Semigroup solutions to stochastic unsteady groundwater flow subject to random parameters

Two methods for the solution of partial differential equations (PDE) for the general case of random in time physical parameters are presented and their application to the solution of unsteady regional groundwater flow equations are illustrated. The first method is the semigroup approach which directly offers a solution without resorting to closure approximations (hierarchy techniques), perturbation techniques, or Montecarlo simulation techniques. The semigroup approach can also handle the general stochastic problem when randomness also appears as initial conditions, boundary conditions or forcing terms. The second method is an approximation scheme to obtain the semigroup solution in complex cases and permits the solution of equations with more than one random coefficient.     

Optimisation of an idealised ocean model,stochastic parameterisation of sub-grid eddies

An optimisation scheme is developed to accurately represent the sub-grid scale forcing of a high dimensional chaotic ocean system. Using a simple parameterisation scheme, the velocity components of a 30 km resolution shallow water ocean model are optimised to have the same climatological mean and variance as that of a less viscous 7.5 km resolution model. The 5 day lag-covariance is also optimised, leading to a more accurate estimate of the high resolution response to forcing using the low resolution model.The system considered is an idealised barotropic double gyre that is chaotic at both resolutions. Using the optimisation scheme, we find and apply the constant in time, but spatially varying, forcing term that is equal to the time integrated forcing of the sub-grid scale eddies. A linear stochastic term, independent of the large-scale flow, with no spatial correlation but a spatially varying amplitude and time scale is used to represent the transient eddies. The climatological mean, variance and 5 day lag-covariance of the velocity from a single high resolution integration is used to provide an optimisation target. No other high resolution statistics are required. Additional programming effort, for example to build a tangent linear or adjoint model, is not required either.The focus of this paper is on the optimisation scheme and the accuracy of the optimised flow. However the forcing can provide insights in the design of deterministic and stochastic parameterisations. In the present study, we found that the stochastic parameterisation correcting the model variance is associated with the spatial pattern of eddy-decorrelation timescales rather than the spatial pattern of the amplitude of the variance. The method can be applied in future investigations into the physical processes that govern barotropic turbulence and it can perhaps be applied to help understand and correct biases in the mean and variance of a more realistic coarse or eddy-permitting ocean model. The method is complementary to current parameterisations and can be applied at the same time without modification.     

Influence of yaw-roll coupling on the behavior of a FPSO: An experimental and numerical investigation

An inconvenience in the experimental set-up of a FPSO in regular waves highlighted occurrence of parametric-roll events promoted by yaw-roll coupling and motivated a combined physical and numerical analysis on the relevance of this phenomenon on the roll resonance, as well as on the water shipping. The model tests examine the ship in head- and bow-sea waves in the zone of the first parametric resonance. Numerically, it is adopted a 3D Domain-Decomposition (DD) strategy combining a weakly-nonlinear potential-flow solver based on the weak-scatterer theory with a shallow-water approximation for the shipped liquid and with a bottom-slamming solution. Detailed comparisons against these and other seakeeping experiments validated the numerical method in its different aspects with global success.At first, a 2-dof equivalent linearized yaw-roll coupled system is examined and the measurements are used to estimate hydrodynamic coefficients required to complete the mathematical model of the problem. Then the DD method is applied to verify the instability occurrence and compared against the experiments. From the analysis, the parametric-roll instability does not occur if all nonlinearities in the roll restoring load are not accounted for. However the amplitude of the resonant roll is affected by the coupling with the other degrees of freedom. Especially the coupling with yaw tends to increase the steady-state roll amplitude. It also affects the water shipping with the trend in reducing its severity for the vessel, this is opposite to the influence of the parametric roll in head-sea waves on the water on deck, as documented in Greco et al. (2014) [4].     

在气候影响研究中引入随机天气发生器的方法和不确定性

通过采用不同的随机天气发生器生成一定气候背景下各种气候变率情景，许多学者在最近的研究中已经认识到气候变率对农作物生长发育影响的重要性。传统的气候影响评估方法直接以大气环流模式的模拟试验结果作为未来气候情景，这样不可能理解如上的重要性。本文着重评述将随机天气发生器应用于气候变化影响研究的一般方法框架，以及作者的具体个例研究方法。文中最后分析了目前该领域研究中还存在的一些不确定性。 在当前的气候变化影响研究中，有不同的方法用来研制一种称为WGEN的典型随机天气发生器的参数化方案及其随机试验方法。不同的研究者也有不同的参数调控方法。通常的思路是通过气候控制试验和2×CO2试验之间的气候变量平均值和方差的变化来扰动随机天气发生器的参数，以生成未来逐日气候变化情景。本文作者根据短期气候预测模式的输出产品建立了一套WGEN的参数化方案及其随机试验方法，并且在时间和空间两个尺度上检验和评估了此参数化方案下WGEN的模拟能力。另外，作者由未来降水的变化，调试随机天气发生器参数，生成了气候变率变化情景。这些参数调节可以产生各种不同类型和定性大小的气候变率变化，用于气候影响评估的敏感性分析。通过如上方法，作为一个个例，文中评估了未来气候变率变化     

具有滞迟耗能装置的高层建筑结构的随机响应分析

本文提出了一个近似分析具有滞迟耗能装置的高层建筑的方法。结果被模拟为一个有滞迟非线性支座的悬壁梁。其控制方程由Ｒｉｔｚ法导出，用等效线性化方法分析。     

Simple stochastic modelling of the eruption history of a basaltic volcano: Nyamuragira,Zaire

Three simple models of the behaviour of a series of basaltic eruptions have been tested against the eruptive history of Nyamuragira. The data set contains the repose periods and the volumes of lava emitted in 22 eruptions since 1901. Model 1 is fully stochastic and eruptions of any volume with random repose intervals are possible. Models 2 and 3 are constrained by deterministic limits on the maximum capacity of the magma reservoir and on the lowest drainage level of the reservoir respectively. The method of testing these models involves (1) seeking change points in the time series to determine regimes of uniform magma supply rate, and (2) applying linear regression to these regimes, which for models 2 and 3 are the determinsstic limits to those models. Two change points in the time series for Nyamuragira, in 1958 and 1980, were determined using a Kolmogorov-Smirnov technique. The latter change involved an increase in the magma supply rate by a factor of 2.5, from 0.55 to 1.37 m³s^-1. Model 2 provides the best fit to the behavior of Nyamuragira with the ratio of variation explained by the model to total variation. R², being greater than 0.9 for all three regimes. This fit can be interpreted to mean that there is a determinstic limit to the elastic strength of the magma reservoir 4–8 km below the summit of the volcano.     

Stochastic space transforms in subsurface hydrology — Part 2: Generalized spectral decompositions and plancherel representations

In earlier publications, certain applications of space transformation operators in subsurface hydrology were considered. These operators reduce the original multi-dimensional problem to the one-dimensional space, and can be used to study stochastic partial differential equations governing groundwater flow and solute transport processes. In the present work we discuss developments in the theoretical formulation of flow models with space-dependent coefficients in terms of space transformations. The formulation is based on stochastic Radon operator representations of generalized functions. A generalized spectral decomposition of the flow parameters is introduced, which leads to analytically tractable expressions of the space transformed flow equation. A Plancherel representation of the space transformation product of the head potential and the log-conductivity is also obtained. A test problem is first considered in detail and the solutions obtained by means of the proposed approach are compared with the exact solutions obtained by standard partial differential equation methods. Then, solutions of three-dimensional groundwater flow are derived starting from solutions of a one-dimensional model along various directions in space. A step-by-step numerical formulation of the approach to the flow problem is also discussed, which is useful for practical applications. Finally, the space transformation solutions are compared with local solutions obtained by means of series expansions of the log-conductivity gradient.     

Carbon and water cycling in a Bornean tropical rainforest under current and future climate scenarios

We examined how the projected increase in atmospheric CO₂ and concomitant shifts in air temperature and precipitation affect water and carbon fluxes in an Asian tropical rainforest, using a combination of field measurements, simplified hydrological and carbon models, and Global Climate Model (GCM) projections. The model links the canopy photosynthetic flux with transpiration via a bulk canopy conductance and semi-empirical models of intercellular CO₂ concentration, with the transpiration rate determined from a hydrologic balance model. The primary forcing to the hydrologic model are current and projected rainfall statistics. A main novelty in this analysis is that the effect of increased air temperature on vapor pressure deficit (D) and the effects of shifts in precipitation statistics on net radiation are explicitly considered. The model is validated against field measurements conducted in a tropical rainforest in Sarawak, Malaysia under current climate conditions. On the basis of this model and projected shifts in climatic statistics by GCM, we compute the probability distribution of soil moisture and other hydrologic fluxes. Regardless of projected and computed shifts in soil moisture, radiation and mean air temperature, transpiration was not appreciably altered. Despite increases in atmospheric CO₂ concentration (C_a) and unchanged transpiration, canopy photosynthesis does not significantly increase if C_i/C_a is assumed constant independent of D (where C_i is the bulk canopy intercellular CO₂ concentration). However, photosynthesis increased by a factor of 1.5 if C_i/C_a decreased linearly with D as derived from Leuning stomatal conductance formulation [R. Leuning. Plant Cell Environ 1995;18:339–55]. How elevated atmospheric CO₂ alters the relationship between C_i/C_a and D needs to be further investigated under elevated atmospheric CO₂ given its consequence on photosynthesis (and concomitant carbon sink) projections.     

A procedure for testing the assumption of homoscedasticity in least squares residuals: a case study of GPS carrier-phase observations

Due to increased demands on the quality of the results of Global Positioning System (GPS) evaluations, various authors have studied improvements of the stochastic model of GPS carrier-phase observations. These improvements are based on the reasonable assumption that the commonly used stochastic model with independent and homoscedastic (i.e. equal variance) errors is unrealistic. However, this has not been proved rigorously so far. A statistical test procedure based on uncorrelated least–squares residuals, which allows verification of the hypothesis of a heterogeneous variance, is provided. The statistical test procedure is of interest in its own right, and is independent of the practical problem considered. The presented technique is applied to GPS carrier-phase observations. Results show that the variances of the investigated observations are far from homogeneous. It is indicated that the error variances of the presented data increase with decreasing GPS satellite elevation. These results confirm the assumption that the commonly used stochastic model of GPS observations is inadequate and has to be improved.