A bivariate gamma distribution for use in multivariate flood frequency analysis

A gamma distribution is one of the most frequently selected distribution types for hydrological frequency analysis. The bivariate gamma distribution with gamma marginals may be useful for analysing multivariate hydrological events. This study investigates the applicability of a bivariate gamma model with five parameters for describing the joint probability behavior of multivariate flood events. The parameters are proposed to be estimated from the marginal distributions by the method of moments. The joint distribution, the conditional distribution, and the associated return periods are derived from marginals. The usefulness of the model is demonstrated by representing the joint probabilistic behaviour between correlated flood peak and flood volume and between correlated flood volume and flood duration in the Madawask River basin in the province of Quebec, Canada. Copyright © 2001 John Wiley & Sons, Ltd.     

A hidden Markov model segmentation procedure for hydrological and environmental time series

In this paper we present a procedure for the segmentation of hydrological and enviromental time series. We consider the segmentation problem from a purely computational point of view which involves the minimization of Huberts segmentation cost; in addition this least squares segmentation is equivalent to Maximum Likelihood segmentation. Our segmentation procedure maximizes Likelihood and minimizes Huberts least squares criterion using a hidden Markov model (HMM) segmentation algorithm. This algorithm is guaranteed to achieve a local maximum of the Likelihood. We evaluate the segmentation procedure with numerical experiments which involve artificial, temperature and river discharge time series. In all experiments, the procedure actually achieves the global minimum of the Likelihood; furthermore execution time is only a few seconds, even for time series with over a thousand terms.     

A multivariate non‐parametric model for synthetic generation of daily streamflow

A p‐order multivariate kernel density model based on kernel density theory has been developed for synthetic generation of multivariate variables. It belongs to a kind of data‐driven approach and is able to avoid prior assumptions as to the form of probability distribution (normal or Pearson III) and the form of dependence (linear or non‐linear). The p‐order multivariate kernel density model is a non‐parametric method for synthesis of streamflow. The model is more flexible than conventional parametric models used in stochastic hydrology. The effectiveness and satisfactoriness of this model are illustrated through its application to the simultaneous synthetic generation of daily streamflow from Pingshan station and Yibin‐Pingshan region (Yi‐Ping region) of the Jinsha River in China. Copyright © 2007 John Wiley & Sons, Ltd.     

Large scale climate and rainfall seasonality in a Mediterranean Area: Insights from a non‐homogeneous Markov model applied to the Agro‐Pontino plain

In the context of climate change and variability, there is considerable interest in how large scale climate indicators influence regional precipitation occurrence and its seasonality. Seasonal and longer climate projections from coupled ocean–atmosphere models need to be downscaled to regional levels for hydrologic applications, and the identification of appropriate state variables from such models that can best inform this process is also of direct interest. Here, a Non‐Homogeneous Hidden Markov Model (NHMM) for downscaling daily rainfall is developed for the Agro‐Pontino Plain, a coastal reclamation region very vulnerable to changes of hydrological cycle. The NHMM, through a set of atmospheric predictors, provides the link between large scale meteorological features and local rainfall patterns. Atmospheric data from the NCEP/NCAR archive and 56‐years record (1951–2004) of daily rainfall measurements from 7 stations in Agro‐Pontino Plain are analyzed. A number of validation tests are carried out, in order to: 1) identify the best set of atmospheric predictors to model local rainfall; 2) evaluate the model performance to capture realistically relevant rainfall attributes as the inter‐annual and seasonal variability, as well as average and extreme rainfall patterns. Validation tests show that the best set of atmospheric predictors are the following: mean sea level pressure, temperature at 1000 hPa, meridional and zonal wind at 850 hPa and precipitable water, from 20°N to 80°N of latitude and from 80°W to 60°E of longitude. Furthermore, the validation tests show that the rainfall attributes are simulated realistically and accurately. The capability of the NHMM to be used as a forecasting tool to quantify changes of rainfall patterns forced by alteration of atmospheric circulation under climate change and variability scenarios is discussed.     

A multivariate Bernstein copula model for permeability stochastic simulation

This paper introduces a general nonparametric method for joint stochastic simulation of petrophysical properties using the Bernstein copula. This method consists basically in generating stochastic simulations of a given petrophysical property (primary variable) modeling the underlying empirical dependence with other petrophysical properties (secondary variables) while reproducing the spatial dependence of the first one.This multivariate approach provides a very flexible tool to model the complex dependence relationships of petrophysical properties. It has several advantages over other traditional methods, since it is not restricted to the case of linear dependence among variables, it does not require the assumption of normality and/or existence of moments.In this paper this method is applied to simulate rock permeability using Vugular Porosity and Shear Wave Velocity (S-Waves) as covariates in a carbonate double-porosity formation at well log scale. Simulated permeability values show a high degree of accuracy compared to the actual values.     

基于马尔科夫链模型的鄱阳湖流域水文气象干旱研究

基于气象和水文干旱的二维变量干旱状态基础上,通过一阶马尔科夫链模型对二维变量干旱状态进行频率、重现期和历时分析,建立水文气象干旱指数,从干旱灾害形成、演变和持续3方面对干旱灾害进行研究,同时预测未来6个月非水文干旱到水文干旱的概率.结果表明:(1)修河流域在干旱形成中危害大,抚河流域和修河流域在干旱演变中危害大,赣江流域和饶河流域在干旱持续中危害大;(2)鄱阳湖流域状态4(气象、水文干旱)发生的频率最高,为0.30,连续湿润或者干旱的概率最大,湿润状态(状态2)与水文干旱(状态4、状态5(气象湿润、水文干旱))的相互转移概率最低;(3)在长期干旱预测中,鄱阳湖流域从状态2转到状态4和状态5的平均概率为0.11,属最低,而状态1(气象、水文无旱)和状态3(气象干旱、水文湿润)到达状态4的概率为0.23,发生概率最大.修河流域在非水文干旱状态下未来发生气象、水文干旱状态的平均概率为0.28,是"五河"中最高的,而赣江流域在正常或者湿润状态下未来发生气象、水文干旱的概率最低,为0.18,该研究对于鄱阳湖流域水文气象干旱的抗旱减灾具有重要理论与现实意义.     

Daily rainfall projections from general circulation models with a downscaling nonhomogeneous hidden Markov model (NHMM) for south‐eastern Australia

An ensemble of stochastic daily rainfall projections has been generated for 30 stations across south‐eastern Australia using the downscaling nonhomogeneous hidden Markov model, which was driven by atmospheric predictors from four climate models for three IPCC emissions scenarios (A1B, A2, and B1) and for two periods (2046–2065 and 2081–2100). The results indicate that the annual rainfall is projected to decrease for both periods for all scenarios and climate models, with the exception of a few scenarios of no statistically significant changes. However, there is a seasonal difference: two downscaled GCMs consistently project a decline of summer rainfall, and two an increase. In contrast, all four downscaled GCMs show a decrease of winter rainfall. Because winter rainfall accounts for two‐thirds of the annual rainfall and produces the majority of streamflow for this region, this decrease in winter rainfall would cause additional water availability concerns in the southern Murray–Darling basin, given that water shortage is already a critical problem in the region. In addition, the annual maximum daily rainfall is projected to intensify in the future, particularly by the end of the 21st century; the maximum length of consecutive dry days is projected to increase, and correspondingly, the maximum length of consecutive wet days is projected to decrease. These changes in daily sequencing, combined with fewer events of reduced amount, could lead to drier catchment soil profiles and further reduce runoff potential and, hence, also have streamflow and water availability implications. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of agricultural drought in Iiuni,Eastern Kenya: application of a Markov model

In semi‐arid Kenya, episodes of agricultural droughts of varying severity and duration occur. The occurrence of these agricultural droughts is associated with seasonal rainfall variability and can be reflected by seasonal soil moisture deficits that significantly affect crop performance and yield. The objective of this study was to stochastically simulate the behaviour of dry and wet spells and rainfall amounts in Iiuni watershed, Kenya. The stochastic behaviour of the longest dry and wet spells (runs) and largest rainfall amounts were simulated using a Markov (order 1) model. There were eight raingauge stations within the watershed. The entire analysis was carried out using probability parameters, i.e. mean, variance, simple and conditional probabilities of dry and rain days. An analysis of variance test (ANOVA ) was used to establish significant differences in rainfall characteristics between the eight stations. An analysis of the number of rain days and rainfall amount per rain day was done on a monthly basis to establish the distribution and reliability of seasonal rainfall. The graphic comparison of simulated cumulative distribution functions (Cdfs) of the longest spells and largest rainfall amounts showed Markovian dependence or persistence. The longest dry spells could extend to 24 days in the long rainy season and 12 in the short rainy season. At 50% (median) probability level, the largest rainfall amounts were 91 mm for the long rainy season and 136 mm for the short rainy season. The short rains were more reliable for crop production than the long rains. The Markov model performed well and gave adequate simulations of the spells and rainfall amounts under semi‐arid conditions. Copyright © 2004 John Wiley & Sons, Ltd.     

Mapping gamma radiation and its uncertainty from weathering products in a Tasmanian landscape with a proximal sensor and random forest kriging

The radionuclides of potassium (⁴⁰ K), uranium (²³⁸U) and thorium (²³²Th) emit from the land surface gamma radiation that is characteristic of the underlying rocks and the distribution of their weathering products in the landscape. We measured the radiation along widely separated transects using a mobile proximal sensor over a 10 000‐ha region of Tasmania. We supplemented the transect data with information from soil and geological maps and dense data from LandSat and SPOT imagery, a digital elevation model and terrain attributes on a grid at 30‐m intervals so as to map the radionuclides. We used a sequence of steps, starting with a spatial bootstrap and random forests to predict emissions across the study area and at sampling points excluded from the bootstrap samples. The predictions at the sampling points were compared with the observed values to obtain residuals, which were then used to krige them at all points on the 30 m grid. We combined the random forest and kriging predictions on the 30‐m grid to obtain our random forest kriging predictions. Repeating the procedure 100 times provided confidence limits on our results and predictions. The resulting maps of the radionuclides accord well with what we know of the soil, lithology and topography of the region from other sources. Alluvial deposits with large amounts of potassium extend from the foot slopes of the Great Western Tiers and along the flood plains of the Meander River, providing evidence of previous widespread weathering and deposition of the material. The fertile Red Ferrosols (roughly equivalent to Ferralic Nitisols in the World reference base (WRB) classification) on the extensive Tertiary basalt plateau emit little gamma radiation as a result of deep weathering and of potassium movement and accumulation down its talus slopes. The maps show the complexity of the region in terms of soil, lithology and terrain, and they show the merits of gamma radiometry for mapping and understanding the distribution of materials in such regions. Copyright © 2013 John Wiley & Sons, Ltd.     

A Bayesian model for lithology/fluid class prediction using a Markov mesh prior fitted from a training image

We consider a Bayesian model for inversion of observed amplitude variation with offset data into lithology/fluid classes, and study in particular how the choice of prior distribution for the lithology/fluid classes influences the inversion results. Two distinct prior distributions are considered, a simple manually specified Markov random field prior with a first-order neighbourhood and a Markov mesh model with a much larger neighbourhood estimated from a training image. They are chosen to model both horizontal connectivity and vertical thickness distribution of the lithology/fluid classes, and are compared on an offshore clastic oil reservoir in the North Sea. We combine both priors with the same linearized Gaussian likelihood function based on a convolved linearized Zoeppritz relation and estimate properties of the resulting two posterior distributions by simulating from these distributions with the Metropolis–Hastings algorithm. The influence of the prior on the marginal posterior probabilities for the lithology/fluid classes is clearly observable, but modest. The importance of the prior on the connectivity properties in the posterior realizations, however, is much stronger. The larger neighbourhood of the Markov mesh prior enables it to identify and model connectivity and curvature much better than what can be done by the first-order neighbourhood Markov random field prior. As a result, we conclude that the posterior realizations based on the Markov mesh prior appear with much higher lateral connectivity, which is geologically plausible.     

Lithology and fluid prediction from prestack seismic data using a Bayesian model with Markov process prior

We invert prestack seismic amplitude data to find rock properties of a vertical profile of the earth. In particular we focus on lithology, porosity and fluid. Our model includes vertical dependencies of the rock properties. This allows us to compute quantities valid for the full profile such as the probability that the vertical profile contains hydrocarbons and volume distributions of hydrocarbons. In a standard point wise approach, these quantities can not be assessed. We formulate the problem in a Bayesian framework, and model the vertical dependency using spatial statistics. The relation between rock properties and elastic parameters is established through a stochastic rock model, and a convolutional model links the reflectivity to the seismic. A Markov chain Monte Carlo (MCMC) algorithm is used to generate multiple realizations that honours both the seismic data and the prior beliefs and respects the additional constraints imposed by the vertical dependencies. Convergence plots are used to provide quality check of the algorithm and to compare it with a similar method. The implementation has been tested on three different data sets offshore Norway, among these one profile has well control. For all test cases the MCMC algorithm provides reliable estimates with uncertainty quantification within three hours. The inversion result is consistent with the observed well data. In the case example we show that the seismic amplitudes make a significant impact on the inversion result even if the data have a moderate well tie, and that this is due to the vertical dependency imposed on the lithology fluid classes in our model. The vertical correlation in elastic parameters mainly influences the upside potential of the volume distribution. The approach is best suited to evaluate a few selected vertical profiles since the MCMC algorithm is computer demanding.     

Enviromental genotoxicity evaluation: Bayesian approach for a mixture statistical model

 The data analyzed in this paper are part of the results described in Bueno et al. (2000). Three cytogenetics endpoints were analyzed in three populations of a species of wild rodent – Akodon montensis – living in an industrial, an agricultural, and a preservation area at the Itajaí Valley, State of Santa Catarina, Brazil. The polychromatic/normochromatic ratio, the mitotic index, and the frequency of micronucleated polychromatic erythrocites were used in an attempt to establish a genotoxic profile of each area. It was assumed that the three populations were in the same conditions with respect to the influence of confounding factors such as animal age, health, nutrition status, presence of pathogens, and intra- and inter-populational genetic variability. Therefore, any differences found in the endpoints analyzed could be attributed to the external agents present in each area. The statistical models used in this paper are mixtures of negative-binomials and Poisson variables. The Poisson variables are used as approximations of binomials for rare events. The mixing distributions are beta densities. The statistical analyzes are under the bayesian perspective, as opposed to the frequentist ones often considered in the literature, as for instance in Bueno et al. (2000).     

A quantitative characterization of the seasonal Lagrangian circulation of the Gulf of California from a three-dimensional numerical model

A set of four indices that quantify Lagrangian properties of the Gulf of California seasonal circulation were implemented from outputs of a three-dimensional numerical model. From trajectories of particles seeded over the entire Gulf, we calculated for 12 one-month periods the following indices: net and total distance traveled by the particles, the number of particles that are found within an area centered on the release positions after one month, and time taken by particles to escape from a 50-km-radius circle. These indices can be used for studies on transport of inert properties and passive planktonic organisms such as eggs and early-stage larvae; their use is illustrated for typical summer and winter conditions in the Gulf of California. These indices show the potential for connecting areas separated by a few hundreds of km along the eastern side of the Gulf, due to the strong seasonal up-gulf and down-gulf current. In the Northern Gulf, large displacements occur at the borders of the basin-wide seasonally reversing eddy that dominates the large-scale circulation (cyclonic in summer, anticyclonic in winter). On the other hand, the potential for self-recruitment areas is found as particles can be trapped for longer than one month within these eddies, as well as in smaller ones in the Northern Gulf, and near the coast of the peninsular side of the Southern Gulf, where current speeds are slow and many small capes and islands are present.     

青藏高原东北缘地震时空迁移的有限元数值模拟

地震在大陆内部断层系统中的时空迁移和丛集的基本力学机制一直是地球科学家关注的重要问题.青藏高原东北缘地震活动频繁,其地震时空迁移和地震丛集现象显著,是研究这个问题的重要区域.我们建立了一个三维黏弹塑性有限元模型,模拟了青藏高原东北缘主要活动断层系统的地震循环和地震时空迁移;计算了断层系统的应力演化;并探讨了断层之间的相互作用及地震时空迁移和地震丛集的原因.模拟结果显示断层之间的相互作用通过增加或降低断层上的库仑应力,加速或延缓了地震发生,使得区域地震可以在短时间内集中发生,从而形成地震丛集;另外,区域经过多个地震循环的长期演化,一些孕震断层上的应力状态恰好都达到屈服的临界状态附近,从而也可以导致这些断层上的地震在短期内集中发生,因此产生地震丛集和地震迁移.我们发现当区域经历地震丛集之后,该区域的应力大大释放,区域进入地震平静期;随着构造加载的持续,区域应力逐渐恢复,为下一次地震丛集或地震序列累积应力和能量;上述过程可以重复发生.因此地震丛集期与平静期交替出现.我们还统计了各个断层的大地震相互迁移的模拟结果,结果显示青藏高原东北缘下一次大地震有很大的概率会发生在海原断层上.

     

Shelf habitat distribution as a legacy of Late Quaternary marine transgressions: A case study from a tropical carbonate province

The legacy of multiple marine transgressions is preserved in a complex morphology of ridges, mounds and reefs on the Carnarvon continental shelf, Western Australia. High-resolution multibeam sonar mapping, underwater photography and sampling across a 280 km² area seaward of the Ningaloo Coast World Heritage Area shows that these raised features provide hardground habitat for modern coral and sponge communities. Prominent among these features is a 20 m high and 15 km long shore-parallel ridge at 60 m water depth. This ridge preserves the largely unaltered form of a fringing reef and is interpreted as the predecessor to modern Ningaloo Reef. Landward of the drowned reef, the inner shelf is covered by hundreds of mounds (bommies) up to 5 m high and linear ridges up to 1.5 km long and 16 m high. The ridges are uniformly oriented to the north-northeast and several converge at their landward limit. On the basis of their shape and alignment, these ridges are interpreted as relict long-walled parabolic dunes. Their preservation is attributed to cementation of calcareous sands to form aeolianite, prior to the post-glacial marine transgression. Some dune ridges abut areas of reef that rise to sea level and are highly irregular in outline but maintain a broad shore-parallel trend. These are tentatively interpreted as Last Interglacial in age. The mid-shelf and outer shelf are mostly sediment covered with relatively low densities of epibenthic biota and have patches of low-profile ridges that may also be relict reef shorelines. An evolutionary model for the Carnarvon shelf is proposed that relates the formation of drowned fringing reefs and aeolian dunes to Late Quaternary eustatic sea level.     

A seismic gap in the eastern margin of the Sea of Japan as inferred from the time-space distribution of past seismicity

Abstract Based on the spatial distribution of the focal areas from previous large earthquakes, a significant seismic gap was found off the coast of the Akita Prefecture at the eastern margin of the Sea of Japan. We forecast that the 75 km segment of plate boundary may be ruptured by a large thrust earthquake with a magnitude of 7.5 in the near future. The time of occurrence is uncertain, but the recurrence interval of large earthquakes in this region suggests that it will be no later than the end of next century. The time sequence of large earthquakes in the eastern margin of the Sea of Japan shows a systematic shortening of the earthquake interval for the past 250 years. This feature is simulated successfully by a simple mechanical model that represents a plate boundary by segmented blocks, each of which is composed of a spring friction slider system. We further propose to revise the conventionally accepted plate boundary between the Eurasian and Okhotsk plates in the eastern margin of the Sea of Japan; the observed data of seismic activity and recent crustal deformation indicate that the southern part of the plate boundary traverses the land region from Niigata to Otari along the Shinanogawa seismic belt. The fault geometries of previous large earthquakes show that the mode of plate convergence in the eastern margin of the Sea of Japan is a collision type rather than a simple eastward subduction as was postulated in early studies.     

海域流动点外部扰动引力无奇异计算模型

针对海域重力场变化特征和远程飞行器机动发射保障应用需求,本文分析研究了地球外部空间扰动引力三类传统计算模型的技术特点及其适用性,指出了采用表层法作为海域流动点扰动引力计算模型的合理性及需要解决的关键问题,分析论证了空中扰动引力计算对地面观测数据的分辨率和精度要求,提出通过引入局部积分域恒等式变换、局域泰勒级数展开和非网格点内插方法,消除表层法计算模型积分奇异性固有缺陷的研究思路,进而推出了适合于海域流动点应用的扰动引力无奇异计算模型,较好地满足了全海域和全高度段对局部扰动重力场快速赋值的实际需求.以超高阶全球位模型EGM2008作为标准场,通过数值计算验证了无奇异计算模型的可行性和有效性,在重力场变化比较剧烈的海沟区,该模型的计算精度优于2×10^-5m·s^-2.

     

Inflow and outflow in a rotating circular container—A laboratory model for the Loop Current of the Gulf of Mexico

The Loop Current of the Gulf of Mexico is simulated in the laboratory. A circular tank is filled with water and is placed off-center on a rotating table and the flow field is generated by injecting and withdrawing water at two openings on the wall. The free surface becomes parabolic due to balance of gravitational and centrifugal forces, simulating the latitudinal change of the Coriolis parameter (-effect) in the ocean. The flow characteristics depend on the influx and the rate of rotation and can be classified according to non-dimensional parameters (Rossby, Ekman and Froude numbers denoted byR ₀,E andF, respectively). When the influx is small and the rotation rate is large (smallR ₀,E andF) the flow will be almost linear, and the fluid flows along the side-wall boundary layer under constraint of the -effect. For a very large influx (largeR ₀ andE) inertial forces become very large compared to the Coriolis force and the flow behaves like a potential flow. The flow studied had characteristics between these two extreme cases and hasR ₀ andF similar to the Gulf circulation, though similarity inE is ambiguous. Photographs of the flow indicate that the inflow penetrates further into the interior when the rotation rate is increased while the influx is kept constant. The numerical analysis of the non-linear vorticity equation confirms this for the parameters corresponding to the experiment. In addition, the photographs reveal eddies embedded on both sides of the main stream, particularly near the inflow region. These eddies are intensified and become uniform in size as the influx increases. It is pointed out that such eddies were actually observed near the Loop Current north of the Yucatan Straits.     

Estimating the distribution of snow water equivalent using remotely sensed snow cover data and a spatially distributed snowmelt model: A multi-resolution,multi-sensor comparison

Time series of fractional snow covered area (SCA) estimates from Landsat Enhanced Thematic Mapper (ETM+), Moderate Resolution Imaging Spectroradiometer (MODIS), and Advanced Very High Resolution Radiometer (AVHRR) data were combined with a spatially distributed snowmelt model to reconstruct snow water equivalent (SWE) in the Rio Grande headwaters (3419 km²). In this reconstruction approach, modeled snowmelt over each pixel is integrated during the period of satellite-observed snow cover to estimate SWE. Due to underestimates in snow cover detection, maximum basin-wide mean SWE using MODIS and AVHRR were, respectively, 45% and 68% lower than SWE estimates obtained using ETM+ data. The mean absolute error (MAE) of SWE estimated at 100-m resolution using ETM+ data was 23% relative to observed SWE from intensive field campaigns. Model performance deteriorated when MODIS (MAE = 50%) and AVHRR (MAE = 89%) SCA data were used. Relative to differences in the SCA products, model output was less sensitive to spatial resolution (MAE = 39% and 73% for ETM+ and MODIS simulations run at 1 km resolution, respectively), indicating that SWE reconstructions at the scale of MODIS acquisitions may be tractable provided the SCA product is improved. When considering tradeoffs between spatial and temporal resolution of different sensors, our results indicate that higher spatial resolution products such as ETM+ remain more accurate despite the lower frequency of acquisition. This motivates continued efforts to improve MODIS snow cover products.     

A coupled hydrology–biogeochemistry model to simulate dissolved organic carbon exports from a permafrost‐influenced catchment

We outline the development of a simple, coupled hydrology–biogeochemistry model for simulating stream discharge and dissolved organic carbon (DOC) dynamics in data sparse, permafrost‐influenced catchments with large stores of soil organic carbon. The model incorporates the influence of active layer dynamics and slope aspect on hydrological flowpaths and resulting DOC mobilization. Calibration and evaluation of the model was undertaken using observations from Granger Basin within the Wolf Creek research basin, Yukon, northern Canada. Results show that the model was able to capture the dominant hydrological response and DOC dynamics of the catchment reasonably well. Simulated DOC was highly correlated with observed DOC (r² = 0.65) for the study period. During the snowmelt period, the model adequately captured the observed dynamics, with simulations generally reflecting the timing and magnitude of the observed DOC and stream discharge. The model was less successful over the later summer period although this partly reflected a lack of DOC observations for calibration. The developed model offers a valuable framework for investigating the interactions between hydrological and DOC processes in these highly dynamic systems, where data acquisition is often very difficult. © 2015 The Authors Hydrological Processes Published by John Wiley & Sons, Ltd.