Evaluation of infiltration‐based stormwater management to restore hydrological processes in urban headwater streams

Urbanization threatens headwater stream ecosystems globally. Watershed restoration practices, such as infiltration‐based stormwater management, are implemented to mitigate the detrimental effects of urbanization on aquatic ecosystems. However, their effectiveness for restoring hydrologic processes and watershed storage remains poorly understood. Our study used a comparative hydrology approach to quantify the effects of urban watershed restoration on watershed hydrologic function in headwater streams within the Coastal Plain of Maryland, USA. We selected 11 headwater streams that spanned an urbanization–restoration gradient (4 forested, 4 urban‐degraded, and 3 urban‐degraded) to evaluate changes in watershed hydrologic function from both urbanization and watershed restoration. Discrete discharge and continuous, high‐frequency rainfall‐stage monitoring were conducted in each watershed. These datasets were used to develop 6 hydrologic metrics describing changes in watershed storage, flowpath connectivity, or the resultant stream flow regime. The hydrological effects of urbanization were clearly observed in all metrics, but only 1 of the 3 restored watersheds exhibited partially restored hydrologic function. At this site, a larger minimum runoff threshold was observed relative to the urban‐degraded watersheds, suggesting enhanced infiltration of stormwater runoff within the restoration structure. However, baseflow in the stream draining this watershed remained low compared to the forested reference streams, suggesting that enhanced infiltration of stormwater runoff did not recharge subsurface storage zones contributing to stream baseflow. The highly variable responses among the 3 restored watersheds were likely due to the spatial heterogeneity of urban development, including the level of impervious cover and extent of the storm sewer network. This study yielded important knowledge on how restoration strategies, such as infiltration‐based stormwater management, modulated—or failed to modulate—hydrological processes affected by urbanization, which will help improve the design of future urban watershed management strategies. More broadly, we highlighted a multimetric approach that can be used to monitor the restoration of headwater stream ecosystems in disturbed landscapes.     

The performance of rainwater tanks for stormwater retention and water supply at the household scale: an empirical study

Urban stormwater run‐off degrades the ecological condition of streams. The use of rainwater tanks to supplement water supply can reduce the frequency and volume of urban stormwater run‐off that is otherwise conveyed directly to streams via conventional stormwater drainage systems. Few studies, however, have examined the use of tanks in the context of managing flow regimes for stream protection, with most focussed uniquely on their water conservation benefits. We used measured tank water level data to assess the performance of 12 domestic rainwater tanks against the dual criteria of their ability to (i) reduce potable mains water usage and (ii) retain run‐off from rainfall events and thus reduce the volume and frequency of stormwater run‐off. We found that five households relied almost entirely on tank water. Three of the tanks achieved stormwater retention performance approaching that of the same area of pre‐developed land, although nine did not – a consequence of limited demand and small tank capacity. Our results suggest that tank water usage can result in substantial reductions in mains water use, if regular and sufficiently large domestic demands are connected to tanks. In many cases, such demands will also result in the best stormwater retention performance. Our results highlight an opportunity to design tank systems to achieve multiple objectives. Application of similar analyses in different locations will help to optimize tanks for simultaneous water supply and stormwater retention purposes. Copyright © 2014 John Wiley & Sons, Ltd.     

Opportunities and challenges of the Sponge City construction related to urban water issues in China

Waterlogging is one of the major water issues in most cities of China and directly restricts their urbanization processes. The construction of Sponge City is an effective approach to solving the urban water issues, particularly for the waterlogging. In this study, both the urban issues emerged at the stage of rapid urbanization in China and the demands as well as problems of Sponge City construction related with the water issues were investigated, and the opportunities and challenges for the Sponge City construction in the future were also proposed. It was found that the current stormwater management focused on the construction of gray infrastructures (e.g., drainage network and water tank) based on the fast discharge idea, which was costly and hard to catch up with the rapid expansion of city and its impervious surface, while green infrastructures (e.g., river, lake and wetland) were ignored. Moreover, the current construction of Sponge City was still limited to low impacted development (LID) approach which was concentrated on source control measures without consideration of the critical functions of surrounding landscapes (i.e., mountain, river, wetland, forest, farmland and lake), while application of the integrated urban water system approach and its supported technologies including municipal engineering, urban hydrology, environmental science, social science and ecoscape were relatively weak and needed to be improved. Besides, the lack of special Sponge City plan and demonstration area was also a considerable problem. In this paper, some perspectives on Good Sponge City Construction were proposed such as the point that idea of urban plan and construction should conform to the integral and systematic view of sustainable urban development. Therefore, both the basic theoretical research and the basic infrastructure construction such as monitoring system, drainage facility and demonstration area should be strengthened, meanwhile, the reformation and innovation in the urban water management system and the education system should also be urgently performed. The study was expected to provide a deeper thinking for the current Sponge City construction in China and to give some of suggestions for the future directions to urban plan and construction, as well as urban hydrology discipline.     

Urban hydrologic trend analysis based on rainfall and runoff data analysis and conceptual model calibration

Urban stormwater is a major cause of urban flooding and natural water pollution. It is therefore important to assess any hydrologic trends in urban catchments for stormwater management and planning. This study addresses urban hydrological trend analysis by examining trends in variables that characterize hydrological processes. The original and modified Mann‐Kendall methods are applied to trend detection in two French catchments, that is, Chassieu and La Lechere, based on approximately 1 decade of data from local monitoring programs. In both catchments, no trend is found in the major hydrological process driver (i.e., rainfall variables), whereas increasing trends are detected in runoff flow rates. As a consequence, the runoff coefficients tend to increase during the study period, probably due to growing imperviousness with the local urbanization process. In addition, conceptual urban rainfall‐runoff model parameters, which are identified via model calibration with an event based approach, are examined. Trend detection results indicate that there is no trend in the time of concentration in Chassieu, whereas a decreasing trend is present in La Lechere, which, however, needs to be validated with additional data. Sensitivity analysis indicates that the original Mann‐Kendall method is not sensitive to a few noisy values in the data series.     

Impacts of urbanisation on hydrological and water quality dynamics,and urban water management: a review

ABSTRACT

As urban space continues to expand to accommodate a growing global population, there remains a real need to quantify and qualify the impacts of urban space on natural processes. The expansion of global urban areas has resulted in marked alterations to natural processes, environmental quality and natural resource consumption. The urban landscape influences infiltration and evapotranspiration, complicating our capacity to quantify their dynamics across a heterogeneous landscape at contrasting scales. Impervious surfaces exacerbate runoff processes, whereas runoff from pervious areas remains uncertain owing to variable infiltration dynamics. Increasingly, the link between the natural hydrological cycle and engineered water cycle has been made, realising the contributions from leaky infrastructure to recharge and runoff rates. Urban landscapes are host to a suite of contaminants that impact on water quality, where novel contaminants continue to pose new challenges to monitoring and treatment regimes. This review seeks to assess the major advances and remaining challenges that remain within the growing field of urban hydrology.

Editor M.C. Acreman; Associate editor E. Rozos     

Evaluation of distributed BMPs in an urban watershed—High resolution modeling for stormwater management

The urban environment modifies the hydrologic cycle resulting in increased runoff rates, volumes, and peak flows. Green infrastructure, which uses best management practices (BMPs), is a natural system approach used to mitigate the impacts of urbanization onto stormwater runoff. Patterns of stormwater runoff from urban environments are complex, and it is unclear how efficiently green infrastructure will improve the urban water cycle. These challenges arise from issues of scale, the merits of BMPs depend on changes to small‐scale hydrologic processes aggregated up from the neighborhood to the urban watershed. Here, we use a hyper‐resolution (1 m), physically based hydrologic model of the urban hydrologic cycle with explicit inclusion of the built environment. This model represents the changes to hydrology at the BMP scale (~1 m) and represents each individual BMP explicitly to represent response over the urban watershed. Our study varies both the percentage of BMP emplacement and their spatial location for storm events of increasing intensity in an urban watershed. We develop a metric of effectiveness that indicates a nonlinear relationship that is seen between percent BMP emplacement and storm intensity. Results indicate that BMP effectiveness varies with spatial location and that type and emplacement within the urban watershed may be more important than overall percent.     

城市场次降雨径流污染负荷快速估算方法

城市降雨径流污染是城市水质恶化的重要原因之一,定量计算城市降雨径流污染负荷,是实施城市水环境污染总量控制管理的基础和关键,可为城市水环境治理和污染控制提供科学依据.本文以污染物累积冲刷理论为基础,提出了“特征面积”的概念和计算公式,建立了场次降雨径流污染负荷数学模型,并结合案例,对数学模型在有效性、预测精度、适用性和局限性等方面进行评价.结果表明,特征面积较好地反映了污染物在各类土地上的污染负荷特性,场次降雨径流污染负荷与特征面积和降雨量的乘积呈正比.利用3场及以上降雨径流污染负荷结果,可较好地率定模型,从而可快速且较准确地估算单场次降雨径流污染负荷.该方法简单实用,获取数据工作量小,适用地区广.对于小降雨事件,建议采用降雨量相近的观测结果对模型进行率定,以提高模型的预测精度.     

Water balance prediction in stormwater infiltration basins using 2-D modeling: An application to evaluate the clogging process

Sustainable urban drainage systems are built along roads and in urban areas to collect urban runoff and avoid flooding, and to filter water pollutants. Sediment collected by runoff is deposited in the stormwater basin and progressively reduces water infiltration efficiency, leading to the clogging of the basin. To help stormwater basin managers and stakeholders better understand and predict clogging rates in order to elaborate maintenance plans and schedules, water transport prediction models are necessary. However,because of the heterogeneous sediment hydrodynamic properties inside the stormwater basin, a twodimensional(2-D) water flow model is required to predict water levels and possible overflow as accurately as possible. Saturated hydraulic conductivity(Ks) and sediment water retention curves were measured in the overall sediment layer of the stormwater basin, in addition to sediment layer thickness and organic matter content(11 sampling points). Sediment depth was used to predict organic matter(OM) content, and the OM was used to predict Ks. Water height in the basin was modeled with the HYDRUS-2 D model by taking into account the sediment hydrodynamic properties distribution. The HYDRUS-2 D model gave a satisfactory representation of the measured data. Scenarios of the hydraulic properties of stormwater basin sediment were tested over time, and hydraulic resistance, R, was calculated to assess the stormwater basin performance. Presently, after 20 years of functioning, the stormwater basin still ensures efficient water infiltration, but the first outflow(Hydraulic resistance,R 24 h)) is expected to appear in the next 5 years, and clogging(R 47 h) in the next 13 years. This 2-D water balance model makes it possible to integrate the hydrodynamic heterogeneity of a stormwater basin. It gives interesting perspectives to better predict 2-D/3-D contaminant transport.     

Current research in urban hydrogeology – A review

Urban groundwater is a heritage at risk because urban land use practises puts enormous and highly complex pressure on this resource. In this article, we review urban groundwater studies in the context of urban water management, discuss advances in hydrogeological investigation, monitoring and modelling techniques for urban areas and highlight the challenges. We present how techniques on contaminant concentration measurements, water balancing and contaminant load estimation were applied and further developed for the special requirements in urban settings. To fully understand and quantify the complex urban water systems, we need to refine these methods and combine them with sophisticated modelling approaches. Only then we will be able to sustainably manage our water resources in and around our urban areas especially in light of growing cities and global climatic change. We believe that over the next few years much more effort will be devoted to research in urban hydrogeology.     

Modelling the impact of stormwater source control infiltration techniques on catchment baseflow

Stormwater management increasingly recognises the need to emulate, to the maximum extent possible, the flow regime of receiving waters in their pre‐development state. Hydrological models play a central role in assessing the catchment‐scale impacts of alternative stormwater management strategies. However, because of the complexity of physical processes involved in urban hydrology, particularly subsurface flows, the predictive performance of such models is often low. We investigated how the structure of hydrological models influenced the prediction of urbanisation and stormwater management impacts on baseflow. We calibrated three conceptual models of the same reference catchment and compared the modelled flow regime from different stormwater management scenarios, using each of the three model structures. Scenarios were assessed using six metrics, characterising the whole streamflow regime and in particular baseflow. Although the three models of the reference catchment represented the observed hydrograph well, the most complex structure developed using a thorough diagnostic of the catchment behaviour better captured the change in hydrological regime during dry years. Predictions of baseflow changes due to urbanisation varied significantly according to the model structure. Similarly, the models showed distinct responses to the stormwater management scenarios applied, especially for scenarios involving infiltration of stormwater at source. Our results confirm the importance of predicting the consequences of land use changes with conceptual models that are consistent with the hydrological behaviour of the study catchment. Future work should help to quantify the uncertainties due to model structure and thus provide practical guidance to the use of catchment models for assessing stormwater management strategies. Copyright © 2013 John Wiley & Sons, Ltd.     

Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity

This paper proposes an approach to estimating the uncertainty related to EPA Storm Water Management Model model parameters, percentage routed (P_R) and saturated hydraulic conductivity (K_sat), which are used to calculate stormwater runoff volumes. The methodology proposed in this paper addresses uncertainty through the development of probability distributions for urban hydrologic parameters through extensive calibration to observed flow data in the Philadelphia collection system. The established probability distributions are then applied to the Philadelphia Southeast district model through a Monte Carlo approach to estimate the uncertainty in prediction of combined sewer overflow volumes as related to hydrologic model parameter estimation. Understanding urban hydrology is critical to defining urban water resource problems. A variety of land use types within Philadelphia coupled with a history of cut and fill have resulted in a patchwork of urban fill and native soils. The complexity of urban hydrology can make model parameter estimation and defining model uncertainty a difficult task. The development of probability distributions for hydrologic parameters applied through Monte Carlo simulations provided a significant improvement in estimating model uncertainty over traditional model sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Hydraulic characterization and hydrological behaviour of a pilot permeable pavement in an urban centre,Brazil

Considering all the alterations on hydrology and water quality that urbanization process brings, permeable pavement (PP) is an alternative to traditional impermeable asphalt and concrete pavement. The goal of the PP and other low impact development devices is to increase infiltration and reduce peak runoff flows. These structures are barely used in Brazil aiming stormwater management, one of the big hydrological issues in cities throughout the country, with increasing urbanization rates. The main objective of this paper is the hydraulic characterization of a PP and the assessment of its hydrological efficiency from the point of view of the infiltration process. The study focuses on a pilot area in a parking lot in an urban area (Recife, Brazil). Soil elements filling the voids between concrete elements were sampled (particle size density, water contents) and tested with water infiltration experiments at several points of the 3 m × 1.5 m surface pilot area. Beerkan Estimation of Soil Transfer parameters algorithm was applied to the infiltration experiment data to obtain the hydraulic characteristics of the soil composing the PP surface layer, the concrete grid pavers (with internal voids filled with natural soil) permeability being neglected. Results show that the soil hydraulic characteristics vary spatially within the pilot area and that the soil samples have different hydraulic behaviours. The hydraulic characteristics derived from Beerkan Estimation of Soil Transfer parameters analysis were implemented into Hydrus code to simulate runoff, infiltration and water balance over a year. The numerical simulation showed the good potential of the PP for rainfall–runoff management, which demonstrates that PP can be used to retrofit existing parking infrastructure and to promote hydrological behaviour close to natural soils. Copyright © 2016 John Wiley & Sons, Ltd.     

Uncertainty analysis of urban sewer system using spatial simulation of radar rainfall fields: New York City case study

The goal of this study is to investigate the uncertainty of an urban sewer system’s response under various rainfall and infrastructure scenarios by applying a recently developed nonparametric copula-based simulation approach to extreme rainfall fields. The approach allows for Monte Carlo simulation of multiple variables with differing marginal distributions and arbitrary dependence structure. The independent and identically distributed daily extreme rainfall events of the corresponding urban area, extracted from nationwide high resolution radar data stage IV, are the inputs of the spatial simulator. The simulated extreme rainfall fields were used to calculate excess runoff using the Natural Resources Conservation Service’s approach. New York City is selected as a case study and the results highlight the importance of preserving the spatial dependence of rainfall fields between the grids, even for simplified hydrologic models. This study estimates the probability of combined sewer overflows under extreme rainfall events and identifies the most effective locations in New York City to install green infrastructure for detaining excess stormwater runoff. The results of this study are beneficial for planners working on stormwater management and the approach is broadly applicable because it does not rely on extensive sewer system information.     

The role of land surface versus drainage network characteristics in controlling water quality and quantity in a small urban watershed

The processes that control run‐off quantity and quality in urban watersheds are complex and not well understood. Although impervious surface coverage has traditionally been used to examine altered hydrologic response in urban watersheds, several studies suggest that other elements of the urban landscape, particularly those associated with urban infrastructure and the drainage system, play an equally important role. The relative importance of impervious surfaces, stormwater ponds, expansion of the drainage network, and drainage network structures in controlling hydrologic response was examined in the subwatersheds of the Kromma Kill, an urban watershed located in Albany County, NY. In this study, geographic information systems was used to compute geospatial land surface and drainage network properties of 5 Kromma Kill subwatersheds. In these same subwatersheds, water quantity (rainfall and run‐off) and quality (macroinvertebrates, nitrate, total nitrogen, dissolved oxygen, total dissolved solids, and nonpurgable organic carbon) parameters were measured. Strong and significant correlations were identified between land surface and drainage network properties and field observations. Causal relationships were then tested using the Environmental Protection Agency's Stormwater Management Model. Field and model analyses suggest that whereas percent imperviousness is a dominant control on water quality, drainage density and slope are equally important. However, for water quantity, whereas imperviousness is positively correlated with increased run‐off volumes, drainage network properties and slope are the dominant controls on run‐off volumes. Results have important implications for stormwater management plans, especially those aimed at reducing the effective impervious surface coverage of urban watersheds. Reducing the percentage of effective imperviousness in a watershed is not a “one size fits all” solution and can help to meet some management objectives, such as reducing nitrogen concentrations and improving water quality, but may not serve as the most effective, and therefore economical, solution for every management objective including reducing run‐off volumes.     

A two-layer model for studying 2D dissolved pollutant runoff over impermeable surfaces

Dissolved pollutants in stormwater are a main contributor to water pollution in urban environments. However, many existing transport models are semi-empirical and only consider one-dimensional flows, which limit their predictive capacity. Combining the shallow water and the advection–diffusion equations, a two-dimensional physically based model is developed for dissolved pollutant transport by adopting the concept of a ‘control layer’. A series of laboratory experiments has been conducted to validate the proposed model, taking into account the effects of buildings and intermittent rainfalls. The predictions are found to be in good agreement with experimental observations, which supports the assumption that the depth of the control layer is constant. Based on the validated model, a parametric study is conducted, focusing on the characteristics of the pollutant distribution and transport rate over the depth. The hyetograph, including the intensity, duration and intermittency, of rainfall event has a significant influence on the pollutant transport rates. The depth of the control layer, rainfall intensity, surface roughness and area length are dominant factors that affect the dissolved pollutant transport. Finally, several perspectives of the new pollutant transport model are discussed. This study contributes to an in-depth understanding of the dissolved pollutant transport processes on impermeable surfaces and urban stormwater management.     

Modelling of stormwater biofilters under random hydrologic variability: a case study of a car park at Monash University,Victoria (Australia)

Biofiltration systems represent an effective technology for the management of urban stormwater runoff volumes and quality. The performance of these systems, although largely dependent on their physical characteristics, is also strongly affected by the natural variability of runoff occurrence and volumes. This article presents a model that describes the statistical behaviour of the main variables involved in the water balance of a biofiltration system, given its main physical properties (filter media and vegetation types) and accounting for the natural inflow variability in terms of occurrence and water volumes. The model permits the analytical derivation of the long‐term (e.g. annual) probability density function of the soil water content in the filter media and the estimation of the main statistics of water fluxes, that is, outflow, evapotranspiration and overflow. By relating the soil water content in the filter media before inflow events to the outflow total nitrogen concentrations, the model also gives estimates of the statistics of nitrogen removal performance as a function of inflow variability. The model was tested against field data collected at a stormwater biofiltration system in Melbourne, Australia. The model could be used to rapidly assess the hydrologic and nitrogen treatment performance of alternative applications of biofiltration for stormwater management across a range of climates. Copyright © 2011 John Wiley & Sons, Ltd.     

Stormwater management network effectiveness and implications for urban watershed function: A critical review

Deleterious effects of urban stormwater are widely recognized. In several countries, regulations have been put into place to improve the conditions of receiving water bodies, but planning and engineering of stormwater control is typically carried out at smaller scales. Quantifying cumulative effectiveness of many stormwater control measures on a watershed scale is critical to understanding how small‐scale practices translate to urban river health. We review 100 empirical and modelling studies of stormwater management effectiveness at the watershed scale in diverse physiographic settings. Effects of networks with stormwater control measures (SCMs) that promote infiltration and harvest have been more intensively studied than have detention‐based SCM networks. Studies of peak flows and flow volumes are common, whereas baseflow, groundwater recharge, and evapotranspiration have received comparatively little attention. Export of nutrients and suspended sediments have been the primary water quality focus in the United States, whereas metals, particularly those associated with sediments, have received greater attention in Europe and Australia. Often, quantifying cumulative effects of stormwater management is complicated by needing to separate its signal from the signal of urbanization itself, innate watershed characteristics that lead to a range of hydrologic and water quality responses, and the varying functions of multiple types of SCMs. Biases in geographic distribution of study areas, and size and impervious surface cover of watersheds studied also limit our understanding of responses. We propose hysteretic trajectories for how watershed function responds to increasing imperviousness and stormwater management. Even where impervious area is treated with SCMs, watershed function may not be restored to its predevelopment condition because of the lack of treatment of all stormwater generated from impervious surfaces; non‐additive effects of individual SCMs; and persistence of urban effects beyond impervious surfaces. In most cases, pollutant load decreases largely result from run‐off reductions rather than lowered solute or particulate concentrations. Understanding interactions between natural and built landscapes, including stormwater management strategies, is critical for successfully managing detrimental impacts of stormwater at the watershed scale.     

Modelling the effects of changes in rainfall event characteristics on TSS loads in urban runoff

The effect of changes in rainfall event characteristics on urban stormwater quality, which was described by total suspended solids (TSS), was studied by means of computer simulations conducted with the Storm Water Management Model for a climate change scenario for northern Sweden. The simulation results showed that TSS event loads depended mainly on rainfall depth and intensity, but not on antecedent conditions. Storms with low‐to‐intermediate depths and intensities showed the highest sensitivity to changes in rainfall input, both for percentage and absolute changes in TSS wash‐off loads, which was explained by the contribution of pervious areas and supply limitations. This has significant implications for stormwater management, because those relatively frequent events generally carry a high percentage of the annual pollutant load. Copyright © 2013 John Wiley & Sons, Ltd.     

The beachwatch pollution monitoring programme: Changing priorities to recognize changed circumstances

Since the commissioning of the three major deepwater outfalls in Sydney, there has been a dramatic improvement in general beach water quality at Sydney's ocean beaches. This has required the NSW Environment Protection Authority's Beachwatch Programme to shift from assessing the impacts of gross sewage pollution due to nearshore outfalls to more diffuse pollution from stormwater and sewer overflows.

The visual indicators of gross sewage pollution originally used by Beachwatch for the daily assessment of bacterial water quality are now of limited value. General linear models (with multiple effects) were constructed to identify the secondary indicators which best describe the levels of bacterial contamination due to stormwater pollution. Data from four representative Sydney beaches were modelled separately due to the site-specific effects of pollution sources and hydrodynamics. Factors which were built into the models and were known on the day of prediction were rain amount, presence of stormwater material, the maximum daily stormwater rating, drain or lagoon flows at the time of sampling, and the drain/lagoon bacterial concentration two days before sampling.

Results indicate that there is a general linear relationship between visual indicators and bacterial density; however, the reliability of the prediction on a daily basis is poor and rainfall alone as a predictor is equivalent to or better than visual assessment alone. The primary source of information for the preparation of Beachwatch daily pollution bulletins now is rainfall reports from a telemetered network of rain gauges along the coast. This is a more cost-effective approach and has allowed the reallocation of resources to address more directly the problem of stormwater pollution at higher risk beaches.     

Radar for hydrology: Unfulfilled promise or unrecognized potential?

Hydrology requires accurate and reliable rainfall input. Because of the strong spatial and temporal variability of precipitation, estimation of spatially distributed rain rates is challenging. Despite the fact that weather radars provide high-resolution (but indirect) observations of precipitation, they are not used in hydrological applications as extensively as one could expect. The goal of the present review paper is to investigate this question and to provide a clear view of the opportunities (e.g., for flash floods, urban hydrology, rainfall spatial extremes) the limitations (e.g., complicated error structure, need for adjustment) and the challenges for the use of weather radar in hydrology (i.e., validation studies, precipitation forecasting, mountainous precipitation, error propagation in hydrological models).