Approximation of interfacial properties in multiphase porous medium systems

We investigate the estimation of interfacial areas, curvatures, and common curve lengths in multiphase porous medium systems. Algorithms are developed to obtain estimates of these quantities based upon a variety of potential data sources and estimation approaches. The accuracy of the derived approximations are evaluated as a function of the data type and resolution of the data. The methods advanced improve upon standard approaches now in use and show excellent accuracy at resolutions on the order of five lattice points per minimum radius of curvature of the object being resolved. Finally, we suggest a promising class of extensions that could lead to further improvements in the accuracy of such methods.     

A spatially and temporally adaptive solution of Richards’ equation

Efficient, robust simulation of groundwater flow in the unsaturated zone remains computationally expensive, especially for problems characterized by sharp fronts in both space and time. Standard approaches that employ uniform spatial and temporal discretizations for the numerical solution of these problems lead to inefficient and expensive simulations. In this work, we solve Richards’ equation using adaptive methods in both space and time. Spatial adaption is based upon a coarse grid solve and a gradient error indicator using a fixed-order approximation. Temporal adaption is accomplished using variable order, variable step size approximations based upon the backward difference formulas up to fifth order. Since the advantages of similar adaptive methods in time are now established, we evaluate our method by comparison with a uniform spatial discretization that is adaptive in time for four different one-dimensional test problems. The numerical results demonstrate that the proposed method provides a robust and efficient alternative to standard approaches for simulating variably saturated flow in one spatial dimension.     

Testing a model for predicting the timing and location of shallow landslide initiation in soil‐mantled landscapes

The growing availability of digital topographic data and the increased reliability of precipitation forecasts invite modelling efforts to predict the timing and location of shallow landslides in hilly and mountainous areas in order to reduce risk to an ever‐expanding human population. Here, we exploit a rare data set to develop and test such a model. In a 1·7 km² catchment a near‐annual aerial photographic coverage records just three single storm events over a 45 year period that produced multiple landslides. Such data enable us to test model performance by running the entire rainfall time series and determine whether just those three storms are correctly detected. To do this, we link a dynamic and spatially distributed shallow subsurface runoff model (similar to TOPMODEL) to an in?nite slope model to predict the spatial distribution of shallow landsliding. The spatial distribution of soil depth, a strong control on local landsliding, is predicted from a process‐based model. Because of its common availability, daily rainfall data were used to drive the model. Topographic data were derived from digitized 1 : 24 000 US Geological Survey contour maps. Analysis of the landslides shows that 97 occurred in 1955, 37 in 1982 and ?ve in 1998, although the heaviest rainfall was in 1982. Furthermore, intensity–duration analysis of available daily and hourly rainfall from the closest raingauges does not discriminate those three storms from others that did not generate failures. We explore the question of whether a mechanistic modelling approach is better able to identify landslide‐producing storms. Landslide and soil production parameters were ?xed from studies elsewhere. Four hydrologic parameters characterizing the saturated hydraulic conductivity of the soil and underlying bedrock and its decline with depth were ?rst calibrated on the 1955 landslide record. Success was characterized as the most number of actual landslides predicted with the least amount of total area predicted to be unstable. Because landslide area was consistently overpredicted, a threshold catchment area of predicted slope instability was used to de?ne whether a rainstorm was a signi?cant landslide producer. Many combinations of the four hydrological parameters performed equally well for the 1955 event, but only one combination successfully identi?ed the 1982 storm as the only landslide‐producing storm during the period 1980–86. Application of this parameter combination to the entire 45 year record successfully identi?ed the three events, but also predicted that two other landslide‐producing events should have occurred. This performance is signi?cantly better than the empirical intensity–duration threshold approach, but requires considerable calibration effort. Overprediction of instability, both for storms that produced landslides and for non‐producing storms, appears to arise from at least four causes: (1) coarse rainfall data time scale and inability to document short rainfall bursts and predict pressure wave response; (2) absence of local rainfall data; (3) legacy effect of previous landslides; and (4) inaccurate topographic and soil property data. Greater resolution of spatial and rainfall data, as well as topographic data, coupled with systematic documentation of landslides to create time series to test models, should lead to signi?cant improvements in shallow landslides forecasting. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluating regional climate model estimates against site-specific observed data in the UK

This paper compares precipitation, maximum and minimum air temperature and solar radiation estimates from the Hadley Centre’s HadRM3 regional climate model (RCM), (50 × 50 km grid cells), with observed data from 15 meteorological station in the UK, for the period 1960–90. The aim was to investigate how well the HadRM3 is able to represent weather characteristics for a historical period (hindcast) for which validation data exist. The rationale was to determine if the HadRM3 data contain systematic errors and to investigate how suitable the data are for use in climate change impact studies at particular locations. Comparing modelled and observed data helps assess and quantify the uncertainty introduced to climate impact studies. The results show that the model performs very well for some locations and weather variable combinations, but poorly for others. Maximum temperature estimations are generally good, but minimum temperature is overestimated and extreme cold events are not represented well. For precipitation, the model produces too many small events leading to a serious under estimation of the number of dry days (zero precipitation), whilst also over- or underestimating the mean annual total. Estimates represent well the temporal distribution of precipitation events. The model systematically over-estimates solar radiation, but does produce good quality estimates at some locations. It is concluded that the HadRM3 data are unsuitable for detailed (i.e. daily time step simulation model based) site-specific impacts studies in their current form. However, the close similarity between modelled and observed data for the historical case raises the potential for using simple adjustment methods and applying these to future projection data.     

The seasonal cycle in coupled ocean-atmosphere general circulation models

We examine the seasonal cycle of near-surface air temperature simulated by 17 coupled ocean-atmosphere general circulation models participating in the Coupled Model Intercomparison Project (CMIP). Nine of the models use ad hoc “flux adjustment” at the ocean surface to bring model simulations close to observations of the present-day climate. We group flux-adjusted and non-flux-adjusted models separately and examine the behavior of each class. When averaged over all of the flux-adjusted model simulations, near-surface air temperature falls within 2?K of observed values over the oceans. The corresponding average over non-flux-adjusted models shows errors up to ～6?K in extensive ocean areas. Flux adjustments are not directly applied over land, and near-surface land temperature errors are substantial in the average over flux-adjusted models, which systematically underestimates (by ～5?K) temperature in areas of elevated terrain. The corresponding average over non-flux-adjusted models forms a similar error pattern (with somewhat increased amplitude) over land. We use the temperature difference between July and January to measure seasonal cycle amplitude. Zonal means of this quantity from the individual flux-adjusted models form a fairly tight cluster (all within ～30% of the mean) centered on the observed values. The non-flux-adjusted models perform nearly as well at most latitudes. In Southern Ocean mid-latitudes, however, the non-flux-adjusted models overestimate the magnitude of January-minus-July temperature differences by ～5?K due to an overestimate of summer (January) near-surface temperature. This error is common to five of the eight non-flux-adjusted models. Also, over Northern Hemisphere mid-latitude land areas, zonal mean differences between July and January temperatures simulated by the non-flux-adjusted models show a greater spread (positive and negative) about observed values than results from the flux-adjusted models. Elsewhere, differences between the two classes of models are less obvious. At no latitude is the zonal mean difference between averages over the two classes of models greater than the standard deviation over models. The ability of coupled GCMs to simulate a reasonable seasonal cycle is a necessary condition for confidence in their prediction of long-term climatic changes (such as global warming), but it is not a sufficient condition unless the seasonal cycle and long-term changes involve similar climatic processes. To test this possible connection, we compare seasonal cycle amplitude with equilibrium warming under doubled atmospheric carbon dioxide for the models in our data base. A small but positive correlation exists between these two quantities. This result is predicted by a simple conceptual model of the climate system, and it is consistent with other modeling experience, which indicates that the seasonal cycle depends only weakly on climate sensitivity.     

Air flow over and through a forest edge: A steady-state numerical simulation

A numerical model was developed to simulate neutrally stratified air flow over and through a forest edge. The spatially averaged equations for turbulent flow in vegetation canopies are derived as the governing equations. A first-order closure scheme with the capability of accounting for the bulk momentum transport process in vegetation canopies is employed. The averaged equations are solved numerically by a fractional time-step method and successive relaxation. The asymptotic solution in time is regarded as the steady-state solution. Comparisons of model output to the field measurements of Raynor (1971) indicate that the model provides a realistic mean flow.Momentum balance computations show that the pressure gradient induced by the wind blowing against the forest edge is significant and has the same order of magnitude as the drag force in the edge region. The edge effect involves the generation of drag forces, the appearance of a large pressure gradient, the upward deflection of mean flow and the transport of momentum into the edge of the canopy.     

Centennial-scale climate change from decadally-paced explosive volcanism: a coupled sea ice-ocean mechanism

Northern Hemisphere summer cooling through the Holocene is largely driven by the steady decrease in summer insolation tied to the precession of the equinoxes. However, centennial-scale climate departures, such as the Little Ice Age, must be caused by other forcings, most likely explosive volcanism and changes in solar irradiance. Stratospheric volcanic aerosols have the stronger forcing, but their short residence time likely precludes a lasting climate impact from a single eruption. Decadally paced explosive volcanism may produce a greater climate impact because the long response time of ocean surface waters allows for a cumulative decrease in sea-surface temperatures that exceeds that of any single eruption. Here we use a global climate model to evaluate the potential long-term climate impacts from four decadally paced large tropical eruptions. Direct forcing results in a rapid expansion of Arctic Ocean sea ice that persists throughout the eruption period. The expanded sea ice increases the flux of sea ice exported to the northern North Atlantic long enough that it reduces the convective warming of surface waters in the subpolar North Atlantic. In two of our four simulations the cooler surface waters being advected into the Arctic Ocean reduced the rate of basal sea-ice melt in the Atlantic sector of the Arctic Ocean, allowing sea ice to remain in an expanded state for?>?100 model years after volcanic aerosols were removed from the stratosphere. In these simulations the coupled sea ice-ocean mechanism maintains the strong positive feedbacks of an expanded Arctic Ocean sea ice cover, allowing the initial cooling related to the direct effect of volcanic aerosols to be perpetuated, potentially resulting in a centennial-scale or longer change of state in Arctic climate. The fact that the sea ice-ocean mechanism was not established in two of our four simulations suggests that a long-term sea ice response to volcanic forcing is sensitive to the stability of the seawater column, wind, and ocean currents in the North Atlantic during the eruptions.