Leveraging ensemble meteorological forcing data to improve parameter estimation of hydrologic models

As continental to global scale high-resolution meteorological datasets continue to be developed, there are sufficient meteorological datasets available now for modellers to construct a historical forcing ensemble. The forcing ensemble can be a collection of multiple deterministic meteorological datasets or come from an ensemble meteorological dataset. In hydrological model calibration, the forcing ensemble can be used to represent forcing data uncertainty. This study examines the potential of using the forcing ensemble to identify more robust parameters through model calibration. Specifically, we compare an ensemble forcing-based calibration with two deterministic forcing-based calibrations and investigate their flow simulation and parameter estimation properties and the ability to resist poor-quality forcings. The comparison experiment is conducted with a six-parameter hydrological model for 30 synthetic studies and 20 real data studies to provide a better assessment of the average performance of the deterministic and ensemble forcing-based calibrations. Results show that the ensemble forcing-based calibration generates parameter estimates that are less biased and have higher frequency of covering the true parameter values than the deterministic forcing-based calibration does. Using a forcing ensemble in model calibration reduces the risk of inaccurate flow simulation caused by poor-quality meteorological inputs, and improves the reliability and overall simulation skill of ensemble simulation results. The poor-quality meteorological inputs can be effectively filtered out via our ensemble forcing-based calibration methodology and thus discarded in any post-calibration model applications. The proposed ensemble forcing-based calibration method can be considered as a more generalized framework to include parameter and forcing uncertainties in model calibration.     

Grid‐resolution effects on a model for integrating urban and rural areas

The impact of grid‐cell size on calibrated parameters and on the performance of a variable source area model intended for urbanizing catchments is studied in this research. The model uses TOPMODEL concepts that were modified to consider urban areas in both the topographic index and the mechanism of surface runoff generation. The revised model known as TOPURBAN, was applied to a small catchment of roughly 8 km² in southern Ontario. Ten different grid‐cell sizes ranging from 10 m to 100 m were selected to study scale effects in this catchment with mild to moderate relief, on three separate time periods. The model performed adequately with calibration efficiencies for all three time periods in the range of 0\65 to 0\85. The verification efficiencies were not as high and ranged from 0\4 to 0\6. Larger cell sizes produced higher averages of topographic index, and this resulted in larger calibrated transmissivities. The most important parameter in determining the quantity of urban runoff was slightly affected by grid resolution. During the calibration process, this parameter was also found to interact with important parameters that dealt primarily with rural runoff generation. As cell size increased, contributions from urban areas increased and overland flow contributions from rural areas decreased. Results showed that in this integrated model of urban and rural areas, predicted processes based on calibrated parameters were dependent on grid resolution. Calibration of internal state variables is recommended to draw conclusions on the influences between urban and rural areas on the overall flow. Copyright © 2000 John Wiley & Sons, Ltd.     

The use of liquefaction features in paleoseismology: Lessons learned in the New Madrid seismic zone, central United States

A recent study in the New Madrid seismic zone demonstrates that large uncertainties, often involved but rarely expressed, in paleoliquefaction studies can be reduced by conducting detailed investigations at the most promising sites for dating liquefaction features. During the site investigations, care must be taken to collect samples that will provide close maximum and minimum dates for liquefaction features. It is advisable to use two-sigma calibrated dates, rather than one-sigma calibrated dates or radiocarbon ages, when estimating ages of liquefaction features. Well-constrained ages of individual liquefaction features should provide the basis for estimating the timing of paleoearthquakes and correlating features across a region. As uncertainty in ages of liquefaction features decreases, confidence in estimates of timing, source areas and magnitudes of paleoearthquakes increases. The New Madrid study also shows that modern or historic earthquakes that induced liquefaction in the same region and whose locations and magnitudes are fairly well know can serve as calibration events for paleoearthquakes. Future efforts that could further improve the usefulness of liquefaction feature in paleoseismology include (1) the development of new techniques for dating liquefaction features directly, (2) case studies of modern earthquakes that focus on the site and spatial distributions of liquefaction feature as well as geotechnical properties of liquefaction sites and (3) more rigorous quantification of uncertainties associated with estimates of timing, source areas and magnitudes of paleoearthquakes.     

Multi‐site calibration using a grid‐based event rainfall–runoff model: a case study of the upstream areas of the Nakdong River basin in Korea

Most runoff analyses using a grid‐based distributed model use one parameter group calibrated at the outlet of a watershed, instead of dividing the watershed into subwatersheds. Significant differences between the observed value and the simulation result of the subwatersheds can occur if just one parameter group is used in all subwatersheds that have different hydrological characteristics from each other. Therefore, to improve the simulation results of the subwatersheds within a watershed, a model calibrated at every subwatershed needs to be used to reflect the characteristics of each subwatershed. In this study, different parameter groups were set up for one or two sites using a distributed model, the GRM (Grid based Rainfall‐runoff Model), and the evaluations were based on the results of rainfall–runoff analysis, which uses a multi‐site calibration (MSC) technique to calibrate the model at the outlet of each site. The Hyangseok watershed in Naeseong River, which is a tributary of Nakdong River in Korea, was chosen as the study area. The watershed was divided into five subwatersheds each with a subwatershed outlet that was applied to the calibration sites . The MSC was applied for five cases. When a site was added for calibration in a watershed, the runoff simulation showed better results than the calibration of only one site at the most downstream area of the watershed. The MSC approach could improve the simulation results on the calibrated sites and even on the non‐calibrated sites, and the effect of MSC was improved when the calibrated site was closer to the runoff site. Copyright © 2014 John Wiley & Sons, Ltd.     

The Aterno valley strong-motion array: seismic characterization and determination of subsoil model

The paper focuses on the strong motion array deployed in the upper Aterno River Valley, in the immediate outskirts north-west of the town of L’Aquila, which is part of the Italian Strong Motion Network operated by the Department of Civil Protection. The array is composed of six accelerometric stations located along a cross section of the valley. The importance of this array relies on the fact that a large amount of high-quality records were obtained during the 2009 L’Aquila seismic sequence, from both the mainshock and several aftershocks. These data are especially important to investigate site effects in sediment-filled valleys during moderate earthquakes in epicentral area because well-documented observational studies are very limited in the literature. However, the main drawback for the study of site effects in the Aterno valley is the lack of a detailed knowledge of the geometry of the valley, soil layering and dynamic properties of materials. The main motivation for this study stems from the need to provide a reliable subsoil model of the valley coupled with high-quality strong motion data. Based on the above, in the framework of S4 project, a major effort was undertaken to get a trustworthy cross section of the valley by an ad hoc investigation, comprising geological and geotechnical surveys as well as an extensive geophysical campaign, characterized by both active and passive measurements. These results were complemented by additional geological and geotechnical data available in the literature. By merging all the information acquired, a 2D subsoil model of the transversal section of the upper Aterno valley has been produced. The valley is characterised by an asymmetric shape with a shallower rock basement at the western edge of the valley that deepens at the valley centre. Moreover, based on the results of geophysical tests, representative V_s values were assigned to the different lithologic units forming the alluvial deposits filling the valley. Shear wave velocity is a fundamental parameter for ground response studies and it is also effective in classifying the accelerometric station from a seismic point of view. The 2D model may be therefore, considered a benchmark model for future studies of site effects. It will offer the possibility to examine site effects with a complex underlying geology and to validate the results of numerical simulations of site response analyses with the numerous observations from earthquake recordings, both for weak and strong ground motion conditions.     

György Kovacs 1925–1988

Abstract

There has been a trend in recent years towards the development and popularity of physically-based deterministic models. However, the application of such models is not without difficulties. This paper investigates the usefulness of a conceptual single-event model for simulating floods from catchments covering a wide variety of climatic and physiographic areas. The model has been calibrated on a group of catchments and the calibrated parameter values related to physical catchment indices. The resulting quantitative relationships are assessed with respect to their value for estimating the parameter values of the model when calibration is not possible. The results indicate that the technique is likely to provide flood estimations for medium sized catchments (5–150 km²) that are more reliable than several flood estimation methods currently in use in South Africa.     

Calibration of Parameter Fields Consisting of Multiple Statistical Populations

If a parameter field to be calibrated consists of more than one statistical population, usually not only the parameter values are uncertain, but the spatial distributions of the populations are uncertain as well. In this study, we demonstrate the potential of the multimodal calibration method we proposed recently for the calibration of such fields, as applied to real-world ground water models with several additional stochastic parameter fields. Our method enables the calibration of the spatial distribution of the statistical populations, as well as their spatially correlated parameterization, while honoring the complete prior geostatistical definition of the multimodal parameter field. We illustrate the implications of the method in terms of the reliability of the posterior model by comparing its performance to that of a "conventional" calibration approach in which the positions of the statistical populations are not allowed to change. Information from synthetic calibration runs is used to show how ignoring the uncertainty involved in the positions of the statistical populations not only denies the modeler the opportunity to use the measurement information to improve these positions but also unduly influences the posterior intrapopulation distributions, causes unjustified adjustments to the cocalibrated parameter fields, and results in poorer observation reproduction. The proposed multimodal calibration allows a more complete treatment of the relevant uncertainties, which prevents the abovementioned adverse effects and renders a more trustworthy posterior model.     

Influence of calibration methodology on ground water flow predictions

We constructed a numerical model of transient ground water flow and solute transport for a portion of the Biscayne Aquifer in Florida, and calibrated the model with three different combinations of data from a 193-day period: head (h) data alone, data on h and ground water discharge to a canal (q), and data on h, q, and ground water chloride concentration (C). We used each of the three calibrated models to predict h and q during a 182-day test period separate from the calibration period. All three calibrated models predicted h equally well during the test period (r = 0.95, where r = 1 indicates perfect agreement between measured and simulated values), though the model calibrated on h alone had significantly different parameter values than the other two models. Predictions of q during the test period depended on calibration methodology; models calibrated with multiple targets simulated q more accurately than the model calibrated on h alone (r = 0.79 compared to r = 0.49). Based on the results of these simulations, we conclude: (1) Post-calibration prediction is important in assessing the value of different data types in automated calibration; (2) inverse-solution uniqueness is not a requirement for accurate h predictions; (3) relatively simple models can predict with reasonable accuracy transient ground water flow in a complex aquifer, and parameters governing this prediction can be estimated by nonlinear regression methods that incorporate both h and q data; (4) addition of C data to the calibration did not improve model predictive capacity because the information in the C data was similar to that in the q data, from the perspective of model calibration (the subsurface chemical signal in question was controlled mainly by seepage of high-chloride canal water into the low-chloride ground water system).     

Impact of the numbers of observations and calibration parameters on equifinality,model performance,and output and parameter uncertainty

The level of model complexity that can be effectively supported by available information has long been a subject of many studies in hydrologic modelling. In particular, distributed parameter models tend to be regarded as overparameterized because of numerous parameters used to describe spatially heterogeneous hydrologic processes. However, it is not clear how parameters and observations influence the degree of overparameterization, equifinality of parameter values, and uncertainty. This study investigated the impact of the numbers of observations and parameters on calibration quality including equifinality among calibrated parameter values, model performance, and output/parameter uncertainty using the Soil and Water Assessment Tool model. In the experiments, the number of observations was increased by expanding the calibration period or by including measurements made at inner points of a watershed. Similarly, additional calibration parameters were included in the order of their sensitivity. Then, unique sets of parameters were calibrated with the same objective function, optimization algorithm, and stopping criteria but different numbers of observations. The calibration quality was quantified with statistics calculated based on the ‘behavioural’ parameter sets, identified using 1% and 5% cut‐off thresholds in a generalized likelihood uncertainty estimation framework. The study demonstrated that equifinality, model performance, and output/parameter uncertainty were responsive to the numbers of observations and calibration parameters; however, the relationship between the numbers, equifinality, and uncertainty was not always conclusive. Model performance improved with increased numbers of calibration parameters and observations, and substantial equifinality did neither necessarily mean bad model performance nor large uncertainty in the model outputs and parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

The role of prior model calibration on predictions with ensemble Kalman filter

This paper, based on a real world case study (Limmat aquifer, Switzerland), compares inverse groundwater flow models calibrated with specified numbers of monitoring head locations. These models are updated in real time with the ensemble Kalman filter (EnKF) and the prediction improvement is assessed in relation to the amount of monitoring locations used for calibration and updating. The prediction errors of the models calibrated in transient state are smaller if the amount of monitoring locations used for the calibration is larger. For highly dynamic groundwater flow systems a transient calibration is recommended as a model calibrated in steady state can lead to worse results than a noncalibrated model with a well-chosen uniform conductivity. The model predictions can be improved further with the assimilation of new measurement data from on-line sensors with the EnKF. Within all the studied models the reduction of 1-day hydraulic head prediction error (in terms of mean absolute error [MAE]) with EnKF lies between 31% (assimilation of head data from 5 locations) and 72% (assimilation of head data from 85 locations). The largest prediction improvements are expected for models that were calibrated with only a limited amount of historical information. It is worthwhile to update the model even with few monitoring locations as it seems that the error reduction with EnKF decreases exponentially with the amount of monitoring locations used. These results prove the feasibility of data assimilation with EnKF also for a real world case and show that improved predictions of groundwater levels can be obtained.     

Données isotopiques (8786/Sr) et changements hydrologiques depuis 15 000 ans sur l'Altiplano andin

Abstract

In catchments characterized by spatially varying hydrological processes and responses, the optimal parameter values or regions of attraction in parameter space may differ with location-specific characteristics and dominating processes. This paper evaluates the value of semi-distributed calibration parameters for large-scale streamflow simulation using the spatially distributed LISFLOOD model. We employ the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm to infer the calibration parameters using daily discharge observations. The resulting posterior parameter distribution reflects the uncertainty about the model parameters and forms the basis for making probabilistic flow predictions. We assess the value of semi-distributing the calibration parameters by comparing three different calibration strategies. In the first calibration strategy uniform values over the entire area of interest are adopted for the unknown parameters, which are calibrated against discharge observations at the downstream outlet of the catchment. In the second calibration strategy the parameters are also uniformly distributed, but they are calibrated against observed discharges at the catchment outlet and at internal stations. In the third strategy a semi-distributed approach is adopted. Starting from upstream, parameters in each subcatchment are calibrated against the observed discharges at the outlet of the subcatchment. In order not to propagate upstream errors in the calibration process, observed discharges at upstream catchment outlets are used as inflow when calibrating downstream subcatchments. As an illustrative example, we demonstrate the methodology for a part of the Morava catchment, covering an area of approximately 10 000 km². The calibration results reveal that the additional value of the internal discharge stations is limited when applying a lumped parameter approach. Moving from a lumped to a semi-distributed parameter approach: (i) improves the accuracy of the flow predictions, especially in the upstream subcatchments; and (ii) results in a more correct representation of flow prediction uncertainty. The results show the clear need to distribute the calibration parameters, especially in large catchments characterized by spatially varying hydrological processes and responses.     

The relevance of preferential flow in catchment scale simulations: Calibrating a 3D dual-permeability model using DREAM

The occurrence of preferential flow in the subsurface has often been shown in field experiments. However, preferential flow is rarely included in models simulating the hydrological response at the catchment scale. If it is considered, preferential flow parameters are typically determined at the plot scale and then transferred to larger-scale simulations. Here, we successfully used the optimization algorithm DiffeRential Evolution Adaptive Metropolis (DREAM) to calibrate a 3D physics-based dual-permeability model directly at the catchment scale. In order to keep computational costs of the optimization routine at a reasonable level, we limited the number of parameters to be calibrated to the ones that had been shown before to be most influential for the simulation of discharge. We also calibrated parameters of the matrix domain and the macropore domain with a fixed parameter ratio between soil layers instead of calibrating every layer separately. These ratios reflected observed depth profiles of soil hydraulic properties at our study site. The dual-permeability parameter sets identified during calibration were able to simulate observed discharge time series satisfactorily but did not outperform a calibrated single-domain reference model scenario. Saturated hydraulic conductivities of the macropore domain were calibrated such that they became very similar to matrix saturated hydraulic conductivities, thereby effectively removing the effect of macropores. This suggests that the incorporation of vertical preferential flow as represented by the dual-permeability approach was not relevant for reproducing the hydrometric response reasonably well in the studied catchment. We also tested the scale-invariance of the calibrated dual-permeability parameter sets by using the parameter sets performing best at catchment scale to simulate plot-scale bromide depth profiles obtained from tracer irrigation experiments. This parameter transfer proved to be not successful, indicating that soil hydraulic parameters are scale-variant, independent of the direction of parameter transfer.     

Constraining water table depth simulations in a land surface model using estimated baseflow

Several recent studies have shown the significance of representing groundwater in land surface hydrologic simulations. However, optimal methods for model parameter calibration in order to realistically simulate baseflow and groundwater depth have received little attention. Most studies still use globally constant groundwater parameters due to the lack of available datasets for calibration. Moreover, when models are calibrated, various parameter combinations are found to exhibit equifinality in simulated total runoff due to model parameter interactions. In this study, a simple lumped groundwater model is incorporated into the Community Land Model (CLM), in which the water table is interactively coupled to soil moisture through the groundwater recharge fluxes. The coupled model (CLMGW) is successfully validated in Illinois using a 22-year (1984–2005) monthly observational dataset. Baseflow estimates from the digital recursive filter technique are used to calibrate the CLMGW parameters. The advantage obtained from incorporating baseflow calibration in addition to traditional calibration based on measured streamflow alone is demonstrated by a Monte Carlo-type simulation analysis. Using the optimal parameter sets identified from baseflow calibration, flow partitioning and water table depth simulations using CLMGW are improved, and the equifinality problem is alleviated. For other regions that lack observations of water table depth, the baseflow calibration approach can be used to enhance parameter estimation and constrain water table depth simulations.     

Towards a simple dynamic process conceptualization in rainfall–runoff models using multi‐criteria calibration and tracers in temperate,upland catchments

Empirically based understanding of streamflow generation dynamics in a montane headwater catchment formed the basis for the development of simple, low‐parameterized, rainfall–runoff models. This study was based in the Girnock catchment in the Cairngorm Mountains of Scotland, where runoff generation is dominated by overland flow from peaty soils in valley bottom areas that are characterized by dynamic expansion and contraction of saturation zones. A stepwise procedure was used to select the level of model complexity that could be supported by field data. This facilitated the assessment of the way the dynamic process representation improved model performance. Model performance was evaluated using a multi‐criteria calibration procedure which applied a time series of hydrochemical tracers as an additional objective function. Flow simulations comparing a static against the dynamic saturation area model (SAM) substantially improved several evaluation criteria. Multi‐criteria evaluation using ensembles of performance measures provided a much more comprehensive assessment of the model performance than single efficiency statistics, which alone, could be misleading. Simulation of conservative source area tracers (Gran alkalinity) as part of the calibration procedure showed that a simple two‐storage model is the minimum complexity needed to capture the dominant processes governing catchment response. Additionally, calibration was improved by the integration of tracers into the flow model, which constrained model uncertainty and improved the hydrodynamics of simulations in a way that plausibly captured the contribution of different source areas to streamflow. This approach contributes to the quest for low‐parameter models that can achieve process‐based simulation of hydrological response. Copyright © 2009 John Wiley & Sons, Ltd.     

基于卫星遥感的太湖蓝藻水华时空分布规律认识

由于大尺度水文模型和无资料区水文研究是当前国际水文研究的重点和难点,通过参数区域化方法来估计大尺度区域和无资料区的模型参数值成为了研究的热点之一将HBV模型应用于东江流域及其子流域,采用代理流域法和全局乎均法来估计该区域内无资料流域的模型参数研究表明：HBV模型能较好得用于东江流域径流模拟;交叉检验中,较小的序和ME值对应的参数,其转移效果不一定比较大的R^2和ME值对应的参数转移效果差;全局平均法中,面积权重平均值和泰森多边形插值后平均并不能明显改进子流域算术平均值估计无资料流域的模型参数的模拟结果;两者都能有效用于东江流域无资料流域的参数估计,且效果相差不大。     

Dual state–parameter estimation of hydrological models using ensemble Kalman filter

Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model.     

Revisiting “An Exercise in Groundwater Model Calibration and Prediction” After 30 Years: Insights and New Directions

In 1988, an important publication moved model calibration and forecasting beyond case studies and theoretical analysis. It reported on a somewhat idyllic graduate student modeling exercise where many of the system properties were known; the primary forecasts of interest were heads in pumping wells after a river was modified. The model was calibrated using manual trial-and-error approaches where a model's forecast quality was not related to how well it was calibrated. Here, we investigate whether tools widely available today obviate the shortcomings identified 30 years ago. A reconstructed version of the 1988 true model was tested using increasing parameter estimation sophistication. The parameter estimation demonstrated the inverse problem was non-unique because only head data were available for calibration. When a flux observation was included, current parameter estimation approaches were able to overcome all calibration and forecast issues noted in 1988. The best forecasts were obtained from a highly parameterized model that used pilot points for hydraulic conductivity and was constrained with soft knowledge. Like the 1988 results, however, the best calibrated model did not produce the best forecasts due to parameter overfitting. Finally, a computationally frugal linear uncertainty analysis demonstrated that the single-zone model was oversimplified, with only half of the forecasts falling within the calculated uncertainty bounds. Uncertainties from the highly parameterized models had all six forecasts within the calculated uncertainty. The current results outperformed those of the 1988 effort, demonstrating the value of quantitative parameter estimation and uncertainty analysis methods.     

Using model error in response history analysis to evaluate component calibration methods

This research is part of a larger effort to better understand and quantify the epistemic model uncertainty in dynamic response-history simulations. This paper focuses on how calibration methods influence model uncertainty. Structural models in earthquake engineering are typically built up from independently calibrated component models. During component calibration, engineers often use experimental component response under quasi-static loading to find parameters that minimize the error in structural response under dynamic loading. Since the calibration and the simulation environments are different, if a calibration method wants to provide optimal parameters for simulation, it has to focus on features of the component response that are important from the perspective of global structural behavior. Relevance describes how efficiently a calibration method can focus on such important features. A framework of virtual experiments and a methodology is proposed to evaluate the influence of calibration relevance on model error in simulations. The evaluation is demonstrated through a case study with buckling-restrained braced frames (BRBF). Two calibration methods are compared in the case study. The first, highly relevant calibration method is based on stiffness and hardening characteristics of braces; the second, less relevant calibration method is based on the axial force response of braces. The highly relevant calibration method consistently identified the preferable parameter sets. In contrast, the less relevant calibration method showed poor to mediocre performance. The framework and methodology presented here are not limited to BRBF. They have the potential to facilitate and systematize the improvement of component-model calibration methods for any structural system.     

Site response studies and seismic microzoning in the Middle Aterno valley (L��aquila, Central Italy)

Following the April 6th, 2009 Abruzzo mainshock, the Italian Civil Protection Department promoted a multidisciplinary study aimed at developing seismic microzonation maps for post-earthquake reconstruction planning. In the framework of this project, a Working Group, including the authors, was assembled to carry out a microzonation study on six villages located in the Middle Aterno valley. This paper focuses on the villages of Castelnuovo and Poggio Picenze, which experienced MCS intensity values of IX–X and VIII–IX, respectively. 1D and 2D linear equivalent site response analyses were carried out on representative geological cross-sections through the damaged centres and the expansion zones. The subsoil models resulting from geological, geotechnical and geophysical investigations were calibrated by comparing numerical amplification functions, in the linear range, with horizontal-to-vertical spectral ratio derived from both aftershocks and noise recordings. The input motions adopted for the analyses were five artificial accelerograms compatible with three response spectra obtained from the Italian seismic code, as well as from ad hoc probabilistic and deterministic studies. The results were expressed in the form of horizontal profiles of amplification factors in terms of peak ground acceleration, F_PGA, as well as of the Housner intensity, FH, in two different range of periods; this latter parameter was shown to be almost independent of the input motion and allowed to express the dependency of site amplification on the frequency range. The amplification factors computed along the representative geological sections were finally extended with a rational procedure to the surrounding areas to draw Grade-3 microzonation maps.