A multivariate geostatistical technique is presented to address two key issues of trend detection and network evaluation of acid deposition data. The proposed technique is specifically designed to be compatible with the distinctive characteristics of acid deposition variables such as non-stationary of their spatial means, non-stationary of their spatial covariances, their complex periodic and non-periodic temporal trends, and the common imbalance between the availability of their spatial and temporal data. To accomplish this, the time series at each measurement point is viewed as a separate, but correlated one-dimensional regionalized variable. Each variable is assumed to be a sum of periodic (e.g. seasonal) and non-periodic (e.g. anthropogenic) temporal random variables, each characterized by its own temporal variogram. To obtain an initial estimate of the frequency of the involved periodic trends, direct quadratic spectrum estimation is conducted. Based on fitted direct and cross variograms, various forms of estimation such as co-kriging of non-periodic components can be performed. The estimated time series may then be tested for the presence of long-term trends. In addition, the fitted sill values of any variogram model at different stations form elements of a coregionalization matrix. This matrix may be regarded as the variance-covariance matrix for the particular temporal-trend scale presented by the variogram model. A coregionalization matrix can be used to generate a spatial correlogram. Viewing the estimated integral scale of each spatial correlogram as an indicator of the radius of information-influence of each measurement station, a monitoring network can be evaluated for its adequacy of coverage at different temporal-trend scales. A coregionalization matrix can also be decomposed through principal-component analysis in order to determine any potential spatial groupings and/or to generate regional indicators of changes at different temporal scales.
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Review of Geostatistics in Geohydrology. I: Basic Concepts
Author: ASCE Task Committee on Geostatistical Techniques in Geohydrology of the Ground Water Hydrology Committee of the ASCE Hydraulics Division | Size: 1.5 MB | Format:PDF | Quality:Unspecified | Publisher: J. Hydraul. Eng(ASCE) | Year: 2007 | pages: 612–632 | ISBN: --
Geostatistics offers a variety of tools that can be used in ground‐water estimation problems, including interpolation, integration, and differentiation. This paper introduces the basic concepts of geostatistics and its proposed linear and nonlinear estimation (kriging) techniques. These techniques view a regionalized variable as one of many possible outcomes of a random function. The spatial variability of the natural phenomenon is characterized by covariance or semivariogram functions, which are the central elements in the estimation techniques, known as simple kriging, ordinary kriging, universal kriging, log‐kriging, disjunctive kriging, and indicator kriging. The paper also discusses techniques that have been developed to infer the statistical structure of the variables of interest.
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Review of Geostatistics in Geohydrology. II: Applications
Author: The ASCE Task Committee on Geostatistical Techniques in Geohydrology of the Ground Water Hydrology Committee of the ASCE Hydraulics Division | Size: 1.8 MB | Format:PDF | Quality:Unspecified | Publisher: Journal of Hydraulic Engineering(ASCE) | Year: 2007 | pages: 633–658 | ISBN: --
Geostatistical techniques are useful tools for analyzing the inherent uncertainties of ground‐water systems. These procedures have been applied to a variety of estimation problems in geohydrology. This paper reviews these applications in five major categories, including: (1) Mapping of ground‐water variables, incorporation of relevant information, and space‐time mapping; (2) conditional and unconditional simulations of geohydrological fields; (3) cointerpolation of groundwater variables using the flow equations, and numerical and analytical approaches to estimate cross and direct covariances of these variables based on ground‐water‐flow equations; (4) global and local sampling designs; and (5) geostatistical ground‐water‐management studies. The paper also includes a comprehensive list of geostatistical and related publications in geohydrology.
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Progress in the design of hydrologic-data networks
Author: M. E. Moss; G. D. Tasker | Size: 872 KB | Format:PDF | Quality:Unspecified | Publisher: American Geophysical Union | Year: 1979 | pages: 1298-1306 | ISBN: --
The design of hydrologic-data networks is a topic that previously has not been raised to the status of a separate article in the U.S. National Reports to the International Union of Geodesy and Geophysics. However, three articles (Matalas, 1975; Peck, 1975; Schwarz, 1975) in the 1970–1974 Report considered it significant enough to be included as specific sections. Thus, because of the novelty of this article, some references will be made to work performed prior to the report period of 1975–1978 for the sake of completeness.
The collection of hydrologie data has been perceived as a design problem only within the past few decades. Although some earlier work had been done in the area of precipitation gaging networks, Langbein (1954) presented the first comprehensive description of what needed to be done to manage objectively a hydrologic-data program.
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A simple approach for improving spatial interpolation of rainfall using ANN
Author: C. Sivapragasam; V. M. Arun; D. Giridhar | Size: 450 KB | Format:PDF | Quality:Unspecified | Publisher: Meteorology and Atmospheric Physics(Springer) | Year: 2010 | pages: 1-7 | ISBN: --
Interpolation of hydrological variables such as rainfall, ground water level, etc. is necessary to arrive at many engineering decisions. This study suggests an innovative and yet simple idea to effectively interpolate the rainfall at non-sampling locations using artificial neural network (ANN). The method has been demonstrated in the Tamirabarani basin of Tamil Nadu State (India), where rain gauge information for 18 rain gauge stations is available. With the help of land use map of the basin and also the proximity of rain gauge stations to each other in the neighbourhood, the most appropriate input variables for ANN are designed and used for training ANN to estimate rainfall in the unknown stations. It is also interesting to note that with appropriate selection of input variables for training ANN, one of the major lacunae of ANN (to have sufficiently lengthy training records) can be suitably addressed. ANN results are compared with Kriging method. Further, the proposed method is applied to improve the prediction of inflow to Ramanadhi reservoir in Tamirabarani basin, and the results seem to be very encouraging.
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Aspects of spatial and temporal rainfall variability and rainfall analysis in relation to some water management problems are surveyed and discussed. It is concluded that relevant modelling of hydrological processes in which the rainfall is a driving force is vital with respect to possibilities of finding solutions to increasing environmental problems following urbanization and industrialization. However, modern computer methods and our knowledge of the spatial and dynamic properties of rainfall fields are seldom used in practical engineering applications. This causes errors and uncertainties in the calculated output. Bridging the gaps between researchers and engineers may overcome some of these problems. It is also argued that experimental studies in a variety of climates and physiographical conditions using an interdisciplinary approach are needed in order to further investigate the scale and dynamics of spatial rainfall variability.
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Author: Phaedon C. Kyriakidis; André G. Journel | Size: 217 KB | Format:PDF | Quality:Unspecified | Publisher: Mathematical Geology(Springer) | Year: 1999 | pages: 651-684 | ISBN: --
Geostatistical space–time models are used increasingly for addressing environmental problems, such as monitoring acid deposition or global warming, and forecasting precipitation or stream flow. Each discipline approaches the problem of joint space–time modeling from its own perspective, a fact leading to a significant amount of overlapping models and, possibly, confusion. This paper attempts an annotated survey of models proposed in the literature, stating contributions and pinpointing shortcomings. Stochastic models that extend spatial statistics (geostatistics) to include the additional time dimension are presented with a common notation to facilitate comparison. Two conceptual viewpoints are distinguished: (1) approaches involving a single spatiotemporal random function model, and (2) approaches involving vectors of space random functions or vectors of time series. Links between these two viewpoints are then revealed; advantages and shortcomings are highlighted. Inference from space–time data is revisited, and assessment of joint space–time uncertainty via stochastic imaging is suggested.
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This paper presents the results of the interpolation of annual precipitation over a regular grid performed in Aragón (Spain). The main objective was the quantification of the improvement in estimation uncertainty by including elevation in the interpolation and by using base 10 logarithms of both annual precipitation and elevation versus the original values.
Long-term annual precipitation (APRE) was available at 182 weather stations. Elevation above sea level (ELEV) was available at those stations and at 1913 additional points over a regular 5 km grid. The spatial variability of APRE, ELEV and their base 10 logarithms (LAPRE and LELEV, respectively), and the spatial correlation between APRE and ELEV, APRE and LELEV, LAPRE and ELEV, and LAPRE and LELEV were described by gaussian direct- and cross-semivariogram models with nugget effects.
Geostatistical interpolation methods, ordinary kriging and cokriging, were used to estimate APRE and LAPRE at the 1913 additional elevation points. Estimates of LAPRE were transformed back to APRE values. Cokriging estimates were in general higher than kriging ones, mainly at points of high elevation. The average percent difference among cokriging and kriging estimates was 9–12%. Cokriging estimates obtained with the different sample data sets were in general terms similar. However, at points of high elevation, cokriging with ELEV as the auxiliary variable seemed to overestimate annual precipitation.
Estimation error standard deviations (EESD) also were computed in each interpolation point. For all points, the EESD obtained using LAPRE values were lower than those obtained using APRE values, being the average percent differences of −38 to −42%. Likewise, for all interpolation points, cokriging EESD were lower than kriging ones. Using LAPRE and LELEV values, the average percent difference among cokriging and kriging EESD was −11.0%, with minimum and maximum percent differences of −6.7 and −35.8%, respectively.
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Precipitation is a key factor in the water cycle. At the same time, precipitation is the focus of study in meteorology and climatology, ecological environmental assessment, non-point source pollution and so on. Understanding the temporal-spatial variation and the corresponding factors of precipitation has become the object of hydrology and environmentology. Based on the annual precipitation data, we analyzed the spatial distribution of precipitation in Sichuan Province in China as well as the temporal-spatial variation and the corresponding influence factors involved. The results show that the amount of precipitation was abundant, but the spatial distribution was not consistent with it and the amount of precipitation gradually declined from the south-east to the north-west in Sichuan Province, China. Moreover, the spatial distribution was different throughout the years. The result of correlation analysis indicated that elevation, temperature and air pressure were three key factors affecting the amount and distribution of precipitation, and the correlation coefficients were −0.56, 0.38 and 0.45 respectively. Notably, the relationship between the slope of topography and precipitation were significantly negative and the average correlation coefficient was −0.28.
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A geostatistical approach for areal rainfall statistics assessment
Author: Th. Lebel; J. P. Laborde | Size: 865 KB | Format:PDF | Quality:Unspecified | Publisher: Stochastic Hydrology and Hydraulics(Springer) | Year: 1988 | pages: 245-261 | ISBN: --
Areal rainfall statistics are more relevant in flood hydrology and water resources management than point rainfall statistics when it comes to help designing dams or hydraulic structures. This paper presents a geostatistically based method to derive the areal statistics from point statistics. Assuming that the distribution models of point rainfall and areal belong to the same class of models and that the rainfall process is stationary, it is shown how the parameters of the areal distribution model can directly be computed from the parameters of the point distribution models in case of a non stationary process, an approximation is derived that yielded good results when applied to a mountainous region in Southern France. The method also allows the computation of the areal reduction factors in a very general form.
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Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data
Author: A. Azimi-Zonooz; W. F. Krajewski; D. S. Bowles; D. J. Seo | Size: 1 MB | Format:PDF | Quality:Unspecified | Publisher: Stochastic Hydrol.Hydraul (springer) | pages: 51-67 | ISBN: --
The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures
that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4x4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.
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