Dynamics of nonlinear error growth and season-dependent predictability of El Nino events in the Zebiak-Cane model

With the intermediate-complexity Zebiak-Cane model, we investigate the 'spring predictability barrier' (SPB) problem for El Nino events by tracing the evolution of conditional nonlinear optimal perturbation (CNOP), where CNOP is superimposed on the El Nino events and acts as the initial error with the biggest negative effect on the El Nino prediction. We show that the evolution of CNOP-type errors has obvious seasonal dependence and yields a significant SPB, with the most severe occurring in predictions made before the boreal spring in the growth phase of El Nino. The CNOP-type errors can be classified into two types: one possessing a sea-surface-temperature anomaly pattern with negative anomalies in the equatorial central-western Pacific, positive anomalies in the equatorial eastern Pacific, and a thermocline depth anomaly pattern with positive anomalies along the Equator, and another with patterns almost opposite to those of the former type. In predictions through the spring in the growth phase of El Nino, the initial error with the worst effect on the prediction tends to be the latter type of CNOP error, whereas in predictions through the spring in the decaying phase, the initial error with the biggest negative effect on the prediction is inclined to be the former type of CNOP error. Although the linear singular vector (LSV)-type errors also have patterns similar to the CNOP-type errors, they cover a more localized area than the CNOP-type errors and cause a much smaller prediction error, yielding a less significant SPB. Random errors in the initial conditions are also superimposed on El Nino events to investigate the SPB. We find that, whenever the predictions start, the random errors neither exhibit an obvious season-dependent evolution nor yield a large prediction error, and thus may not be responsible for the SPB phenomenon for El Nino events. These results suggest that the occurrence of the SPB is closely related to particular initial error patterns. The two kinds of CNOP-type error are most likely to cause a significant SPB. They have opposite signs and, consequently, opposite growth behaviours, a result which may demonstrate two dynamical mechanisms of error growth related to SPB: in one case, the errors grow in a manner similar to El Nino; in the other, the errors develop with a tendency opposite to El Nino. The two types of CNOP error may be most likely to provide the information regarding the 'sensitive area' of El Nino-Southern Oscillation (ENSO) predictions. If these types of initial error exist in realistic ENSO predictions and if a target method or a data assimilation approach can filter them, the ENSO forecast skill may be improved. Copyright (C) 2009 Royal Meteorological Society

Progress of large-scale air-sea interaction studies in China

This paper summarizes the progress of large-scale air-sea interaction studies that has been achieved in China in the four-year period from July 1998 to July 2002, including seven aspects in the area of the air-sea interaction, namely air-sea interaction related to the tropical Pacific Ocean, monsoon-related air-sea interaction, air-sea interaction in the north Pacific Ocean, air-sea interaction in the Indian Ocean, air-sea interactions in the global oceans, field experiments, and oceanic cruise surveys. However more attention has been paid to the first and the second aspects because a large number of papers in the reference literature for preparing and organizing this paper are concentrated in the tropical Pacific Ocean, such as the ENSO process with its climatic effects and dynamics, and the monsoon-related air-sea interaction. The literature also involves various phenomena with their different time and spatial scales such as intraseasonal, annual, interannual, and interdecadal variabilities in the atmosphere/ocean interaction system, reflecting the contemporary themes in the four-year period at the beginning of an era from the post-TOGA to CLIVAR studies. Apparently, it is a difficult task to summarize the great progress in this area, as it is extracted from a large quantity of literature, although the authors tried very hard.

Sea surface height and transport stream function of the South China Sea from a variable-grid global ocean circulation model

A fine-grid model (1/6degrees) covering the South China Sea (SCS), East China Sea and Japan/East Sea, which is embedded into a coarse-grid (3degrees) global model, was established to study the SCS circulation. In the present paper, we report the model-produced monthly and annual mean transport stream functions and sea surface heights(SSH) and their anomalies of the SCS. Comparison to the TOPEX/Poseidon data shows that the model-produced monthly sea surface height anomalies (SSHA) are in good agreement with altimeter measurements. Based on the results, the circulation of the SCS, especially the upper layer circulation, is discussed. In the surface layer, the western Philippine Sea water intrudes into the SCS through the Luzon Strait in autumn, winter and spring, but not in summer. However, as far as the whole water column is concerned, the water intrudes into the SCS through the Luzon Strait all the year round. This indicates that in summer the water still intrudes into the SCS in the subsurface and intermediate layers. The area near the northern continental slope of the SCS is dominated by a cyclonic circulation all the year round. The SCS Southern Anticyclonic Gyre, SE Vietnam Off-Shore Current in summertime and SCS Southern Cyclonic Gyre in wintertime are reproduced reasonably. The difference between the monthly averaged SSH and SSHA is significant, indicating the importance of the mean SSH in the SCS circulation.

EAWM-related air-sea-land interaction and the Asian summer monsoon circulation

Based on the data analysis, this study further explores the characteristics of East Asian winter monsoon (hereafter, EAWM, for brevity) as well as the related air-sea-land system, and illustrates how and to what degree anomalous signals of the subsequent Asian summer monsoon are rooted in the preceding EAWM activity. We identified an important air-sea coupled mode, i.e., the EAWM mode illustrated in Section 3. In cold seasons, strong EAWM-related air-sea two-way interaction is responsible for the development and persistence of the SSTA pattern of EAWM mode. As a consequence, the key regions, i.e., the western Pacific and South China Sea (hereafter, SCS, for brevity), are dominated by such an SSTA pattern from the winter to the following summer. In the strong EAWM years, the deficient snow cover dominates eastern Tibetan Plateau in winter, and in spring, this anomaly pattern is further strengthened and extended to the northwestern side of Tibetan Plateau. Thus, the combined effect of strong EAWM-related SSTA and Tibetan snow cover constitutes an important factor in modulating the Asian monsoon circulation. The active role of the EAWM activity as well as the related air-sea-land interaction would, in the subsequent seasons, lead to: 1) the enhancement of SCS monsoon and related stronger rainfall; 2) the northward displacement of subtropical high during Meiyu period and the related deficient rainfall over Meiyu rainband; 3) above-normal precipitation over the regions from northern Japan to northeastern China in summer; 4) more rainfall over the Arabian Sea and Northeast India, while less rainfall over southwest India and the Bay of Bengal. The strong EAWM-related air-sea interaction shows, to some degree, precursory signals to the following Asian summer monsoon. However, the mechanism for the variability of Indian summer monsoon subsequent to the strong EAWM years remains uncertain.

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.

Analysis of the sea-level variability along the Chinese coast and estimation of the impact of a CO2-perturbed atmospheric circulation

The relationship between monthly sea-level data measured at stations located along the Chinese coast and concurrent large-scale atmospheric forcing in the period 1960-1990 is examined. It is found that sea-level varies quite coherently along the whole coast, despite the geographical extension of the station set. A canonical correlation analysis between sea-level and sea-level pressure (SLP) indicates that a great part of the sea-level variability can be explained by the action of the wind stress on the ocean surface. The relationship between sea-level and sea-level pressure is analyzed separately for the summer and winter half-years. In winter, one factor affecting sea-level variability at all stations is the SLP contrast between the continent and the Pacific Ocean, hence the intensity of the winter Monsoon circulation. Another factor that affects coherently all stations is the intensity of the zonal circulation at mid-latitudes. In the summer half year, on the other hand, the influence of SLP on sea-level is spatially less coherent: the stations in the Yellow Sea are affected by a more localized circulation anomaly pattern, whereas the rest of the stations is more directly connected to the intensity of the zonal circulation. Based on this analysis, statistical models (different for summer and winter) to hindcast coastal sealevel anomalies from the large-scale SLP field are formulated. These models have been tested by fitting their internal parameters in a test period and reproducing reasonably the sea-level evolution in an independent period. These statistical models are also used to estimate the contribution of the changes of the atmospheric circulation on sea-level along the Chinese coast in an altered climate. For this purpose the ouput of 150 year-long experiment with the coupled ocean-atmosphere model ECHAM1-LSG has been analyzed, in which the atmospheric concentration of greenhouse gases was continuously increased from 1940 until 2090, according to the Scenario A projection of the Intergovermental Panel on Climate Change. In this experiment the meridional (zonal) circulation relevant for sea-level tends to become weaker (stronger) in the winter half year and stronger (weaker) in summer. The estimated contribution of this atmospheric circulation changes to coastal sea-level is of the order of a few centimeters at the end of the integration, being in winter negative in the Yellow Sea and positive in the China Sea with opposite signs in the summer half-year.

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.

Observation of the seasonal evolution of the Yellow Sea Cold Water Mass in 1996-1998

We use the hydrographic data obtained during the joint survey of the Yellow Sea by the First Institute of Oceanography, China and the Korea Ocean Research and Development Institute, Korea, to quantify the spatial structures and temporal evolution of the southern Yellow Sea Cold Water Mass (YSCWM). It is indicated that the southern YSCWM is a water mass that develops in summer and decays in fall. In winter, due to the intrusion of the Yellow Sea Warm Current (YSWC), the central area (approximately between 34 degrees N and 35 degrees N, 122 degrees E and 124 degrees E) of the Yellow Sea is mainly occupied by relatively high temperature water (T > 10 degrees C). By contrast, from early summer to fall, under the seasonal thermocline, the central area of Yellow Sea is occupied by cold water (T < 10 degrees C). In summer, the southern YSCWM has two cold cores. One is formed locally southeast of Shandong Peninsula, and the other one has a tongue-like feature occupying the area approximately between 34 degrees N and 37 degrees N, 123 degrees E and 126 degrees E. The bottom layer temperature anomalies from February to July in the cold tongue region, along with the trajectories of the bottom floaters, suggest that the cold water mass in the northeast region has a displacement from the north to the central area of the Yellow Sea during the summer. (c) 2007 Elsevier Ltd. All rights reserved.

Comparison of nonlinear and linear PCA on surface wind, surface height, and SST in the South China Sea

We compared nonlinear principal component analysis (NLPCA) with linear principal component analysis (LPCA) with the data of sea surface wind anomalies (SWA), surface height anomalies (SSHA), and sea surface temperature anomalies (SSTA), taken in the South China Sea (SCS) between 1993 and 2003. The SCS monthly data for SWA, SSHA and SSTA (i.e., the anomalies with climatological seasonal cycle removed) were pre-filtered by LPCA, with only three leading modes retained. The first three modes of SWA, SSHA, and SSTA of LPCA explained 86%, 71%, and 94% of the total variance in the original data, respectively. Thus, the three associated time coefficient functions (TCFs) were used as the input data for NLPCA network. The NLPCA was made based on feed-forward neural network models. Compared with classical linear PCA, the first NLPCA mode could explain more variance than linear PCA for the above data. The nonlinearity of SWA and SSHA were stronger in most areas of the SCS. The first mode of the NLPCA on the SWA and SSHA accounted for 67.26% of the variance versus 54.7%, and 60.24% versus 50.43%, respectively for the first LPCA mode. Conversely, the nonlinear SSTA, localized in the northern SCS and southern continental shelf region, resulted in little improvement in the explanation of the variance for the first NLPCA.

Variation in joint mode of the tropical Indian-Pacific Ocean thermodynamic anomaly

Previous research has defined the index of the Indian-Pacific thermodynamic anomaly joint mode (IPTAJM) and suggested that the winter IPTAJM has an important impact on summer rainfall over China. However, the possible causes for the interannual and decadal variability of the IPTAJM are still unclear. Therefore, this work investigates zonal displacements of both the western Pacific warm pool (WPWP) and the eastern Indian Ocean warm pool (EIOWP). The relationships between the WPWP and the EIOWP and the IPTAJM are each examined, and then the impacts of the zonal wind anomalies over the equatorial Pacific and Indian Oceans on the IPTAJM are studied. The WPWP eastern edge anomaly displays significant interannual and decadal variability and experienced a regime shift in about 1976 and 1998, whereas the EIOWP western edge exhibits only distinct interannual variability. The decadal variability of the IPTAJM may be mainly caused by both the zonal migration of the WPWP and the 850 hPa zonal wind anomaly over the central equatorial Pacific. On the other hand, the zonal migrations of both the WPWP and the EIOWP and the zonal wind anomalies over the central equatorial Pacific and the eastern equatorial Indian Ocean may be all responsible for the interannual variability of the IPTAJM.

Mixed-layer water oscillations in tropical Pacific for ENSO cycle

The main modes of interannal variabilities of thermocline and sea surface wind stress in the tropical Pacific and their interactions are investigated, which show the following results. (1) The thermocline anomalies in the tropical Pacific have a zonal dipole pattern with 160 W as its axis and a meridional seesaw pattern with 6-8 degrees N as its transverse axis. The meridional oscillation has a phase lag of about 90 to the zonal oscillation, both oscillations get together to form the El Nino/La Nina cycle, which behaves as a mixed layer water oscillates anticlockwise within the tropical Pacific basin between equator and 12 degrees N. (2) There are two main patterns of wind stress anomalies in the tropical Pacific, of which the first component caused by trade wind anomaly is characterized by the zonal wind stress anomalies and its corresponding divergences field in the equatorial Pacific, and the abnormal cross- equatorial flow wind stress and its corresponding divergence field, which has a sign opposite to that of the equatorial region, in the off-equator of the tropical North Pacific, and the second component represents the wind stress anomalies and corresponding divergences caused by the ITCZ anomaly. (3) The trade winds anomaly plays a decisive role in the strength and phase transition of the ENSO cycle, which results in the sea level tilting, provides an initial potential energy to the mixed layer water oscillation, and causes the opposite thermocline displacement between the west side and east side of the equator and also between the equator and 12 degrees N of the North Pacific basin, therefore determines the amplitude and route for ENSO cycle. The ITCZ anomaly has some effects on the phase transition. (4) The thermal anomaly of the tropical western Pacific causes the wind stress anomaly and extends eastward along the equator accompanied with the mixed layer water oscillation in the equatorial Pacific, which causes the trade winds anomaly and produces the anomalous wind stress and the corresponding divergence in favor to conduce the oscillation, which in turn intensifies the oscillation. The coupled system of ocean-atmosphere interactions and the inertia gravity of the mixed layer water oscillation provide together a phase-switching mechanism and interannual memory for the ENSO cycle. In conclusion, the ENSO cycle essentially is an inertial oscillation of the mixed layer water induced by both the trade winds anomaly and the coupled ocean-atmosphere interaction in the tropical Pacific basin between the equator and 12 degrees N. When the force produced by the coupled ocean-atmosphere interaction is larger than or equal to the resistance caused by the mixed layer water oscillation, the oscillation will be stronger or maintain as it is, while when the force is less than the resistance, the oscillation will be weaker, even break.

中太平洋海区富钴结壳地球化学特征及成因机制

本文利用ICP-AES、EPMA、X-ray衍射等测试技术以及聚类分析和因子分析等多种数理统计方法，系统地对中太平洋海区富钴结壳的元素地球化学特征、矿物组成和微观组构进行了研究，并探讨了其成因机制，获得以下主要认识： 1中太平洋海区富钴结壳类型多样，均为水成成因，其矿物相主要由锰矿物相、铁矿物相和非金属矿物相组成；富钴结壳壳层发育多种原生和次生构造类型。 2磷酸盐化作用不仅强烈改变富钴结壳元素初始含量，而且造成富钴结壳某些元素间的相关性发生改变，这些敏感型元素对可用于指示富钴结壳是否发生磷酸盐化。在不同水深段内，未磷酸盐化型富钴结壳的主要元素随经向、纬向的变化趋势相似，表明其受水体化学障、表面生产力和物质来源等环境参数控制；而随水深的变化则具有区域一致性，表明水体化学具有区域成层性。 3未磷酸盐化富钴结壳稀土元素含量和轻重稀土分馏程度随水深发生规律变化，这种变化不仅与它们在海洋中的含量和行为有关，也与海洋背景颗粒的吸附有关；铈(Ce)在富钴结壳中基本上呈4价，且动力学因素控制了其富集过程，因此Ce异常不能用于指示富钴结壳形成环境的氧化程度。 4基于富钴结壳微层呈锯齿状且同一微层生长速率不同，提出了富钴结壳在各种基底表面生长以及后继发育过程受固液界面双电层控制的发育模式。在富钴结壳整个发育过程中，经历了从贫氧环境向富氧环境的转变，但微环境则呈富氧-低氧过程的交替。 关键词： 富钴结壳；中太平洋；元素地球化学；界面双电层

三门峡宋家店黄土－古土壤序列的地层学研究及其古环境记录

The Sanmen Gorge area is located in the southernmost margin of the Chinese Loess Plateau with well developed eolian deposit sequence for the past 2.6 Ma, providing a key site for further understanding of the evolution history of the East Asian monsoon since late Pliocene. This study attempted to characterize the stratigraphy and paleoclimate record of the loess-paleosol sequence in the Songjiadian section. The work involved includes systematic field investigation, paleomagnetic and rock magnetic analyses, grain size and major chemical composition analyses, and multiple proxy measurements of magnetic susceptibility, color reflectance and the ratio of CBD-dissolvable iron to the total iron (FeD/FeT). By comparisons of the Songjiadian section with well studied loess sections in the west of the Sanmen Gorge, the spatial variations of the East Asian monsoon was evaluated for some periods during which typical loess or paleosols developed. The following conclusions have been obtained. 1. Stratigraphic correlation and paleomagnetic result demonstrate that the loess-paleosol sequence in the Songjiadian section was accumulated from 2.6Ma, and is generally a complete and continuous loess sequence. However, notable differences from type loess sections have been identified for a few loess and paleosol units, featured by absence or anomalous thickness in the Songjiadian section. 2. Magnetic susceptibility and chromaticity records clearly reveal the loess-paleosol cycles, and indicate that the Sanmen Gorge area has been warmer and more humid than the Lingtai and Jingchuan sections in the western central Loess Plateau since the Early Pleistocene. 3. Grain size distribution patterns are typical of eolian dust, and show a great similarity between various units of loess and paleosols, and between the S32 and the underlying Red Clay through the Songjiadian profile, suggesting the eolian origin for the loess, paleosols and the Red Clay. 4. Comparison of the FeD/FeT curves from different loess sections indicates a stronger chemical weathering in the Songjiadian section and notable enhancement around 1800, 800 and 600 ka BP, implying the strengthening of the East Asian monsoon during these periods. In contrast, it was weakened at 1100 ka BP. Generally, the summer monsoon shows a gradually decreasing trend during the entire Pleostocene, but the spatial pattern typified by an increasing trend in weathering intensity from north to south remained the same. 5. The loess unit L9 in the Songjiadian section displays two geomagnetic field anomalies with the midpoint ages of 0.917 and 0.875 Ma respectively, with a segment of 12 ka. They are demonstrated to be equivalent to the Santa Rosa and Kamikatsura geomagnetic excursions. 6. Magnetite is the main magnetic carrier for both loess and paleosols. Maghemite concentration is higher in paleosols than in loess, and is an important carrier for the enhanced magnetic susceptibility in paleosols. Magnetic fabric analysis suggests a dominant N-S wind direction prevailing in the L9 and L15, while the summer winds were dominantly in NNE-SSW direction during the S8 period, notably differing from previous studies.

青藏高原横波速度与各向异性结构及其壳幔形变印迹

As the most spectacular and youngest case of continental collision on the Earth, to investigate the crust and mantle of Tibetan plateau, and then to reveal its characters of structure and deformation, are most important to understand its deformation mechanism and deep process. A great number of surface wave data were initially collected from events occurred between 1980 and 2002, which were recorded by 13 broadband digital stations in Eurasia and India. Up to 1,525 source-station Rayleigh waveforms and 1,464 Love wave trains were analysed to obtain group velocity dispersions, accompanying with the detail and quantitative assessment of the fitness of the classic Ray Theory, errors from focal and measurements. Assuming the model region covered by a mesh of 2ox2o-sized grid-cells, we have used the damped least-squares approach and the SVD to carry out tomographic inversion, SV- and SH-wave velocity images of the crust and upper mantle beneath the Tibetan Plateau and surroundings are obtained, and then the radial anisotropy is computed from the Love-Rayleigh discrepancy. The main results demonstrate that follows, a) The Moho beneath the Tibetan Plateau presents an undulating shape that lies between 65 and 74 km, and a clear correlation between the elevations of the plateau and the Moho topography suggests that at least a great part of the highly raised plateau is isostatically compensated. b) The lithospheric root presents a depth that can be substantiated at ~140 km (Qiangtang Block) and exceptionally at ~180 km (Lhasa Block), and exhibits laterally varying fast velocity between 4.6 and 4.7 km/s, even ~4.8 km/s under northern Lhasa Block and Qiangtang Block, which may be correlated with the presence of a shield-like upper mantle beneath the Tibetan Plateau and therefore looked as one of the geophysical tests confirming the underthrusting of India, whose leading edge might have exceeded the Bangong-Nujiang Suture, even the Jinsha Suture. c) The asthenosphere is depicted by a low velocity channel at depths between 140 and 220 km with negative velocity gradient and velocities as low as 4.2 km/s; d) Areas in which transverse radial anisotropy is in excess of ~4% and 6% on the average anisotropy are found in the crust and upper mantle underlying most of the Plateau, and up to 8% in some places. The strength, spatial configuration and sign of radial anisotropy seem to indicate the existence of a regime of horizontal compressive forces in the frame of the convergent orogen at the same time that laterally varying lithospheric rheology and a differential movement as regards the compressive driving forces. e) Slow-velocity anomalies of 12% or more in southern Tibet and the eastern edge of the Plateau support the idea of a mechanically weak middle-to-lower crust and the existence of crustal flow in Tibet.

油气勘探中的弱磁异常提取与区域场分析

Petroleum and natural gas is an important strategic resources. The short of the reserves will block the development of economy and threaten the safety of nation, along with the main oil fields of our country coming to the height of power and splendor of the exploitation and exploration. Therefore, it makes a great sense to inaugurate new explorative field and increase the reserves of petroleum and natural gas. Magnetic exploration is a main method of geophysics exploration. the developing observation apparatus and the perfect processing method provide wide space for magnetic exploration in these years. The method of magnetic bright spot is an application of magnetic exploration. The vertical migration of the hydrocarbon changes physical and chemical environment above the hydrocarbon reservoir, the new environment make tervalent iron translate into bivalent iron, that produce small scale magnetic anomaly, that is magnetic bright spot. The method of magnetic bright spot explores oil and gas field by the relation between the hydrocarbon and magnetic anomaly. This paper systemically research to pick-up and identify magnetic bright spot combining an oil field item, then point out advantaged area. In order to test the result, the author use the seismic information to superpose the magnetic bright spot, that prove the magnetic bright spot is reliable. then, the author complete a software to pick and identify the magnetic bright spot. The magnetic basement is very important to research forming and evolvement of the basin, especially, it is a crucial parameter of exploring residual basin in the research on pre-Cenozoic residual. This paper put forward a new method to inverse the interface of the magnetic layer on the basis of previous work, that is the method of separation of magnetic field step by step. The theory of this method is to translate the result of magnetic layer fluctuation to the result of magnetization density change, and the magnetic layer is flat, the paper choose thickness of magnetic layer as unit thickness, and define magnetic layer as a unit-thickness layer in order to convenient calculation, at the same time, define the variational magnetization density as equivalent magnetic density. Then we translate the relation between magnetic field and layer fluctuation to the relation between magnetic field and equivalent magnetic density, then, we can obtain the layer fluctuation through calculating equivalent magnetic density. Contrast to conventional parker method, model experimentation and example checkout prove this method is effective. The merit of this method is to avoid flat result in a strongly fluctuant area because of using a uniform average depth, the result of this method is closer to the fact, and this method is to inverse equivalent magnetic density, then translate equivalent magnetic density to layer fluctuation, this lays a foundation to inverse variational magnetic density in the landscape orientation and portrait.