Algorithms for solving the diffusive wave flood routing equation

Generally, the diffusive wave equation, obtained by neglecting the acceleration terms in the Saint-Venant equations, is used in flood routing in rivers. Methods based on the finite-difference discretization techniques are often used to calculate discharges at each time step. A modified form of the diffusive wave equation has been developed and new resolution algorithms proposed which are better adapted to flood routing along a complex river network. The two parameters of the equation, celerity and diffusivity, can then be taken as functions of the discharge. The resolution algorithm allows the use of any distribution of lateral inflow in space and time. The accuracy of the new algorithms were compared with a traditional algorithm by numerical experimentation. Special attention was given to the instability caused by the inflow signal which constitutes the upstream boundary condition. For the fully diffusive wave flood routing problem, all three algorithms tested gave good results. The results also indicate that the efficiency of the new algorithms could be significantly improved if the position of the x-axis is modified by rotation. The new algorithms were applied to flood routing simulation over the Gardon d'Anduze catchment (542 km²) in southern France.     

扩散对流温盐台阶结构的数值模拟

热盐驱动下的扩散对流现象是海洋中高纬度海域普遍存在的一种现象, 对其进行数值模拟可更细致地研究海洋小尺度动力过程。文章分析了扩散对流的形成机制, 建立了二维方腔模型, 通过有限体积法求解控制方程, 对其分层现象进行了数值模拟。研究给出了流场的温度及盐度随时间演化的关系, 展现了流场中速度的涡旋结构, 分析了温盐台阶结构的生成、合并的演化过程, 并对其物质和能量的输运进行了初步的理论解释。另外, 对不同热流密度情况下的扩散对流现象进行了对比研究, 发现随着热流密度的增加, 台阶结构的演变速率变快, 而且上边界冷却对其演化速率具有促进作用, 但热流密度的改变并没有对台阶结构的演变趋势产生明显的影响。     

南海北部中深层细结构混合研究

基于2007年8月获得的ADCP（声学多普勒流速剖面仪）海流资料和CTD（温盐深剖面仪）水文资料,应用Gregg模型对南海中深层内波尺度的混合进行估计,同时应用Thorpe尺度对中深层存在的垂向翻转及由此引起的混合进一步分析。两种方法均显示,吕宋海峡附近上层400m的耗散率及混合率均强于18°N断面,中深层两个区域的混合率并没有显著区别。这表明吕宋海峡上层400m,可能存在更活跃的内波活动,从而产生更强的内波混合和垂向水团翻转。Gregg模型估计的耗散率和混合率量级分别为10^-9W·kg^-1和10^-6m^2·s^-1。大部分CTD站位在中深层均存在垂向翻转,而且保持较高的发生率,翻转所对应的混合率并不随深度增加而减小。以上南海北部的细结构混合特征增强对南海中深层混合的认识。     

Revisiting effect of ocean diapycnal mixing on Atlantic meridional overturning circulation recovery in a freshwater perturbation simulation

The effects of ocean density vertical stratification and related ocean mixing on the transient response of the Atlantic meridional overturning circulation （AMOC） are examined in a freshwater perturbation simulation using the Bergen Climate Model （BCM）. The results presented here are based on the model outputs of a previous freshwater experiment： a 300-year control integration （CTRL）, a freshwater integration （FW1） which started after 100 years of running the CTRL with an artificially and continuously threefold increase in the freshwater flux to the Greenland-Iceland-Norwegian （GIN） Seas and the Arctic Ocean throughout the following 150-year simulation. In FW1, the transient response of the AMOC exhibits an initial decreasing of about 6 Sv （1 Sv=106 m3 s^-1） over the first 50-year integration and followed a gradual recovery during the last 100-year integration. Our results show that the vertical density stratification as the crucial property of the interior ocean plays an important role for the transient responses of AMOC by regulating the convective and diapycnal mixings under the enhanced freshwater input to northern high latitudes in BCM in which the ocean diapycnal mixing is stratification-dependent. The possible mechanism is also investigated in this paper.     

湿地沉积物-水界面营养盐交换的定量估算

为有效控制湖泊内源营养盐的释放,探讨了不同物理改良措施(覆沙、底质疏松)对沉积物-水界面营养盐的释放通量控制效果。利用原位孔隙水采样技术(Peeper)来获得沉积物孔隙水剖面,对改良后湿地沉积物孔隙水营养盐的垂向分布及其扩散通量进行了研究。结果发现,改良后沉积含水率、孔隙率分别提高了91%和54%。水土界面附近,随剖面深度增加,孔隙水中PO₄3-、NH₄+、NO₃-及NO₂-浓度分布符合指数关系,PO₄3-、NH₄+在8 cm左右达到最大值。种植芦苇后沉积物孔隙水中PO₄3-、NH₄+均有不同程度的下降,改良措施能有效降低表层弱结合态磷在总磷中比例但增加铁磷的比例,种植芦苇可强化这一效应。运用Fick第一定律对剖面孔隙水营养盐的扩散通量进行估算,发现沉积物经疏松后,NH₄+、PO₄3-的扩散通量由57.47~72.19μg/(m2·d)和2.55~3.21μg/(m2·d)变为-95.54~-130.94μg/(m2·d)和1.50~2.05μg/(m2·d),可考虑疏松沉积物-水界面附近沉积物来作为控制湖泊内源污染的有效手段之一。     

扩散边界层对沉积物盐分释放的阻滞影响

扩散边界层是水环境沉积物与上覆水之间物质交换的必经区。通过无风和有风条件下两组沉积物盐分释放实验,研究海湾水库砂质沉积物-水界面扩散边界层的形成情况,并通过水动力扰动下穿过扩散边界层的实测盐分通量与Fick第一定律理论计算通量的比较,以及扰动与无扰动时通量的比较,探讨扩散边界层对沉积物盐分释放的影响。研究结果表明,在稳定风场条件下,沉积物-水界面处存在厚度约3.5 cm的扩散边界层,有风条件下的界面盐分交换通量略大于无风时的通量;分子扩散是边界层内盐分运移的主要机制,扩散边界层对沉积物盐分释放具有阻滞作用,并且边界层越厚,阻滞效应越显著。另外,由于扩散边界层的存在,限制了水动力对沉积物与上覆水之间物质交换的增强作用,所以海湾水库沉积物中蓄积盐分对上覆水的影响将是长期的过程。     

Role of the Water Vapour Greenhouse Effect in the Forecasting Of Fog Occurrence

Nocturnal measurements of air temperature, relative humidity, temperatureinversion-layer thickness, water vapour path and visibility-through-fog, madeunder non-foggy and foggy conditions in winter over two seasons at Delhi,are analysed to study the decrease in both rate of cooling and temperature inversion-layer thickness during the course of nights followed by fog occurrence.In particular, the decrease in the rate of cooling, compared to that on non-foggynights, is explained as due to the greenhouse warming effect by a layer of excessive,near-saturated water vapour trapped in a temperature inversion. Next, the linearprogramming technique is employed to forecast the occurrence of fog, where thevisibility-through-fog is minimized through its linear regression equation with thepair of variables, mean air temperature and temperature decrease over one hour(measuring rate of cooling at two convenient hours) in the pre-midnight period.This technique provides feasible solutions that enables one to forecast the occurrenceof radiative fog.     

Quantifying peakflow attenuation/amplification in a karst river using the diffusive wave model with lateral flow

The aim of this paper is to quantify peakflow attenuation and/or amplification in a river, investigating lateral flow from the intermediate catchment during floods. This is a challenge for the study of the hydrological response of permeable/intermittent streams, and our contribution refers to a modelling framework based on the inverse problem for the diffusive wave model applied in a karst catchment. Knowing the upstream and downstream hydrographs on a reach between two stations, we can model the lateral one, given information on the hydrological processes involved in the intermediate catchment. The model is applied to 33 flood events in the karst reach of the Iton River in French Normandy where peakflow attenuation is observed. The monitored zone consists of a succession of losing and gaining reaches controlled by strong surface‐water/groundwater (SW/GW) interactions. Our results show that despite a high baseflow increase in the reach, peakflow is attenuated. Model application shows that the intensity of lateral outflow for the flood component is linked to upstream discharge. A combination of river loss and overbank flow for highest floods is proposed for explaining the relationships. Our approach differentiates the role of outflow (river loss and overbank flow) and that of wave diffusion on peakflow attenuation. Based on several sets of model parameterization, diffusion is the main attenuation process for most cases, despite high river losses of up to several m³/s (half of peakflow for some parameterization strategies). Finally, this framework gives new insight into the SW/GW interactions during floods in karst basins, and more globally in basins characterized by disconnected river‐aquifer systems.     

Stochastic modelling of a diffusive wave for flood propagation using the random walk particle tracking method in a hypothetical city

Deterministic numerical schemes have been widely used for the solution of the diffusive wave (DW) equation, however, these schemes are computationally costly and suffer instability issues. This paper presents a stochastic random walk particle tracking (RWPT) method to solve such an equation for a dam‐break flow problem. Three different wave duration scenarios are presented for simulations of the DW for flood flows in a hypothetical city. The hypothetical city is represented by a domain of size 2,000 m by 500 m in x and y directions, respectively. The domain is divided into 25 m by 25 m cells. A dam is located at the upstream of the hypothetical city. Each scenario has a distinct propagation pattern after the dam is breached. Analysed and presented are 18 different simulations, which are composed of three different building configurations, two different bed slopes, and three different shapes of hydrographs. In this method, the flood volume is divided into a large number of particles where each particle carries a fixed amount of the flood volume. These particles undergo convective and diffusive movements, and their superposition represents propagation of the DW in the flow domain. The solution algorithm of the RWPT‐based equations is used to compute flood inundation depths in the hypothetical city. Comparison is drawn among the simulated results from three different shapes of the inflow hydrographs. The proposed stochastic method has two major advantages over traditional deterministic schemes: (a) greater efficiency, thus lesser computational costs, and (b) no instability issues.     

Shock acceleration of solar cosmic rays

We investigated the acceleration of solar cosmic rays (SCRs) by the shock waves produced by coronal mass ejections. We performed detailed numerical calculations of the SCR spectra produced during the shock propagation in the solar corona in terms of a model based on the diffusive transport equation using a realistic set of physical parameters for the corona. The resulting SCR energy spectrum N(ε) ∝ ε^?γ exp [? (ε/ε_max)^α] is shown to include a power-law portion with an index γ?2 that ends with an exponential tail with α ? 2.5 ? β, where β is the spectral index of the background Alfvén turbulence. The maximum SCR energy lies within the range ε_max = 1–300 MeV, depending on the shock velocity. Because of the steep spectrum of the SCRs, their backreaction on the shock structure is negligible. The decrease in the Alfvén Mach number of the shock due to the increase in the Alfvén velocity with heliocentric distance r causes the efficient SCR acceleration to terminate when the shock reaches a distance of r = 2–3R_⊙. Since the diffusive SCR propagation in this case is faster than the shock expansion, SCR particles intensively escape from the shock vicinity. A comparison of the calculated SCR fluxes expected near the Earth’s orbit with available experimental data indicates that the theory satisfactorily explains all of the main observed features.