Conditional nonlinear optimal perturbation: Applications to stability,sensitivity, and predictability

Conditional nonlinear optimal perturbation (CNOP) is a nonlinear generalization of linear singular vector (LSV) and features the largest nonlinear evolution at prediction time for the initial perturbations in a given constraint. It was proposed initially for predicting the limitation of predictability of weather or climate. Then CNOP has been applied to the studies of the problems related to predictability for weather and climate. In this paper, we focus on reviewing the recent advances of CNOP’s applications, which involves the ones of CNOP in problems of ENSO amplitude asymmetry, block onset, and the sensitivity analysis of ecosystem and ocean’s circulations, etc. Especially, CNOP has been primarily used to construct the initial perturbation fields of ensemble forecasting, and to determine the sensitive area of target observation for precipitations. These works extend CNOP’s applications to investigating the nonlinear dynamical behaviors of atmospheric or oceanic systems, even a coupled system, and studying the problem of the transition between the equilibrium states. These contributions not only attack the particular physical problems, but also show the superiority of CNOP to LSV in revealing the effect of nonlinear physical processes. Consequently, CNOP represents the optimal precursors for a weather or climate event; in predictability studies, CNOP stands for the initial error that has the largest negative effect on prediction; and in sensitivity analysis, CNOP is the most unstable (sensitive) mode. In multi-equilibrium state regime, CNOP is the initial perturbation that induces the transition between equilibriums most probably. Furthermore, CNOP has been used to construct ensemble perturbation fields in ensemble forecast studies and to identify sensitive area of target observation. CNOP theory has become more and more substantial. It is expected that CNOP also serves to improve the predictability of the realistic predictions for weather and climate events plays an increasingly important role in exploring the nonlinear dynamics of atmospheric, oceanic and coupled atmosphere-ocean system. Supported by National Basic Research Program of China (Grant Nos. 2006CB403606, 2007CB411800), National Natural Science Foundation of China (Grant Nos. 40830955, 40675030, 40505013), Institute of Atmospheric Physics, Chinese Academy of Sciences (Grant No. IAP07202), and LASG State Key Laboratory Special Fund     

Hydrothermal hexahydrite spherules erupted during the 2008–2010 summit eruption of Kīlauea Volcano,Hawai`i

Small (1–3 mm), hollow spherules of hexahydrite have been collected falling out of the magmatic gas plume downwind of Kīlauea’s summit vent. The spherules were observed on eight separate occasions during 2009–2010 when a lake of actively spattering lava was present ~150–200 m below the rim of the vent. The shells of the spherules have a fine bubbly foam structure less than 0.1 mm thick, composed almost entirely of hexahydrite [MgSO₄·6H₂O] Small microspherules of lava (<5 μm across) along with mineral and rock fragments from the magmatic plume adhered to the outside of the hexahydrite spherules. Phase relationships and the particulate matter in the magmatic plume indicate that the spherules originated as a bubbly solution injected into and mixed with the magmatic plume. The most likely mechanism for production of hexahydrite spherules is boiling of MgSO₄-saturated meteoric water in the walls of the conduit above the surface of the lava lake. Solfataric sulfates may thus be recycled and reinjected into the plume, creating particulates of sulfate minerals that can be distributed far from their original source.     

Assessment of the pseudo total metal content in alluvial sediments from Danube River,Serbia

We used elemental carbon, nitrogen, hydrogen and sulfur as well as ratios of hydrogen and nitrogen with total organic carbon for investigation of source and conditions of organic matter in alluvial Danube sediments. We also determined the pseudo total concentrations of metals presented as a sum of extracted concentration after five sequential extraction steps. The pseudo total metal concentrations were found to be (mg kg⁻¹) for Mn, 666; Fe, 25,852; Mg, 16,193; K, 2,063; Ni, 32.4; Zn, 72.2; Pb, 15.0; Cu, 26.0 and for Cr, 15.9. Correlation analysis and two multivariate analysis methods (principal component and cluster analysis) were helpful in determining the associations between the pseudo total extracted fractions of metals and with elemental carbon, hydrogen, nitrogen, sulfur, total inorganic and organic carbon. These correlations will help us to identify substrates of trace metals in different oxic/anoxic conditions. The correlation results of the trace metals and Fe, K, Mg and Mn suggest their adsorption, mainly onto Fe and Mn (hydro)oxides and K alumosilicates, whereas correlations of metals with sulfur indicate that they were precipitated as Fe-sulfides.     

Tropical instability wave interactions within the Galápagos Archipelago

The effects of tropical instability waves (TIW) within the eastern equatorial Pacific during the boreal fall of 2005 were observed in multiple data sets. The TIW cause oscillations of the sea surface temperature (SST), meridional currents (V), and 20 °C isotherm (thermocline). A particularly strong 3-wave packet of ～15-day period TIW passed through the Galápagos Archipelago in Sep and Oct 2005 and their effects were recorded by moored near-surface sensors. Repeat Argo profiles in the archipelago showed that the large temperature (>5 °C) oscillations that occurred were associated with a vertical adjustment within the water column. Numerical simulations report strong oscillations and upwelling magnitudes of ～5.0 m d^?1 near the Tropical Atmosphere Ocean (TAO) buoy at 0°, 95°W and in the Archipelago at 92°W and 90°W. A significant biological response to the TIW passage was observed within the archipelago. Chlorophyll a measured by the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) increased by >30% above 1998–2007 mean concentrations within the central archipelago. The increases coincide with coldest temperatures and the much larger increases within the archipelago as compared to those of 95°W indicate that TIW induced upwelling over the island platform itself brought more iron-enriched upwelling waters into the euphotic zone.     

Measurement on soil deformation caused by expanded-base pile in transparent soil using particle image velocimetry (PIV)

A new small-scale geotechnical physical model in 1-g and unconfined condition, combining the transparent soil, close-range photogrammetry and particle image velocimetry (PIV), was employed, which provides a non-intrusively internal deformation measurement approach to monitor the internal deformation of soil caused by expanded-base pile jacking with casing. The transparent soil was made of fused quartz and its refractive index matched blended oil, adding reflective particles (glass beads). Close-range photogrammetry was employed to record the images of the process of casing jacking and extraction in transparent soil, allowing the use of Matlab-based Geo-PIV to figure out the displacement field converted from image space to object space. Analysis of test results indicates that the maximum displacement caused by casing jacking for expanded-conical-base pile is decreased by 29% compared with that for expanded-flat-base pile. The main movement happens at the early stage of casing extraction. The maximum displacement caused by casing extraction for the conical base is about 43% of that for the flat base, while the affected zone caused by casing extraction for the conical base accounts for about 1/3 of that for the flat base. The contraction for horizontal displacements tends to decrease with the depth increasing. By contrast, the contraction under pile base decreases with the increasing of displacement. The displacements generated by jacking a conventional pile having a diameter equal to the casing diameter of the expanded-base pile were comparable to the net displacement taking place due to expanded-base pile installation for the conical base pile.     

Characteristics and interpretation of the seismic signal of a field-scale landslide dam failure experiment

Outburst floods caused by breaches of landslide dams may cause serious damages and loss of lives in downstream areas; for this reason the study of the dynamic of the process is of particular interest for hazard and risk assessment. In this paper we report a field-scale landslide dam failure experiment conducted in Nantou County, in the central of Taiwan.The seismic signal generated during the dam failure was monitored using a broadband seismometer and the signal was used to study the dam failure process.We used the short-time Fourier transform(STFT) to obtain the time–frequency characteristics of the signal and analyzed the correlation between the power spectrum density(PSD) of the signal and the water level. The results indicate that the seismic signal generated during the process consisted of three components: a low-frequency band(0–1.5 Hz), an intermediate-frequency band(1.5–10 Hz) and a highfrequency band(10–45 Hz). We obtained the characteristics of each frequency band and the variations of the signal in various stages of the landslide dam failure process. We determined the cause for the signal changes in each frequency band and its relationship with the dam failure process. The PSD sediment flux estimation model was used to interpret the causes of variations in the signal energy before the dam failure and the clockwise hysteresis during the failure. Our results show that the seismic signal reflects the physical characteristics of the landslide dam failure process. The method and equipment used in this study may be used to monitor landslide dams and providing early warnings for dam failures.     

Spatial patterns and storage composition of woody debris in a natural secondary forest dominated by <Emphasis Type="Italic">Pinus tabulaeformis</Emphasis> on Loess Plateau,China

Woody debris (WD) is an important part of natural Pinus tabulaeformis mixed stands, and it affects the forest ecosystem stability and development. The WD spatial patterns are especially important structural characteristics that can provide insights into forest dynamics. In this paper, the WD storage, WD spatial patterns and WD associations among the main species were examined in the natural secondary forest on Loess Plateau in northwest China. Data were collected in a 1 ha (100 m × 100 m) permanent plot, and all the trees with a diameter at breast height of more than 3 cm were measured and stem-mapped. Ripley’s K functions from the spatial-point-pattern-analysis method were used to analyze the spatial distribution and associations. The results showed that: (1) The total storage of WD was 10.73 t/ha, fallen wood was the main source of WD, and the majority diameters were greater than 20 cm, and in intermediate levels of decay; (2) The overall spatial pattern was closely related to the spatial scale, which exhibited an aggregated pattern on a small scale, and a random pattern on a large scale. The spatial patterns of coarse woody debris also gradually transitioned from an aggregated pattern in fine scales to a random pattern in broader spatial scales, which matched the overall spatial pattern. The spatial intensity was gradually decreased with the increasing diameters, and increased with the decomposition classes; (3) The WD of Pinus tabulaeformis species was negatively associated with Betula platyphylla and Populus davidiana on a small scale but positively associated with these species on a large scale. The spatial pattern and interspecies relations were the results of long-term interactions between the natural secondary forest community and the surrounding natural environment. These findings would provide a scientific basis for the sustainable management and protection of natural secondary forest ecosystems on Loess Plateau.     

A novel model to assess soil productivity in the dry-hot valleys of China

Accurate evaluation of soil productivity has been a long-standing challenge. Although numerous models for productivity assessment exist, most are cumbersome to use and require substantial parameter inputs. We developed a new empirical soil productivity model based on field investigations of soil erosion, soil physicochemical properties, and crop yields in the dry-hot valleys (DHVs) in China. We found that soil pH, and organic matter and available potassium contents significantly affected crop yields under eroded conditions of the DHVs. Moreover, available potassium content was the key factor affecting soil productivity. We then modified an existing soil productivity model by adding the following parameters: contents of effective water, potassium, organic matter, and clay, soil pH, and root weighting factor. The modified soil productivity model explained 63.5% of the crop yield. We concluded that the new model was simple, realistic, and exhibited strong predictability. In addition to providing an accurate assessment of soil productivity, our model could potentially be applied as a soil module in comprehensive crop models.     

A back-propagation neural-network-based displacement back analysis for the identification of the geomechanical parameters of the Yonglang landslide in China

Xigeda formation is a type of hundred-meter-thick lacustrine sediments of being prone to triggering landslides along the trunk channel and tributaries of the upper Yangtze River in China. The Yonglang landslide located near Yonglang Town of Dechang County in Sichuan Province of China, which was a typical Xigeda formation landslide, was stabilized by anti-slide piles. Loading tests on a loading-test pile were conducted to measure the displacements and moments. The uncertainty of the tested geomechanical parameters of the Yonglang landslide over certain ranges would be problematic during the evaluation of the landslide. Thus, uniform design was introduced in the experimental design, and by which, numerical analyses of the loading-test pile were performed using Fast Lagrangian Analysis of Continua (FLAC^3D) to acquire a database of the geomechanical parameters of the Yonglang landslide and the corresponding displacements of the loading-test pile. A three-layer back-propagation neural network was established and trained with the database, and then tested and verified for its accuracy and reliability in numerical simulations. Displacement back analysis was conducted by substituting the displacements of the loading-test pile to the well-trained three-layer back-propagation neural network so as to identify the geomechanical parameters of the Yonglang landslide. The neural-network-based displacement back analysis method with the proposed methodology is verified to be accurate and reliable for the identification of the uncertain geomechanical parameters of landslides.