Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records

Abstract

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naïve approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to those obtained from all the other spatial interpolation methods tested in this study.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Teegavarapu, R.S.V., 2012. Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records. Hydrological Sciences Journal, 57 (3), 383–406.     

Simulated precipitation fields with variance-consistent interpolation

Abstract

Gridded meteorological data are available for all of Norway as time series dating from 1961. A new way of interpolating precipitation in space from observed values is proposed. Based on the criteria that interpolated precipitation fields in space should be consistent with observed spatial statistics, such as spatial mean, variance and intermittency, spatial fields of precipitation are simulated from a gamma distribution with parameters determined from observed data, adjusted for intermittency. The simulated data are distributed in space, using the spatial pattern derived from kriging. The proposed method is compared to indicator kriging and to the current methodology used for producing gridded precipitation data. Cross-validation gave similar results for the three methods with respect to RMSE, temporal mean and standard deviation, whereas a comparison on estimated spatial variance showed that the new method has a near perfect agreement with observations. Indicator kriging underestimated the spatial variance by 60–80% and the current method produced a significant scatter in its estimates.

Citation Skaugen, T. & Andersen, J. (2010) Simulated precipitation fields with variance-consistent interpolation. Hydrol. Sci. J. 55(5), 676–686.     

Statistical corrections of spatially interpolated missing precipitation data estimates

Spatial interpolation methods used for estimation of missing precipitation data generally under and overestimate the high and low extremes, respectively. This is a major limitation that plagues all spatial interpolation methods as observations from different sites are used in local or global variants of these methods for estimation of missing data. This study proposes bias‐correction methods similar to those used in climate change studies for correcting missing precipitation estimates provided by an optimal spatial interpolation method. The methods are applied to post‐interpolation estimates using quantile mapping, a variant of equi‐distant quantile matching and a new optimal single best estimator (SBE) scheme. The SBE is developed using a mixed‐integer nonlinear programming formulation. K‐fold cross validation of estimation and correction methods is carried out using 15 rain gauges in a temperate climatic region of the U.S. Exhaustive evaluation of bias‐corrected estimates is carried out using several statistical, error, performance and skill score measures. The differences among the bias‐correction methods, the effectiveness of the methods and their limitations are examined. The bias‐correction method based on a variant of equi‐distant quantile matching is recommended. Post‐interpolation bias corrections have preserved the site‐specific summary statistics with minor changes in the magnitudes of error and performance measures. The changes were found to be statistically insignificant based on parametric and nonparametric hypothesis tests. The correction methods provided improved skill scores with minimal changes in magnitudes of several extreme precipitation indices. The bias corrections of estimated data also brought site‐specific serial autocorrelations at different lags and transition states (dry‐to‐dry, dry‐to‐wet, wet‐to‐wet and wet‐to‐dry) close to those from the observed series. Bias corrections of missing data estimates provide better serially complete precipitation time series useful for climate change and variability studies in comparison to uncorrected filled data series. Copyright © 2013 John Wiley & Sons, Ltd.     

Combining regression and spatial proximity for catchment model regionalization: a comparative study

Abstract

Spatial error regression is employed to regionalize the parameters of a rainfall–runoff model. The approach combines regression on physiographic watershed characteristics with a spatial proximity technique that describes the spatial dependence of model parameters. The methodology is tested for the monthly abcd model at a network of gauges in southeast United States and compared against simpler regression and spatial proximity approaches. Unlike other comparative regionalization studies that only evaluate the skill of regionalized streamflow predictions in ungauged catchments, this study also examines the fit between regionalized parameters and their optimal (i.e. calibrated) values. Interestingly, the spatial error model produces parameter estimates that better resemble the optimal parameters than either of the simpler methods, but the spatial proximity method still yields better hydrologic simulations. The analysis suggests that the superior streamflow predictions of spatial proximity result from its ability to better preserve correlations between compensatory hydrological parameters.

Editor D. Koutsoyiannis; Associate editor Y. Gyasi-Agyei     

Sensitivity of regionalized transfer-function noise models to the input and parameter transfer method / Sensibilité de modèles de type fonction de transfert bruit régionalisée (FTBR) aux données d'entrée et aux méthodes de transfert de paramètres

Abstract

Monthly shallow water-table depths can be predicted from climate forcings on a large scale by the combination of a transfer-function noise (TFN) model with a parameter regionalization scheme. To investigate the sensitivity of regionalized transfer-function noise (RTFN) models, simulations with different input series and parameter regionalization methods, combined with topographic external drifts, are presented. The input series include the precipitation, precipitation surplus or infiltration calculated by the variable infiltration capacity (VIC) land surface model, and the regionalization methods include those based on a combination of the principal component analysis (PCA) classification or Gaussian mixture model (GMM) clustering, with the external drifts, such as the elevation or terrain slope, generated from digital elevation models (DEM). Verification and cross-validation show that the infiltration series reduces the errors for regionalization by 12.5–18.8%, but cannot improve the calibration. The PCA method outperforms its alternative GMM method for the input series and the external drifts. The combination of the infiltration series and the regionalization method based on PCA classification and elevation produces the best results with respect to the mean absolute error and root mean squared error. The spatial and temporal variations of water-table depths at a macro-scale in continental China are predicted by the combination.     

Analysis of hydrological seasonality across northern catchments using monthly precipitation–runoff polygon metrics

Abstract

Seasonality is an important hydrological signature for catchment comparison. Here, the relevance of monthly precipitation–runoff polygons (defined as scatter points of 12 monthly average precipitation–runoff value pairs connected in the chronological monthly sequence) for characterizing seasonality patterns was investigated to describe the hydrological behaviour of 10 catchments spanning a climatic gradient across the northern temperate region. Specifically, the research objectives were to: (a) discuss the extent to which monthly precipitation–runoff polygons can be used to infer active hydrological processes in contrasting catchments; (b) test the ability of quantitative metrics describing the shape, orientation and surface area of monthly precipitation–runoff polygons to discriminate between different seasonality patterns; and (c) examine the value of precipitation–runoff polygons as a basis for catchment grouping and comparison. This study showed that some polygon metrics were as effective as monthly average runoff coefficients for illustrating differences between the 10 catchments. The use of precipitation–runoff polygons was especially helpful to look at the dynamics prevailing in specific months and better assess the coupling between precipitation and runoff and their relative degree of seasonality. This polygon methodology, linked with a range of quantitative metrics, could therefore provide a new simple tool for understanding and comparing seasonality among catchments.

Editor Z.W. Kundzewicz; Associate editor K. Heal

Citation Ali, G., Tetzlaff, D., Kruitbos, L., Soulsby, C., Carey, S., McDonnell, J., Buttle, J., Laudon, H., Seibert, J., McGuire, K., and Shanley, J., 2013. Analysis of hydrological seasonality across northern catchments using monthly precipitation–runoff polygon metrics. Hydrological Sciences Journal, 59 (1), 56–72.     

Delineation of precipitation regions in two Canadian study areas: the role of the temporal resolution of the precipitation data

The identification of homogeneous precipitation regions has value in many water resources engineering applications (infrastructure planning, design, operations; climate forecasting, modelling). The objective of this paper is to assess the sensitivity of precipitation regions to the temporal resolution (monthly, seasonal, annual and the annual maximum series) of the data. The presented method uses the fuzzy c-means clustering algorithm to partition climate sites into statistically homogeneous precipitation regions. The regions are validated using an approach based on L-moment statistics. The method is conducted in two climatically different study areas in western and eastern Canada. There does not appear to be a relationship between the spatial distributions of the regions formed using different temporal resolutions of the precipitation data. It is recommended to delineate precipitation regions that are specific to the task at hand, and to select a temporal resolution that is consistent with the final application of the regional precipitation dataset.

EDITOR A. Castellarin; ASSOCIATE EDITOR T. Kjeldsen     

Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application

Abstract

The present research study investigates the application of nonlinear normalizing data transformations in conjunction with ordinary kriging (OK) for the accurate prediction of groundwater level spatial variability in a sparsely-gauged basin. We investigate three established normalizing methods, Gaussian anamorphosis, trans-Gaussian kriging and the Box-Cox method to improve the estimation accuracy. The first two are applied for the first time to groundwater level data. All three methods improve the mean absolute prediction error compared to the application of OK to the non-transformed data. In addition, a modified Box-Cox transformation is proposed and applied to normalize the hydraulic heads. The modified Box-Cox transformation in conjunction with OK is found to be the optimal spatial model based on leave-one-out cross-validation. The recently established Spartan semivariogram family provides the optimal model fit to the transformed data. Finally, we present maps of the groundwater level and the kriging variance based on the optimal spatial model.

Editor D. Koutsoyiannis; Associate editor A. Montanari

Citation Varouchakis, E.A., Hristopoulos, D.T., and Karatzas, G.P., 2012. Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application. Hydrological Sciences Journal, 57 (7), 1404–1419.     

Classification of natural flow regimes in Iran to support environmental flow management

Abstract

Development of environmental flow standards at the regional scale has been proposed as a means to manage the influence of hydrological alterations on riverine ecosystems in view of the rapid pace of global water resources management. Flow regime classification forms a critical part in such environmental flow assessments. We present a national-scale classification of hydrological regimes for Iran based on a set of hydrological metrics. It describes ecologically relevant characteristics of the natural hydrological regime derived from 15- to 47-year-long records of daily mean discharge data for 539 streamgauges within a 47-year period. The classification was undertaken using a fuzzy partitional method within Bayesian mixture modelling. The analysis resulted in 12 classes of distinctive flow regime types that differ in various hydrological aspects. This classification is being used for further research in regional-scale environmental flow studies in Iran.

Editor D. Koutsoyiannis     

Characterizing and classifying urban watersheds with compositional and structural attributes

Current land-use classifications used to assess urbanization effects on stream water quality date back to the 1980s when limited information was available to characterize watershed attributes that mediate non-point source pollution. With high resolution remote sensing and widely used GIS tools, there has been a vast increase in the availability and precision of geospatial data of built environments. In this study, we leverage geospatial data to expand the characterization of developed landscapes and create a typology that allows us to better understand the impact of complex developed landscapes across the rural to urban gradient. We assess the ability of the developed landscape typology to reveal patterns in stream water chemistry previously undetected by traditional land-cover based classification. We examine the distribution of land-cover, infrastructure, topography and geology across 3876 National Hydrography Dataset Plus catchments in the Piedmont region of North Carolina, USA. From this dataset, we generate metrics to evaluate the abundance, density and position of landscape features relative to streams, catchment outlets and topographic wetness metrics. While impervious surfaces are a key distinguishing feature of the urban landscape, sanitary infrastructure, population density and geology are better predictors of baseflow stream water chemistry. Unsupervised clustering was used to generate a distinct developed landscape typology based on the expanded, high-resolution landscape feature information. Using stream chemistry data from 37 developed headwater catchments, we compared the baseflow water chemistry grouped by traditional land-cover based classes of urbanization (rural, low, medium and high density) to our composition and structure-based classification (a nine-class typology). The typology based on 22 metrics of developed landscape composition and structure explained over 50% of the variation in NO₃⁻-N, TDN, DOC, Cl⁻, and Br⁻ concentration, while the ISC-based classification only significantly explained 23% of the variation in TDN. These results demonstrate the importance of infrastructure, population and geology in defining developed landscapes and improving discrete classes for water management.     

Rainfall screening methodology using TRMM data over a river basin

ABSTRACT

A regionalized rain/no-rain classification (RNC) based on scattering index methodology is developed for detecting rainfall signatures over the land regions of the Mahanadi basin (India), using data products from the passive and active sensors onboard the Tropical Rainfall Measuring Mission (TRMM), namely the TRMM Microwave Imager (TMI) and Precipitation Radar (PR). The proposed model, developed using data for two years from the orbital database, was validated using PR and in-situ data for selected case study events in 2011 and 2012. Performance evaluation of the model is discussed using 10 metrics derived from the contingency table. Overall, the results show superior performance, with an average probability of detection of 0.83, bias of 1.10 and odds ratio skill score greater than 0.93. Accurate rainfall detection is obtained for 95% of case study events. The relative performance of the proposed model is dependent on rainfall type, but it should be useful in rainfall retrieval algorithms for current missions such as the Global Precipitation Measurement Mission.

Editor M.C. Acreman; Associate editor Y. Gyasi-Agyei     

Exploration of optimal time steps for daily precipitation bias correction: a case study using a single grid of RCM on the River Exe in southwest England

ABSTRACT

Bias correction is a necessary post-processing procedure in order to use regional climate model (RCM)-simulated local climate variables as the input data for hydrological models due to systematic errors of RCMs. Most of the present bias-correction methods adjust statistical properties between observed and simulated data based on a predefined duration (e.g. a month or a season). However, there is a lack of analysis of the optimal period for bias correction. This study attempted to address the question whether there is an optimal number for bias-correction groups (i.e. optimal bias-correction period). To explore this we used a catchment in southwest England with the regional climate model HadRM3 precipitation data. The proposed methodology used only one grid of RCM in the Exe catchment, one emissions scenario (A1B) and one member (Q0) among 11 members of HadRM3. We tried 13 different bias-correction periods from 3-day to 360-day (i.e. the whole of one year) correction using the quantile mapping method. After the bias correction a low pass filter was used to remove the high frequencies (i.e. noise) followed by estimating Akaike’s information criterion. For the case study catchment with the regional climate model HadRM3 precipitation, the results showed that a bias-correction period of about 8 days is the best. We hope this preliminary study on the optimum number bias-correction period for daily RCM precipitation will stimulate more research to improve the methodology with different climatic conditions. Future efforts on several unsolved problems have been suggested, such as how strong the filter should be and the impact of the number of bias correction groups on river flow simulations.

Editor M.C. Acreman Associate editor S. Kanae     

Assessing impervious area ratios of grid-based land-use classifications on the example of an urban watershed

ABSTRACT

When applying a distributed hydrological model in urban watersheds, grid-based land-use classification data with 10 m resolution are typically used in Japan. For urban hydrological models, the estimation of the impervious area ratio (IAR) of each land-use classification is a crucial factor for accurate runoff analysis. In order to assess the IAR accurately, we created a set of vector-based “urban landscape GIS delineation” data for a typical urban watershed in Tokyo. By superimposing the vector-based delineation map on the grid-based map, the IAR of each grid-based land-use classification was estimated, after calculating the IARs of all grid cells in the entire urban watershed. As a result, we were able to calculate the frequency distribution of IAR for each land-use classification, as well as the spatial distribution of IARs for the urban watershed. It is evident from the results that the reference values of IAR for the land-use classifications were estimated very roughly and inherited errors of between about 7% and 70%, which corresponds to more than 100 mm increase of direct runoff for the 1500 mm annual average precipitation.

Editor D. Koutsoyiannis; Guest editor E. Volpi     

Spatial patterns of homogeneous pooling groups for flood frequency analysis

Abstract

Several methods for the exploration and modelling of spatial point patterns are introduced to study the spatial patterns of homogeneous pooling groups for flood frequency analysis. The study is based on selected catchments in Great Britain, where a high density of gauging stations has been established. Initial pooling groups are formed using the K-means clustering algorithm with appropriately selected similarity measures. The pooling groups are subsequently revised to improve the homogeneity in the hydrological response. Spatial patterns of the initial and final pooling groups are explored in terms of intensity and dependence of the spatial distribution of the catchments. A test against a spatial point process is used to confirm or reject the initial impression of spatial clustering. Changes in the spatial patterns from the initial to the final pooling groups are examined using two comparison methods. The spatial pattern analysis described above can be used to answer the following questions: whether homogeneous catchments tend to exist in the vicinity of each other; whether the improvement in homogeneity tends to form more clustered pooling groups; and how the spatial patterns observed can be used to direct the selection of pooling variables.     

Regional precipitation and temperature scenarios for climate change

Abstract

To investigate the consequences of climate change on the water budget in small catchments, it is necessary to know the change of local precipitation and temperature. General Circulation Models (GCM) cannot provide regional climate parameters yet, because of their coarse resolution and imprecise modelling of precipitation. Therefore downscaling of precipitation and temperature has to be carried out from the GCM grids to a small scale of a few square kilometres. Daily rainfall and temperature are modelled as processes conditioned on atmospheric circulation. Rainfall is linked to the circulation patterns (CPs) using conditional probabilities and conditional rainfall amount distribution. Both temperature and precipitation are downscaled to several locations simultaneously taking into account the CP dependent spatial correlation. Temperature is modelled using a simple autoregressive approach, conditioned on atmospheric circulation and local areal precipitation. The model uses the classification scheme of the German Weather Service and a fuzzy rule-based classification. It was applied in the Aller catchment for validation using observed rainfall and temperature, and observed classified geopotential pressure heights. GCM scenarios of the ECHAM model were used to make climate change predictions (using classified GCM geopotential heights); simulated values agree fairly well with historical data. Results for different GCM scenarios are shown.     

Dam safety: an evaluation of some procedures for design flood estimation

Abstract

This paper analyses a number of aspects related to the estimation of the design flood for a dam. A new approach to the estimation of the probable maximum precipitation (PMP) is described which takes advantage of the spatial variability of precipitation by using radar-derived distributed rainfall measurements. Procedures which utilize storm transposition and storm maximization are introduced to estimate the probable maximum flood (PMF) and are compared with regionalized statistical methods based upon the Wakeby and generalized extreme value distributions.     

Water quality monitoring at a virtual watershed monitoring station using a modified deep extreme learning machine

ABSTRACT

A new deep extreme learning machine (ELM) model is developed to predict water temperature and conductivity at a virtual monitoring station. Based on previous research, a modified ELM auto-encoder is developed to extract more robust invariance among the water quality data. A weighted ELM that takes seasonal variation as the basis of weighting is used to predict the actual value of water quality parameters at sites which only have historical data and no longer generate new data. The performance of the proposed model is validated against the monthly data from eight monitoring stations on the Zengwen River, Taiwan (2002–2017). Based on root mean square error, mean absolute error, mean absolute percentage error and correlation coefficient, the experimental results show that the new model is better than the other classical spatial interpolation methods.     

Determining Spatially-Distributed Annual Water Balances for Ungauged Locations on Shikoku Island,Japan: A Comparison of Two Interpolators/Détermination de Bilans Hydriques Spatialisés pour des Sites Non-Jaugés de L'Īle de Shikoku,au Japon: Comparaison de Deux Interpolateurs

Abstract

Methods were evaluated for interpolating precipitation (P), evapotranspiration (ET), and runoff (RO) at ungauged points on Shikoku Island, Japan, using data gathered from gauged stations on the same island. Two methods were examined: a “local” cubic spline interpolator, which, for a given point, fitted the function exactly to nearby gauged data points; and a “global” multivariate regression interpolator, which fitted the function to all gauged data points based on their topographic positions (i.e. latitude, longitude, altitude). Local and global interpolators did not generate similar results for P and temperature (T). The spatial density of gauged data points used in the interpolation affected the performance of the interpolators. With any given density of gauged data points included in the interpolation, the local interpolator outperformed the global interpolator. The findings indicate that local interpolators are more accurate predictors of the spatial distribution of water balance components in mountainous regions such as Shikoku Island.     

Assessment of flow–ecology relationships for environmental flow standards: a synthesis focused on the southeast USA

ABSTRACT

Environmental flow standards are a management tool that can help to protect the ecosystem services sustained by rivers. Although environmental flow requirements can be assessed using a variety of methods, most of these methods require establishing relationships between flow and habitat of species of concern. Here, we conducted a synthesis of past flow–ecology studies in the southeast USA. For each state or interstate river basin, we used the published data to determine the flow metrics that resulted in the greatest changes in ecological metrics, and the ecological metrics that were most sensitive to hydrologic alteration. The flow metrics that were most important in preserving ecological metrics were high-flow duration and frequency, 3-day maximum and minimum, and number of reversals. The ecological metrics most sensitive to hydrologic alteration were mostly related to presence or absence of key indicator species.