Hydrological model for urban catchments – analytical development using copulas and numerical solution

Abstract

A model based on analytical development and numerical solution is presented for estimating the cumulative distribution function (cdf) of the runoff volume and peak discharge rate of urban floods using the joint probability density function (pdf) of rainfall volume and duration together with information about the catchment's physical characteristics. The joint pdf of rainfall event volume and duration is derived using the theory of copulas. Four families of Archimedean copulas are tested in order to select the most appropriate to reproduce the dependence structure of those variables. Frequency distributions of runoff event volume and peak discharge rate are obtained following the derived probability distribution theory, using the functional relationship given by the rainfall–runoff process. The model is tested in two urban catchments located in the cities of Chillán and Santiago, Chile. The results are compared with the outcomes of continuous simulation in the Storm Water Management Model (SWMM) and with those from another analytical model that assumes storm event duration and volume to be statistically independent exponentially distributed variables.

Citation Zegpi, M. & Fernández, B. (2010) Hydrological model for urban catchments – analytical development using copulas and numerical solution. Hydrol. Sci. J. 55(7), 1123–1136.     

A parcel formulation of Hamiltonian layer models

Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of Hamiltonian ordinary differential equations bound together by integral transport laws. In particular, we show that this parcel Hamiltonian structure is compatible with the stacking of layers under isentropic or isothermal constraints. The appeal of the parcel formulation is the simplification of various calculations, in particular the derivation of the continuum Poisson bracket and the proof of the Jacobi identity. A comparison and connection is made between the Hamiltonian dynamics of fluid parcels and the Hamiltonian system of partial differential equations. The parcel formulation can be seen as a precursor and tool for the study of Hamiltonian numerical schemes.     

Range imaging: a new method for high‐resolution topographic measurements in small‐ and medium‐scale field sites

Topographic measurements are essential for the study of earth surface processes. Three‐dimensional data have been conventionally obtained through terrestrial laser scanning or photogrammetric methods. However, particularly in steep and rough terrain, high‐resolution field measurements remain challenging and often require new creative approaches. In this paper, range imaging is evaluated as an alternative method for obtaining surface data in such complex environments. Range imaging is an emerging time‐of‐flight technology, using phase shift measurements on a multi‐pixel sensor to generate a distance image of a surface. Its suitability for field measurements has yet not been tested. We found ambient light and surface reflectivity to be the main factors affecting error in distance measurements. Low‐reflectivity surfaces and strong illumination contrasts under direct exposure to sunlight lead to noisy distance measurements. However, regardless of lighting conditions, the accuracy of range imaging was markedly improved by averaging multiple images of the same scene. For medium ambient lighting (shade) and a light‐coloured surface the measurement uncertainty was approximately 9 mm. To further test the suitability of range imaging for field applications we measured a reach of a steep mountain stream with a horizontal resolution of approximately 1 cm (in the focal plane of the camera), allowing for the interpolation of a digital elevation model on a 2 cm grid. Comparison with an elevation model obtained from terrestrial laser scanning for the same site revealed that both models show similar degrees of topographic detail. Despite limitations in measurement range and accuracy, particularly at bright ambient lighting, range imaging offers three‐dimensional data in real time and video mode without the need of post‐processing. Therefore, range imaging is a useful complement or alternative to existing methods for high‐resolution measurements in small‐ to medium‐scale field sites. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis and modelling of rainfall fields at different resolutions in southern Italy

Abstract

The spatial and temporal variability of the scaling properties and correlation structure of a data set of rainfall time series, aggregated over different temporal resolutions, and observed in 70 raingauges across the Basilicata and Calabria regions of southern Italy, is investigated. Two types of random cascade model, namely canonical and microcanonical models, were used for each raingauge and selected season. For both models, different hypotheses concerning dependency of parameters on time scale and rainfall height can be adopted. In particular, a new approach is proposed which consists of several combinations of models with a different scale dependence of parameters for different temporal resolutions. The goal is to improve the modelling of the main features of rainfall time series, especially for cases where the variability of rainfall changes irregularly with temporal aggregation. The results obtained with the new methodology showed good agreement with the observed data, in particular, for the summer months. In fact, during this season, rainfall heights aggregated at fine temporal resolutions (from 5 to 20 min) are more similar (relative to the winter season) to the values cumulated on 1 or 3 h (due to convective phenomena) and, consequently, the process of rainfall breakdown is nearly stationary for a range of finer temporal resolutions.

Editor D. Koutsoyiannis; Associate editor A. Montanari     

Hydro-climatic variability and forest fires in Mexico’s northern temperate forests

Global warming is likely modifying the hydrological cycle of forested watersheds. This report set as objectives to: a) assess the hydrological variables interception loss, I, potential and actual evapo-transpiration, E, Et, runoff, Q, and soil moisture content, θ; b) evaluate whether these variables are presenting consistent trends or oscillations that can be associated to global warming or climate variability; and c) relate θ to the number of wildfires and the burned area in Durango, Mexico. A mass balance approach estimated daily variables of the water cycle using sub-models for I and Et to calculate Q and θ for a time series from 1945 to 2007. Regression and auto-regressive and moving averaging (ARIMA) techniques evaluated the statistical significance of trends. The cumulative standardized z value magnified and ARIMA models projected statistically similar monthly and annual time series data of all variables of the water cycle. Regression analysis and ARIMA models showed monthly and annual P, I, E, and Et, Q, and θ do not follow consistent up or downward linear tendencies over time with statistical significance; they rather follow oscillations that could be adequately predicted by ARIMA models (r² ≥ 0.70). There was a consistent statistical association (p ≤ 0.05) of θ with the number of wildfires and the area burned regardless of the different spatial scales used in evaluating these variables. The analysis shows seasonal variability is increasing over time as magnifying pulses of dryness and wetness, which may be the response of the hydrological cycle to climate change. Further research must center on using longer time series data, testing seasonal variability with additional statistical analysis, and incorporating new variables in the analysis.     

Monitoring wetland ditch water levels in the North Kent Marshes,UK, using Landsat TM imagery and ground-based measurements

Abstract

An understanding of hydrology is a prerequisite for ensuring the successful management, conservation and restoration of wetland environments. Frequently, however, little is known about historical hydrological conditions, such as water levels, within wetlands. Moreover, many channel and ditch systems in wetlands are not routinely monitored, except perhaps for research purposes. A methodology is presented herein which makes use of satellite imagery to indirectly provide remotely sensed observations of water levels within channels and ditches. Using multi-temporal Landsat Thematic Mapper (TM) imagery and simultaneous ground-based measurements of water levels, statistical relationships are established between satellite-derived effective wet ditch widths and measured water levels in the drainage system of the Elmley Marshes, southeast England. These relationships can be used subsequently to estimate historical ditch water levels and to monitor contemporary ditch water levels in the wetland. The study shows that satellite imagery has much to offer in monitoring changes in the hydrological regime of wetlands and in providing complimentary approaches to field monitoring.     

Adaptive neural-based fuzzy inference system (ANFIS) approach for modelling hydrological time series

Abstract

The main aim of this study is to develop a flow prediction method, based on the adaptive neural-based fuzzy inference system (ANFIS) coupled with stochastic hydrological models. An ANFIS methodology is applied to river flow prediction in Dim Stream in the southern part of Turkey. Application is given for hydrological time series modelling. Synthetic series, generated through autoregressinve moving-average (ARMA) models, are then used for training data sets of the ANFIS. It is seen that the extension of input and output data sets in the training stage improves the accuracy of forecasting by using ANFIS.     

Updating digital elevation models via change detection and fusion of human and remote sensor data in urban environments

OpenStreetMap (OSM) currently represents the most popular project of Volunteered Geographic Information (VGI): geodata are collected by common people and made available for public use. Airborne Laser Scanning (ALS) enables the acquisition of high-resolution digital elevation models that are used for many applications. This study combines the advantages of both ALS and OSM, offering a promising new approach that enhances data quality and allows change detection: the mainly up-to-date 2D data of OSM can be combined with the high-resolution – but rarely updated – elevation information provided by ALS. This case study investigates building objects of OSM and ALS data of the city of Bregenz, Austria. Data quality of OSM is discerned by the comparison of building footprints using different true positive definitions (e.g. overlapping area). High quality of OSM data is revealed, yet also limitations of each method with respect to heterogeneous regions and building outlines are identified. For the first time, an up-to-date Digital Surface Model (DSM) combining 2D OSM and ALS data is achieved. A multitude of applications such as flood simulations and solar potential assessments can directly benefit from this data combination, since their value and reliability strongly depend on an up-to-date DSM.     

Web-based visualization of large 3D urban building models

Adaptive rendering of large urban building models has become an important research issue in three-dimensional (3D) geographic information system (GIS) applications. This study explores a way for rendering web-based 3D urban building models. A client–server hybrid rendering approach is presented for large 3D city models, stored on a remote server through a network. The approach combines an efficient multi-hierarchical building representation with a novel image-based method, 3D image impostor generated on demand by a remote server. This approach allows transferring complex scenes progressively while keeping high visualization quality. We also evaluated the rendering and data transferring performance of the proposed approach.