Sensitivity and uncertainty analysis of a sediment transport model: a global approach

Computerized sediment transport models are frequently employed to quantitatively simulate the movement of sediment materials in rivers. In spite of the deterministic nature of the models, the outputs are subject to uncertainty due to the inherent variability of many input parameters in time and in space, along with the lack of complete understanding of the involved processes. The commonly used first-order method for sensitivity and uncertainty analyses is to approximate a model by linear expansion at a selected point. Conclusions from the first-order method could be of limited use if the model responses drastically vary at different points in parameter space. To obtain the global sensitivity and uncertainty features of a sediment transport model over a larger input parameter space, the Latin hypercubic sampling technique along with regression procedures were employed. For the purpose of illustrating the methodologies, the computer model HEC2-SR was selected in this study. Through an example application, the results about the parameters sensitivity and uncertainty of water surface, bed elevation and sediment discharge were discussed.     

Efficient Bayesian sensor placement algorithm for structural identification: a general approach for multi‐type sensory systems

In this paper, a Bayesian sequential sensor placement algorithm, based on the robust information entropy, is proposed for multi‐type of sensors. The presented methodology has two salient features. It is a holistic approach such that the overall performance of various types of sensors at different locations is assessed. Therefore, it provides a rational and effective strategy to design the sensor configuration, which optimizes the use of various available resources. This sequential algorithm is very efficient due to its Bayesian nature, in which prior distribution can be incorporated. Therefore, it avoids the possible unidentifiability problem encountered in a sequential process, which starts with small number of sensors. The proposed algorithm is demonstrated using a shear building and a lattice tower with consideration of up to four types of sensors. Copyright © 2014 John Wiley & Sons, Ltd.     

Application of the SPARROW model in watersheds with limited information: a Bayesian assessment of the model uncertainty and the value of additional monitoring

How can spatially explicit nonlinear regression modelling be used for obtaining nonpoint source loading estimates in watersheds with limited information? What is the value of additional monitoring and where should future data‐collection efforts focus on? In this study, we address two frequently asked questions in watershed modelling by implementing Bayesian inference techniques to parameterize SPAtially Referenced Regressions On Watershed attributes (SPARROW), a model that empirically estimates the relation between in‐stream measurements of nutrient fluxes and the sources/sinks of nutrients within the watershed. Our case study is the Hamilton Harbour watershed, a mixed agricultural and urban residential area located at the western end of Lake Ontario, Canada. The proposed Bayesian approach explicitly accounts for the uncertainty associated with the existing knowledge from the system and the different types of spatial correlation typically underlying the parameter estimation of watershed models. Informative prior parameter distributions were formulated to overcome the problem of inadequate data quantity and quality, whereas the potential bias introduced from the pertinent assumptions is subsequently examined by quantifying the relative change of the posterior parameter patterns. Our modelling exercise offers the first estimates of export coefficients and delivery rates from the different subcatchments and thus generates testable hypotheses regarding the nutrient export ‘hot spots’ in the studied watershed. Despite substantial uncertainties characterizing our calibration dataset, ranging from 17% to nearly 400%, we arrived at an uncertainty level for the whole‐basin nutrient export estimates of only 36%. Finally, we conduct modelling experiments that evaluate the potential improvement of the model parameter estimates and the decrease of the predictive uncertainty if the uncertainty associated with the current nutrient loading estimates is reduced. Copyright © 2012 John Wiley & Sons, Ltd.     

Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment,part 1: mesh resolution effects

High‐resolution data obtained from airborne remote sensing is increasing opportunities for representation of small‐scale structural elements (e.g. walls, buildings) in complex floodplain systems using two‐dimensional (2D) models of flood inundation. At the same time, 2D inundation models have been developed and shown to provide good predictions of flood inundation extent, with respect to both full solution of the depth‐averaged Navier–Stokes equations and simplified diffusion‐wave models. However, these models have yet to be applied extensively to urban areas. This paper applies a 2D raster‐based diffusion‐wave model to determine patterns of fluvial flood inundation in urban areas using high‐resolution topographic data and explores the effects of spatial resolution upon estimated inundation extent and flow routing process. Model response shows that even relatively small changes in model resolution have considerable effects on the predicted inundation extent and the timing of flood inundation. Timing sensitivity would be expected, given the relatively poor representation of inertial processes in a diffusion‐wave model. Sensitivity to inundation extent is more surprising, but is associated with: (1) the smoothing effect of mesh coarsening upon input topographical data; (2) poorer representation of both cell blockage and surface routing processes as the mesh is coarsened, where the flow routing is especially complex; and (3) the effects of (1) and (2) upon water levels and velocities, which in turn determine which parts of the floodplain the flow can actually travel to. It is shown that the combined effects of wetting and roughness parameters can compensate in part for a coarser mesh resolution. However, the coarser the resolution, the poorer the ability to control the inundation process, as these parameters not only affect the speed, but also the direction of wetting. Thus, high‐resolution data will need to be coupled to a more sophisticated representation of the inundation process in order to obtain effective predictions of flood inundation extent. This is explored in a companion paper. Copyright © 2005 John Wiley & Sons, Ltd.     

Removal of water‐surface reflection effects with a temporal minimum filter for UAV‐based shallow‐water photogrammetry

The recent development of structure‐from‐motion (SfM) and multi‐view stereo (MVS) photogrammetry techniques has enabled semi‐automatic high‐resolution bathymetry using aerial images taken by consumer‐grade digital cameras mounted on unmanned aerial vehicles (UAVs). However, the applicability of these techniques is sometimes limited by sun and sky reflections at the water surface, which render the point‐cloud density and accuracy insufficient. In this research, we present a new imaging technique to suppress the effect of these water‐surface reflections. In this technique, we order a drone to take a short video instead of a still picture at each waypoint. We then apply a temporal minimum filter to the video. This filter extracts the smallest RGB values in all the video frames for each pixel, and composes an image with greatly reduced reflection effects. To assess the performance of this technique, we applied it at three small shallow‐water sites. Specifically, we evaluated the effect of the technique on the point cloud density and the accuracy and precision of the photogrammetry. The results showed that the proposed technique achieved a far denser point cloud than the case in which a randomly chosen frame was used for each waypoint, and also showed better overall accuracy and precision in estimating water‐bottom elevation. The effectiveness of this new technique should depend on the surface wave state and sky radiance distribution, and this dependence, as well as the applicability to large areas, should be investigated in future research. Copyright © 2018 John Wiley & Sons, Ltd.     

Stage‐discharge uncertainty derived with a non‐stationary rating curve in the Choluteca River,Honduras

Uncertainty in discharge data must be critically assessed before data can be used in, e.g. water resources estimation or hydrological modelling. In the alluvial Choluteca River in Honduras, the river‐bed characteristics change over time as fill, scour and other processes occur in the channel, leading to a non‐stationary stage‐discharge relationship and difficulties in deriving consistent rating curves. Few studies have investigated the uncertainties related to non‐stationarity in the stage‐discharge relationship. We calculated discharge and the associated uncertainty with a weighted fuzzy regression of rating curves applied within a moving time window, based on estimated uncertainties in the observed rating data. An 18‐year‐long dataset with unusually frequent ratings (1268 in total) was the basis of this study. A large temporal variability in the stage‐discharge relationship was found especially for low flows. The time‐variable rating curve resulted in discharge estimate differences of ? 60 to + 90% for low flows and ± 20% for medium to high flows when compared to a constant rating curve. The final estimated uncertainty in discharge was substantial and the uncertainty limits varied between ? 43 to + 73% of the best discharge estimate. Copyright © 2010 John Wiley & Sons, Ltd.     

Plant source water apportionment using stable isotopes: A comparison of simple linear,two‐compartment mixing model approaches

Plant source water identification using stable isotopes is now a common practice in ecohydrological process investigations. Notwithstanding, little critical evaluation of the approaches for source apportionment have been conducted. Here, we present a critical evaluation of the main methods used for source apportionment between vadose and saturated zone water: simple mass balance and Bayesian mixing models. We leverage new isotope stem water samples from a diverse set of tree species in a strikingly uniform terrain and soil conditions at the Christchurch Botanic Garden, New Zealand. Our results show that using δ²H alone in a simple, two‐source mass balance approach leads to erroneous results, particularly an apparent overestimation of groundwater contribution to xylem. Alternatively, using both δ²H and δ¹⁸O in a Bayesian inference framework improves the source water estimates and is more useful than the simple mass balance approach, particularly when soil and groundwater contributions are relatively disproportionate. We suggest that plant source water quantification methods should take into consideration the possible effects of ²H/¹H fractionation. The Bayesian inference approach used here may be less sensitive to ²H/¹H fractionation effects than simple mass balance methods.     

Distribution of water quality parameters in two cross‐sections of the river Elbe measured with high local,temporal, and analytic resolution

The river Elbe is a large eutrophic lowland river with high primary production and high phytoplankton biomass in the growing season. The objective of the study was to gain basic knowledge of the role of dead zones for phytoplankton distribution and the oxygen balance of the river Elbe. At two sampling stations water temperature, oxygen concentration, conductivity, pH value, turbidity, and chlorophyll fluorescence were measured with high precision to learn about the distribution of these parameters across the cross‐sections. The structures indicate differences in the intensity of physical and biological processes between the shallow waters near the shores, which are characterized by groyne fields, and the deep bulk flow. The conductivity clearly shows the high transverse mixing intensity in the groyne fields in contrast to the bulk flow. Groyne fields and the first, the groyne head near margin lamella of the bulk flow can be regarded as a unit. Groyne field results indicate higher primary production of phytoplankton, oxygen release, and higher pH. The turbidity of water entering the groyne fields decreases rapidly because of sedimentation within a short time. The groyne head lamella of the bulk flow sometimes shows higher chlorophyll fluorescence than the central lamella of the bulk flow and the water of the groyne field. The processes which contribute to the observed distribution are discussed, but could not yet be quantified. A modification of the dead zone model is proposed.     

Gully‐head erosion processes on a semi‐arid valley floor in Kenya: a case study into temporal variation and sediment budgeting

A three year monitoring programme of gully‐head retreat was established to assess the significance of sediment production in a drainage network that expanded rapidly by gully‐head erosion on the low‐angled alluvio‐lacustrine Njemps Flats in semi‐arid Baringo District, Kenya. This paper discusses the factors controlling the large observed spatial and temporal variation in gully‐head retreat rates, ranging from 0 to 15 m a^?1. The selected gullies differed in planform and in runoff‐contributing catchment area but soil material and land use were similar. The data were analysed at event and annual timescales. The results show that at annual timescale rainfall amount appears to be a good indicator of gully‐head retreat, while at storm‐event timescale rainfall distribution has to be taken into account. A model is proposed, including only rainfall (P) and the number of dry days (DD) between storms: which explains 56 per cent of the variation in retreat rate of the single‐headed gully of Lam1. A detailed sediment budget has been established for Lam1 and its runoff‐contributing area (RCA). By measuring sediment input from the RCA, the sediment output by channelized flow and linear retreat of the gully head for nine storms, it can be seen that erosion shifts between different components of the budget depending on the duration of the dry period (DD) between storms. Sediment input from the RCA was usually the largest component for the smaller storms. The erosion of the gully head occurred as a direct effect of runoff falling over the edge (GH_waterfall) and of the indirect destabilization of the adjacent walls by the waterfall erosion and by saturation (GH_mass/storage). The latter component (GH_mass/storage) was usually much larger that the former (GH_waterfall). The sediment output from the gully was strongly related to the runoff volume while the linear retreat, because of its complex behaviour, was not. Overall, the results show that the annual retreat is the optimal timescale to predict retreat patterns. More detailed knowledge about relevant processes and interactions is necessary if gully‐head erosion is to be included in event‐based soil erosion models. Copyright © 2001 John Wiley & Sons, Ltd.     

Gully catchments as a sediment sink,not just a source: Results from a long‐term (~12 500 year) sediment budget

Sediment delivery from hillslopes to trunk streams represents a significant pathway of mass transfer in the landscape, with a large fraction facilitated by gully systems. The internal gully geomorphic dynamics represent a considerable gap in many landscape and empirical erosion models, therefore a better understanding of these processes over longer timescales (10–10⁴ years) is needed. This study analyses the sediment mass balance and storage dynamics within a headwater gully catchment in central Europe over the last ~12 500 years. Human induced erosion resulted in hillslope erosion rates ~2.3 times higher than under naturally de‐vegetated conditions (during the Younger Dryas), however the total sediment inputs to the gully system (and therefore gully aggradation), were similar. Net gully storage has consistently increased to become the second largest term in the sediment budget after hillslope erosion (storage is ~45% and ~73% of inputs during two separate erosion and aggradation cycles). In terms of the depletion of gully sediment storage, the sediment mass balance shows that export beyond the gully fan was not significant until the last ~500 years, due to reduced gully fan accommodation space. The significance of storage effects on the gully sediment mass balance, particularly the export terms, means that it would be difficult to determine the influences of human impact and/or climatic changes from floodplain or lake sedimentary archives alone and that the sediment budgets of the headwater catchments from which they drain are more likely to provide these mechanistic links. Copyright © 2015 John Wiley & Sons, Ltd.     

Estimating suspended sediment concentrations in areas with limited hydrological data using a mixed‐effects model

Sediment rating curves are commonly used to estimate the suspended sediment load in rivers and streams under the assumption of a constant relation between discharge (Q) and suspended sediment concentrations (SSC) over time. However, temporal variation in the sediment supply of a watershed results in shifts in this relation by increasing variability and by introducing nonlinearities in the form of hysteresis or a path‐dependent relation. In this study, we used a mixed‐effects linear model to estimate an average SSC–Q relation for different periods of time within the hydrologic cycle while accounting for seasonality and hysteresis. We tested the performance of the mixed‐effects model against the standard rating curve, represented by a generalized least squares regression, by comparing observed and predicted sediment loads for a test case on the Chilliwack River, British Columbia, Canada. In our analyses, the mixed‐effects model reflected more accurate patterns of interpolated SSC from Q data than the rating curve, especially for the low‐flow summer months when the SSC–Q relation is less clear. Akaike information criterion scores were lower for the mixed‐effects model than for the standard model, and the mixed‐effects model explained nearly twice as much variance as the standard model (52% vs 27%). The improved performance was achieved by accounting for variability in the SSC–Q relation within each month and across years for the same month using fixed and random effects, respectively, a characteristic disregarded in the sediment rating curve. Copyright © 2012 John Wiley & Sons, Ltd.     

Daily river water temperature forecast model with a k‐nearest neighbour approach

Water temperature is a key abiotic variable that modulates both water chemistry and aquatic life in rivers and streams. For this reason, numerous water temperature models have been developed in recent years. In this paper, a k‐nearest neighbour model (KNN) is proposed and validated to simulate and eventually produce a one‐day forecast of mean water temperature on the Moisie River, a watercourse with an important salmon population in eastern Canada. Numerous KNN model configurations were compared by selecting different attributes and testing different weight combinations for neighbours. It was found that the best model uses attributes that include water temperature from the two previous days and an indicator of seasonality (day of the year) to select nearest neighbours. Three neighbours were used to calculate the estimated temperature, and the weighting combination that yielded the best results was an equal weight on all three nearest neighbours. This nonparametric model provided lower Root Mean Square Errors (RMSE = 1·57 °C), Higher Nash coefficient (NTD = 0·93) and lower Relative Bias (RB = ? 1·5%) than a nonlinear regression model (RMSE = 2·45 °C, NTD = 0·83, RB = ? 3%). The k‐nearest neighbour model appears to be a promising tool to simulate of forecast water temperature where long time series are available. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluating the effect of land use changes on soil erosion and sediment yield using a grid‐based distributed modelling approach

Processes of soil erosion and sediment transport are strongly influenced by land use changes so the modelling of land use changes is important with respect to the simulation of soil degradation and its on‐site and off‐site consequences. The reliability of simulation results from erosion models is circumscribed by considerable spatial variation in many parameters. However, most of the currently widely used erosion models at the mesoscale are semidistributed, which leads to difficulties in incorporating a high degree of spatial information, especially land use information, so that the effects of land use changes on soil erosion have hitherto not been investigated in detail using these models. In this article, a grid‐based distributed erosion and sediment transport model is introduced, which simulates the spatial pattern of erosion and deposition rates and sediment transport processes in river channels. In this model, land use affects soil erosion through altering soil loss and influencing sediment delivery. Simulated soil erosion for events recorded in 1989 and 1996 in the Lushi basin in China was analyzed by comparing it with historical land use maps. The results indicated that even relatively minor land use changes had a significant effect on regional soil erosion rates and sediment transport to rivers. The average erosion rate increased from 1989 to 1996, after the transformation of forest to farmland. The results of the study suggest that the proposed soil erosion model can be applied in similar river basins. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimating source regions for snowmelt runoff in a Rocky Mountain basin: tests of a data‐based conceptual modeling approach

In many mountain basins, river discharge measurements are located far away from runoff source areas. This study tests whether a basic snowmelt runoff conceptual model can be used to estimate relative contributions of different elevation zones to basin‐scale discharge in the Cache la Poudre, a snowmelt‐dominated Rocky Mountain river. Model tests evaluate scenarios that vary model configuration, input variables, and parameter values to determine how these factors affect discharge simulation and the distribution of runoff generation with elevation. Results show that the model simulates basin discharge well (NSCE and R >0.90) when input precipitation and temperature are distributed with different lapse rates, with a rain‐snow threshold parameter between 0 and 3.3 °C, and with a melt rate parameter between 2 and 4 mm °C^?1 d^?1 because these variables and parameters can have compensating interactions with each other and with the runoff coefficient parameter. Only the hydrograph recession parameter can be uniquely defined with this model structure. These non‐unique model scenarios with different configurations, input variables, and parameter values all indicate that the majority of basin discharge comes from elevations above 2900 m, or less than 25% of the basin total area, with a steep increase in runoff generation above 2600 m. However, the simulations produce unrealistically low runoff ratios for elevations above 3000 m, highlighting the need for additional measurements of snow and discharge at under‐sampled elevations to evaluate the accuracy of simulated snow and runoff patterns. Copyright © 2013 John Wiley & Sons, Ltd.     

Use of multi‐platform,multi‐temporal remote‐sensing data for calibration of a distributed hydrological model: an application in the Arno basin,Italy

Images from satellite platforms are a valid aid in order to obtain distributed information about hydrological surface states and parameters needed in calibration and validation of the water balance and flood forecasting. Remotely sensed data are easily available on large areas and with a frequency compatible with land cover changes. In this paper, remotely sensed images from different types of sensor have been utilized as a support to the calibration of the distributed hydrological model MOBIDIC, currently used in the experimental system of flood forecasting of the Arno River Basin Authority. Six radar images from ERS‐2 synthetic aperture radar (SAR) sensors (three for summer 2002 and three for spring–summer 2003) have been utilized and a relationship between soil saturation indexes and backscatter coefficient from SAR images has been investigated. Analysis has been performed only on pixels with meagre or no vegetation cover, in order to legitimize the assumption that water content of the soil is the main variable that influences the backscatter coefficient. Such pixels have been obtained by considering vegetation indexes (NDVI) and land cover maps produced by optical sensors (Landsat‐ETM). In order to calibrate the soil moisture model based on information provided by SAR images, an optimization algorithm has been utilized to minimize the regression error between saturation indexes from model and SAR data and error between measured and modelled discharge flows. Utilizing this procedure, model parameters that rule soil moisture fluxes have been calibrated, obtaining not only a good match with remotely sensed data, but also an enhancement of model performance in flow prediction with respect to a previous calibration with river discharge data only. Copyright © 2006 John Wiley & Sons, Ltd.     

Spatio‐temporal variability of the isotopic input signal in a partly forested catchment: Implications for hydrograph separation

The isotopic composition of precipitation (D and ¹⁸O) has been widely used as an input signal in water tracer studies. Whereas much recent effort has been put into developing methodologies to improve our understanding and modelling of hydrological processes (e.g., transit‐time distributions or young water fractions), less attention has been paid to the spatio‐temporal variability of the isotopic composition of precipitation, used as input signal in these studies. Here, we investigated the uncertainty in isotope‐based hydrograph separation due to the spatio‐temporal variability of the isotopic composition of precipitation. The study was carried out in a Mediterranean headwater catchment (0.56 km²). Rainfall and throughfall samples were collected at three locations across this relatively small catchment, and stream water samples were collected at the outlet. Results showed that throughout an event, the spatial variability of the input signal had a higher impact on hydrograph separation results than its temporal variability. However, differences in isotope‐based hydrograph separation determined preevent water due to the spatio‐temporal variability were different between events and ranged between 1 and 14%. Based on catchment‐scale isoscapes, the most representative sampling location could also be identified. This study confirms that even in small headwater catchments, spatio‐temporal variability can be significant. Therefore, it is important to characterize this variability and identify the best sampling strategy to reduce the uncertainty in our understanding of catchment hydrological processes.     

Predictability of river flow and suspended sediment transport in the Mississippi River basin: a non‐linear deterministic approach

As the Mississippi River plays a major role in fulfilling various water demands in North America, accurate prediction of river flow and sediment transport in the basin is crucial for undertaking both short‐term emergency measures and long‐term management efforts. To this effect, the present study investigates the predictability of river flow and suspended sediment transport in the basin. As most of the existing approaches that link water discharge, suspended sediment concentration and suspended sediment load possess certain limitations (absence of consensus on linkages), this study employs an approach that presents predictions of a variable based on history of the variable alone. The approach, based on non‐linear determinism, involves: (1) reconstruction of single‐dimensional series in multi‐dimensional phase‐space for representing the underlying dynamics; and (2) use of the local approximation technique for prediction. For implementation, river flow and suspended sediment transport variables observed at the St. Louis (Missouri) station are studied. Specifically, daily water discharge, suspended sediment concentration and suspended sediment load data are analysed for their predictability and range, by making predictions from one day to ten days ahead. The results lead to the following conclusions: (1) extremely good one‐day ahead predictions are possible for all the series; (2) prediction accuracy decreases with increasing lead time for all the series, but the decrease is much more significant for suspended sediment concentration and suspended sediment load; and (3) the number of mechanisms dominantly governing the dynamics is three for each of the series. Copyright © 2005 John Wiley & Sons, Ltd.     

On determining the geometric and kinematic characteristics of coherent flow structures over a gravel bed: a new approach using combined PLIF‐PIV

In gravel‐bed rivers, the microtopography of the bed is known to exert a significant influence on the generation of turbulent flow structures that owe their origin to fluid shear generated near the bed. Although field and laboratory measurements have indicated that flows over gravel beds contain a range of coherent flow structures, the kinematic and dynamic properties of these structures are still poorly understood. This paper describes a new experimental methodology to quantify simultaneously both the kinematic and dynamic characteristics of coherent flow structures based upon combined planar laser‐induced fluorescence and particle imaging velocimetry (PLIF‐PIV). The results confirm that the primary generative mechanism of coherent flow structures is at the bed, where merging hairpin vortices form around bed clasts and generate larger‐scale fluid motions that advect downstream. Copyright © 2010 John Wiley & Sons, Ltd.     

Reduced‐complexity flow routing models for sinuous single‐thread channels: intercomparison with a physically‐based shallow‐water equation model

Reduced‐complexity models of fluvial processes use simple rules that neglect much of the underlying governing physics. This approach is justified by the potential to use these models to investigate long‐term and/or fundamental river behaviour. However, little attention has been given to the validity or realism of reduced‐complexity process parameterizations, despite the fact that the assumptions inherent in these approaches may limit the potential for elucidating the behaviour of natural rivers. This study presents two new reduced‐complexity flow routing schemes developed specifically for application in single‐thread rivers. Output from both schemes is compared with that from a more sophisticated model that solves the depth‐averaged shallow water equations. This comparison provides the first demonstration of the potential for deriving realistic predictions of in‐channel flow depth, unit discharge, energy slope and unit stream power using simple flow routing schemes. It also highlights the inadequacy of modelling unit stream power, shear stress or sediment transport capacity as a function of local bed slope, as has been common practice in a number of previous reduced‐complexity models. Copyright © 2009 John Wiley & Sons, Ltd.     

Application of 1D paleo‐fluvial process modelling at a basin scale to augment sparse borehole data: example of a Permian formation in the Galilee Basin,Australia

The heterogeneous hydraulic conductivity (K) in water‐bearing formations controls subsurface flow and solute transport processes. Geostatistical techniques are often employed to characterize the K distribution in space based on the correlation between K measurements. However, at the basin scale, there are often insufficient measurements for inferring the spatial correlation. This is a widespread problem that we address in this study using the example of the Betts Creek Beds (BCB) in the Galilee Basin, Australia. To address the lack of data, we use a 1D stochastic fluvial process‐based model (SFPM) to quantify the total sediment thickness, Z( x ), and the sandstone proportion over the total thickness, P_s( x ), in the BCB. The semivariograms of Z( x ) and P_s( x ) are then extracted and used in sequential Gaussian simulation to construct the 2D spatial distribution of Z( x ) and P_s( x ). P_s( x ) can be converted to a K distribution based on classical averaging methods. The results demonstrate that the combination of SFPM and geostatistical simulation allows for the evaluation of upscaled K distribution with a limited number of K measurements. Copyright © 2015 John Wiley & Sons, Ltd.