes of climate and environment since the last 70 ka in the Weinan region. The climate and environment in this region experienced the following changes: relative warm and humid stage from 67.5-20.3 cal. ka B.P., a period of forest-steppe or steppe developed; cold and arid stage from 20.3-15.5 cal. ka B.P., a dry steppe period, later wetter and colder; cold and humid period once time from 15.5 to 12.3 cal. ka B.P., a typical steppe or forest-steppe stage; cold and humid again from 12.3 cal. ka B.P. to 8.2 cal. ka B.P., a tropical steppe stage; warm and humid climate, a forest-steppe developed. 2) The climate during the period of the last glacial maximum (LGM) in Weinan was characterized by a general cold-humid condition, represented by occurrence of a number of the cool-humidiphilous mollusk species such as Gastocopta amigerella and Vallonia cf. pulchella in the section. 3) Comparison of the variations in abundance of Puncture orphana at Weinan with those at Luochuan and Changwu sections suggests that the summer monsoon intensity influenced differently at the three regions during the LGM period. The Weinan was weaker summer monsoon impact during all the period, the Luochuan was influenced occasionally, and Changwu was only a very short time affected, which indicated it might be located at the western margin of the summer monsoon influence during that period. 4) The ratio of thermo-humidiphilous mollusk group to cold-aridiphilous one shows an increase tendency at about 15 cal. ka B.P., reflecting the climate warming after the deglaciation in Weinan, which is approximately corresponding to the timing of warming period of the last deglaciation, found in the East Atlantic Ocean, the South China Sea and the Loess Plateau (indicated by the phytolith study). 5) A remarkable decrease in the number of thermo-humidiphilous and cool-humidiphilous mollusk species from 12.7 - 11.6 cal. ka B.P. indicates a cooling in climate and might be the reflection of the Younger Dryas event in Weinan. 6) Variations in the ratios of thermo-humidiphilous mollusk species to cold-aridiphilous ones reflect the climate instability in Holocene. There were four warm-humid periods (10-8.1 cal. ka B.P., 6.9-6.1 cal. ka B.P., 5.2-2.6cal. ka B.P., 1.6cal. ka B.P. to the present ) and three relative cold-arid periods (8.1-6.9 cal. ka B.P., 6.1-5.2 cal. ka B.P., 2.6-1.6 cal. ka B.P.), showing about a 1,000 year climatic oscillation.

COASTAL SEA-LEVEL AND THE LARGE-SCALE CLIMATE STATE - A DOWNSCALING EXERCISE FOR THE JAPANESE ISLANDS

A major problem which is envisaged in the course of man-made climate change is sea-level rise. The global aspect of the thermal expansion of the sea water likely is reasonably well simulated by present day climate models; the variation of sea level, due to variations of the regional atmospheric forcing and of the large-scale oceanic circulation, is not adequately simulated by a global climate model because of insufficient spatial resolution. A method to infer the coastal aspects of sea level change is to use a statistical ''downscaling'' strategy: a linear statistical model is built upon a multi-year data set of local sea level data and of large-scale oceanic and/or atmospheric data such as sea-surface temperature or sea-level air-pressure. We apply this idea to sea level along the Japanese coast. The sea level is related to regional and North Pacific sea-surface temperature and sea-level air pressure. Two relevant processes are identified. One process is the local wind set-up of water due to regional low-frequency wind anomalies; the other is a planetary scale atmosphere-ocean interaction which takes place in the eastern North Pacific.

Optical analysis of dislocation-related physical processes in GaN-based epilayers

In this paper, recent progresses in optical analysis of dislocation-related physical properties in GaN-based epilayers are surveyed with a brief review. The influence of dislocations on both near-band edge emission and yellow luminescence (YL) is examined either in a statistical way as a function of dislocation density or focused on individual dislocation lines with a high spatial resolution. Threading dislocations may introduce non-radiative recombination centers and enhance YL, but their effects are affected by the structural and chemical environment. The minority carrier diffusion length may be dependent on either dislocation density or impurity doping as confirmed by the result of photovoltaic spectra. The in situ optical monitoring of the strain evolution process is employed during GaN heteroepitaxy using an AIN interlayer. A typical transition of strain from compression to tension is observed and its correlation with the reduction and inclination of threading dislocation lines is revealed. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Equatorial pacific SSTA-related decadal variations of potential predictability of ENSO and interannual climate

Based on analysis of NCEP reanalysis data and SST indices of the recent 50 years, decadal changes of the potential predictability of ENSO and interannual climate anomalies were investigated. Autocorrelation of Nino3 SST anomalies (SSTA) and correlation between atmospheric anomalies fields and Nino3 SSTA exhibit obvious variation in different decades, which indicates that Nino3 SSTA-related potential predictability of ENSO and interannual climate anomalies has significant decadal changes. Time around 1977 is not only a shift point of climate on the interdecadal time scale but also a catastrophe point of potential predictability of ENSO and interannual climate. As a whole, ENSO and the PNA pattern in boreal winter are more predictable in 1980s than in 1960s and 1970s, while the Nino3 SSTA-related potential predictability of the Indian monsoon and the East Asian Monsoon is lower in 1980s than in 1960s and 1970s.

Weak Zone Related Seismic Cycles in Progressive Failure Leading to Collapse in Brittle Crust

Until quite recently our understanding of the basic mechanical process responsible for earthquakes and faulting was not well known. It can be argued that this was partly a consequence of the complex nature of fracture in crust and in part because evidence of brittle phenomena in the natural laboratory of the earth is often obliterated or obscured by other geological processes. While it is well understood that the spatial and temporal complexity of earthquakes and the fault structures emerge from geometrical and material built-in heterogeneities, one important open question is how the shearing becomes localized into a band of intense fractures. Here the authors address these questions through a numerical approach of a tectonic plate by considering rockmass heterogeneity both in microscopic scale and in mesoscopic scale. Numerical simulations of the progressive failure leading to collapse under long-range slow driving forces in the far-field show earthquake-like rupture behavior. $En Echelon$ crack-arrays are reproduced in the numerical simulation. It is demonstrated that the underlying fracturing induced acoustic emissions (or seismic events) display self-organized criticality------from disorder to order. The seismic cycles and the geometric structures of the fracture faces, which are found greatly depending on the material heterogeneity (especially on the macroscopic scale), agree with that observed experimentally in real brittle materials. It is concluded that in order to predict a main shock, one must have extremely detailed knowledge on very minor features of the earth's crust far from the place where the earthquake originated. If correct, the model proposed here seemingly provides an explanation as to why earthquakes to date are not predicted so successfully. The reason is not that the authors do not understand earthquake mechanisms very well but that they still know little about our earth's crust.

Two Bifurcation Transition Processes in Floating Half Zone Convection of Larger Prandtl Number Fluid

Processes of the onset oscillation in the thermocapillaxy convection under the Earth's gravity are investigated by the numerical simulation and experiments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection of m=1 for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge. It implies that, there are two critical Marangoni numbers related, respectively, to these two bifurcation transitions for the fat liquid bridge. The computational results agree with the results of ground-based experiments.

Studies on terrestrial interface processes in arid areas, China

In the present paper, we have elucidated the importance of energy and water cycling in arid areas to investigate global climate and local economics. Then, we were concerned with the physical arguments as how to stratify the soil, and the stability of the numerical scheme in the mathematical model for predicting temperature variation and water motion. Furthermore, we discuss the methods to estimate evaporation in arid areas. Numerical simulation of energy and water cycling at the Acsu Observatory, CAS, Xinjiang province and Shapuotou Observatory, CAS, Ningxia Province are conducted as case studies. The results show that the laws of terrestrial processes are rather typical in these arid areas. Planting drought-endurable trees can alleviate unfavourable conditions to a certain extent. (C) 1997 Academic Press Limited.

Two bifurcation processes for onset of oscillatory thermocapillary convection in a floating half zone

An overview on the onset of thermocapillary oscillatory convection in a floating half zone is provided, and it is a typical subject in the microgravity sciences related to the space materials science, especially the floating zone processing, and also to the microgravity fluid physics. The main interests are focused around the process for onset of oscillatory thermocapillary convection, which is known also as the bifurcation transition from quasi-steady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, such as the Marangoni number, Prandtl number, geometrical parameters, and heat transfer parameters. Recent studies show that, there exists the bifurcation transition from steady and axial symmetric convection to the steady and axial non-symmetric convection before the onset of oscillation in cases of small Prandtl number fluids and in cases of larger Prandtl number fluids of fat liquid bridge with small aspect ratio. The transition process is a strong non-linear process because the velocity deviation has the same order of magnitude as that of an average flow after the onset of oscillation, and unsteady 3-D numerical simulation is suitable to do in depth analysis on strong non-linear process, and leads generally to a better comparison with the experimental results.