A two steps disaggregation method for highly seasonal monthly rainfall

 The need for high resolution rainfall data at temporal scales varying from daily to hourly or even minutes is a very important problem in hydrology. For many locations of the world, rainfall data quality is very poor and reliable measurements are only available at a coarse time resolution such as monthly. The purpose of this work is to apply a stochastic disaggregation method of monthly to daily precipitation in two steps: 1. Initialization of the daily rainfall series by using the truncated normal model as a reference distribution. 2.␣Restructuring of the series according to various time series statistics (autocorrelation function, scaling properties, seasonality) by using a Markov chain Monte Carlo based algorithm. The method was applied to a data set from a rainfall network of the central plains of Venezuela, in where rainfall is highly seasonal and data availability at a daily time scale or even higher temporal resolution is very limited. A detailed analysis was carried out to study the seasonal and spatial variability of many properties of the daily rainfall as scaling properties and autocorrelation function in order to incorporate the selected statistics and their annual cycle into an objective function to be minimized in the simulation procedure. Comparisons between the observed and simulated data suggest the adequacy of the technique in providing rainfall sequences with consistent statistical properties at a daily time scale given the monthly totals. The methodology, although highly computationally intensive, needs a moderate number of statistical properties of the daily rainfall. Regionalization of these statistical properties is an important next step for the application of this technique to regions in where daily data is not available.     

The spatial and temporal characteristics of the seasonal precipitation over India

Three extreme cases of seasonal precipitation over 31 contiguous meteorological subdivisions of India were decomposed into orthogonal components using eigenvector technique to examine their spatial and temporal behaviour. The first two eigenvectors combined were found to represent the seasonal precipitation over India to a sufficient high degree of accuracy retaining 90–95 percent of the total variance. These two components show high spatial similarity in all the three cases of the precipitation examined.The first component is characterized by a coherent variation over the area with large coherent variation over the north-east India, Central India and the west coast of India. The coefficients of the component show annual behaviour with the peak values generally reached during July. This component is representative of the summer monsoon (June–September) mode.The second component characterizes out of phase variation in precipitation between Central India, adjoining parts of the area, and peninsular India. The coefficients of the component show the semi-annual oscillation. It appears that the role of the second eigenvector might be to represent regionality of the seasonal march of the monsoon rain.     

A cluster-optimizing regression-based approach for precipitation spatial downscaling in mountainous terrain

Precipitation temporal and spatial variability often controls terrestrial hydrological processes and states. Common remote-sensing and modeling precipitation products have a spatial resolution that is often too coarse to reveal hydrologically important spatial variability. A statistical algorithm was developed for downscaling low-resolution spatial precipitation fields. This algorithm auto-searches precipitation spatial structures (rain-pixel clusters), and orographic effects on precipitation distribution without prior knowledge of atmospheric setting. It is composed of three components: rain-pixel clustering, multivariate regression, and random cascade. The only required input data for the downscaling algorithm are coarse-pixel precipitation map and a topographic map. The algorithm was demonstrated with 4 km × 4 km Next Generation Radar (NEXRAD) precipitation fields, and tested by downscaling NEXRAD-aggregated 16 km × 16 km precipitation fields to 4 km × 4 km pixel precipitation, which was then compared to the original NEXRAD data. The demonstration and testing were performed at both daily and hourly temporal resolutions for the northern New Mexico mountainous terrain and the central Texas Hill Country. The algorithm downscaled daily precipitation fields are in good agreement with the original 4 km × 4 km NEXRAD precipitation, as measured by precipitation spatial structures and the statistics between the downscaling and the original NEXRAD precipitation maps. For three daily precipitation events, downscaled precipitation map reproduces precipitation variance of the disaggregation field, and with Pearson correlation coefficients between the downscaled map and the NEXRAD map of 0.65, 0.71, and 0.80. The algorithm does not perform as well on downscaling hourly precipitation fields at the examined scale range (from 16 km to 4 km), which underestimates precipitation variance of the disaggregation field. For a scale range from 4 km to 1 km, the algorithm has potential to perform well at both daily and hourly precipitation fields, indicated from good regression performance.     

Simulation and spatio-temporal disaggregation of multi-site rainfall data for urban drainage applications

Abstract

For urban drainage and urban flood modelling applications, fine spatial and temporal rainfall resolution is required. Simulation methods are developed to overcome the problem of data limitations. Although temporal resolution higher than 10–20 minutes is not well suited for detailed rainfall—runoff modelling for urban drainage networks, in the absence of monitored data, longer time intervals can be used for master planning or similar purposes. A methodology is presented for temporal disaggregation and spatial distribution of hourly rainfall fields, tested on observations for a 10-year period at 16 raingauges in the urban catchment of Dalmuir (UK). Daily rainfall time series are simulated with a generalized linear model (GLM). Next, using a single-site disaggregation model, the daily data of the central gauge in the catchment are downscaled to an hourly time scale. This hourly pattern is then applied linearly in space to disaggregate the daily data into hourly rainfall at all sites. Finally, the spatial rainfall field is obtained using inverse distance weighting (IDW) to interpolate the data over the whole catchment. Results are satisfactory: at individual sites within the region the simulated data preserve properties that match the observed statistics to an acceptable level for practical purposes.     

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.     

Monthly spatial rainfall correlation functions and interpretations for Turkey

Abstract

Monthly spatial rainfall distribution features and their effects on spatial correlation patterns are significant in any regional study. In this paper, first a number of statistical terms and properties are explained with reference to the spatial correlation functions (SCFs). This is followed by the analysis of a theoretical spatial correlation model and its parameter estimation. Monthly empirical SCFs are examined in relation to spatial rainfall characteristics. In order to obtain a definite pattern, the SCF values are averaged in successive equal-distance groups. This average spatial correlation function shows a decreasing pattern with distance. Some interpretations of these spatial correlation functions are given for Turkey with discussion of the results obtained.     

An exploratory study of spatial annual maximum of monthly precipitation in the northern region of Portugal

Adequately analyzing and modeling the extreme rainfall events is of great importance because of the effects that their magnitude and frequency can have on human life, agricultural productivity and economic aspects, among others. A single extreme event may affect several locations, and their spatial dependence has to be appropriately taken into account. Classical geostatistics is a well-developed field for dealing with location referenced data, but it is largely based on Gaussian processes and distributions, that are not appropriate for extremes. In this paper, an exploratory study of the annual maximum of monthly precipitation recorded in the northern area of Portugal from 1941 to 2006 at 32 locations is performed. The aim of this paper is to apply max-stable processes, a natural extension of multivariate extremes to the spatial set-up, to briefly describe the models considered and to estimate the required parameters to simulate prediction maps.     

Spatial variability and interpolation of daily precipitation amount

Daily precipitation amounts show spatial variation over sub-continential regions. Point measurements, representative for regions of land, have to be interpolated towards unobserved locations. In this study four days in 1984 were selected to investigate the spatial variability of daily precipitation amount in North-western Europe in relation to the meteorological conditions. Data were interpolated using Kriging. Crossvalidation was used to compare interpolated values with measured values. Large differences in the spatial structure of daily precipitation amount are obsered as a result of different meterological conditions. Stratification of the study area into a coastal, a mountainous and an interior stratum proved to be successful, reducing the Mean Squared Error of Prediction with up to 55%.     

Spatial variability and interpolation of daily precipitation amount

Daily precipitation amounts show spatial variation over sub-continential regions. Point measurements, represntative for regions of land, have to be interpolated towards unobserved locations. In this study four days in 1984 were selected to investigate the spatial variability of daily precipitation amount in north-western Europe in relation to the meteorological conditions. Data were interpolated using kriging. Crossvalidation was used to compare interpolated values with measured values. Large differences in the spatial structure of daily precipitation amount are observed as a result of different meteorological conditions. Stratification of the study area into a coast, a mountain and an interior stratum proved to be successful, reducing the Mean Squared Error of Prediction with up to 55%.This article was inadvertently printed in SHH 6(3) 1992 without figures and figure legends. The article is being reprinted in this issue in complete form. The editor apologizes for this error in publication.     

Statistical probability distribution of snow depth at the model sub‐grid cell spatial scale

Comprehensive snow depth data, collected using georadar and hand probing, were used for statistical analyses of snow depths inside 1 km grid cells. The sub‐grid cell spatial scale was 100 m. Statistical distribution functions were found to have varying parameters, and an attempt was made to connect these statistical parameters to different terrain variables. The results showed that the two parameters mean and standard deviation of snow depth were significantly related to the sub‐grid terrain characteristics. Linear regression models could explain up to 50% of the variation for both of the snowcover parameters mentioned. Copyright © 2004 John Wiley & Sons, Ltd.     

A new magnitude category disaggregation approach for temporal high‐resolution rainfall intensities

Simulation of quick runoff components such as surface runoff and associated soil erosion requires temporal high‐resolution rainfall intensities. However, these data are often not available because such measurements are costly and time consuming. Current rainfall disaggregation methods have shortcomings, especially in generating the distribution of storm events. The objectives of this study were to improve point rainfall disaggregation using a new magnitude category rainfall disaggregation approach. The procedure is introduced using a coupled disaggregation approach (Hyetos and cascade) for multisite rainfall disaggregation. The new procedure was tested with ten long‐term precipitation data sets of central Germany using summer and winter precipitation to determine seasonal variability. Results showed that dividing the rainfall amount into four daily rainfall magnitude categories (1–10, 11–25, 26–50, >50 mm) improves the simulation of high rainfall intensity (convective rainfall). The Hyetos model category approach (Hyetos_Cat) with seasonal variation performs representative to observed hourly rainfall compared with without categories on each month. The mean absolute percentage accuracy of standard deviation for hourly rainfall is 89.7% in winter and 95.6% in summer. The proposed magnitude category method applied with the coupled Hyetos_Cat–cascade approach reproduces successfully the statistical behaviour of local 10‐min rainfall intensities in terms of intermittency as well as variability. The root mean square error performance statistics for disaggregated 10‐min rainfall depth ranges from 0.20 to 2.38 mm for summer and from 0.12 to 2.82 mm for the winter season in all categories. The coupled stochastic approach preserves the statistical self‐similarity and intermittency at each magnitude category with a relatively low computational burden. Copyright © 2014 John Wiley & Sons, Ltd.     

Improving interpolation of daily precipitation for hydrologic modelling: spatial patterns of preferred interpolators

Detailed hydrologic models require high‐resolution spatial and temporal data. This study aims at improving the spatial interpolation of daily precipitation for hydrologic models. Different parameterizations of (1) inverse distance weighted (IDW) interpolation and (2) A local weighted regression (LWR) method in which elevation is the explanatory variable and distance, elevation difference and aspect difference are weighting factors, were tested at a hilly setting in the eastern Mediterranean, using 16 years of daily data. The preferred IDW interpolation was better than the preferred LWR scheme in 27 out of 31 validation gauges (VGs) according to a criteria aimed at minimizing the absolute bias and the mean absolute error (MAE) of estimations. The choice of the IDW exponent was found to be more important than the choice of whether or not to use elevation as explanatory data in most cases. The rank of preferred interpolators in a specific VG was found to be a stable local characteristic if a sufficient number of rainy days are averaged. A spatial pattern of the preferred IDW exponents was revealed. Large exponents (3) were more effective closer to the coast line whereas small exponents (1) were more effective closer to the mountain crest. This spatial variability is consistent with previous studies that showed smaller correlation distances of daily precipitation closer to the Mediterranean coast than at the hills, attributed mainly to relatively warm sea‐surface temperature resulting in more cellular convection coastward. These results suggest that spatially variable, physically based parameterization of the distance weighting function can improve the spatial interpolation of daily precipitation. Copyright © 2009 John Wiley & Sons, Ltd.     

The spatio‐temporal variability of annual precipitation and its local impact factors during 1724–2010 in Beijing,China

Rapid population growth and increased economic activity impose an urgent challenge on the sustainability of water resources in Beijing. Understanding the spatial and temporal variability of precipitation is of the upmost importance in order to sustain the region's water resources. Two time series, one long term (1724–2010) from a single meteorological station and a shorter time series (1980–2010) from 20 different meteorological stations within the Beijing area, were analysed using Linear Regression, Moving Average, Mann–Kendall, Rescaled Range and Spatial Interpolation methods. Results from both the long‐ and short‐term meteorological data show a mean annual precipitation rate of 600 mm and 540 mm respectively. Annual precipitation rates have decreased during the 21st century by an estimated 100 mm or 16% in comparison to the 1990s. The 1980–2010 data show an increase in precipitation during the early 1990s followed by a sharp decrease during the subsequent years. The change of annual precipitation with time is more random and diverse in comparison to space. The main local impact factors (terrain, urbanization and elevation) and how they work on the local precipitation especially the spatial diversity are identified qualitatively. Generally speaking, (1) the annual precipitation of the plain area is more than that of the mountainous area (terrain effect), (2) the annual precipitation of the urban area in the plain area is obviously more than that of the surrounding suburb area (urbanization effect) and (3) the annual precipitation of the lower location is approximately more than that of the higher location (elevation effect). Copyright © 2013 John Wiley & Sons, Ltd.     

Spatial-temporal rainfall modelling for flood risk estimation

Some recent developments in the stochastic modelling of single site and spatial rainfall are summarised. Alternative single site models based on Poisson cluster processes are introduced, fitting methods are discussed, and performance is compared for representative UK hourly data. The representation of sub-hourly rainfall is discussed, and results from a temporal disaggregation scheme are presented. Extension of the Poisson process methods to spatial-temporal rainfall, using radar data, is reported. Current methods assume spatial and temporal stationarity; work in progress seeks to relax these restrictions. Unlike radar data, long sequences of daily raingauge data are commonly available, and the use of generalized linear models (GLMs) (which can represent both temporal and spatial non-stationarity) to represent the spatial structure of daily rainfall based on raingauge data is illustrated for a network in the North of England. For flood simulation, disaggregation of daily rainfall is required. A relatively simple methodology is described, in which a single site Poisson process model provides hourly sequences, conditioned on the observed or GLM-simulated daily data. As a first step, complete spatial dependence is assumed. Results from the River Lee catchment, near London, are promising. A relatively comprehensive set of methodologies is thus provided for hydrological application.     

Factors controlling spatial and seasonal distributions of precipitation δ18O in China

Utilising datasets from the Global Network of Isotopes in Precipitation of the International Atomic Energy Agency, and previous isotopic studies, we investigated δ¹⁸O spatial and temporal patterns in Chinese precipitation. Significantly positive relationships existed between precipitation δ¹⁸O and air temperature above the north of 35°N and in high altitude regions above 32°N. Significantly negative relationships between precipitation δ¹⁸O and the precipitation amount existed below south of 35°N. These temperature and precipitation effects became stronger with increasing altitude except in high altitude regions between 32°N and 35°N. The NCEP/NCAR reanalysis data from 1980 to 2004 showed that variations in spatial and seasonal wind fields at 700 hpa and total precipitable water from the ground to the top of the atmosphere were correlated with the monthly spatial distribution of precipitation δ¹⁸O. Basing on this relationship, we established quantitative correlations between the mean monthly precipitation δ¹⁸O and both latitude and temperature in different seasons. We found that spatial variations in precipitation δ¹⁸O could be described well using the Bowen–Wilkinson model and second‐order equations developed during the present study only in winter (from December to February). During the rest of the year, patterns were too complex to predict using simple models. The results suggest that it is difficult to demonstrate variations of precipitation δ¹⁸O throughout the year and for all regions of China using a single model. Moreover, the new models for the relationships among precipitation, latitude, and temperature were better able to depict the variations in precipitation δ¹⁸O than the Bowen–Wilkinson model. Copyright © 2011 John Wiley & Sons, Ltd.     

A steepness index unit volume flood hydrograph approach for sub‐daily flow disaggregation

The estimation of sub‐daily flows from daily flood flows is important for many hydrological and hydraulic applications. Flows during flood events often vary significantly within sub‐daily time‐scales, and failure to capture the sub‐daily flood characteristic can result in an underestimation of the instantaneous flood peaks, with possible risk of design failure. It is more common to find a longer record of daily flow series (observed or modelled using daily rainfall series) than sub‐daily flow data. This paper describes a novel approach, known as the steepness index unit volume flood hydrograph approach, for disaggregating daily flood flows into sub‐daily flows that takes advantage of the strong relationship between the standardized instantaneous flood peak and the standardized daily flood hydrograph rising‐limb steepness index. The strength of this relationship, which is considerably stronger than the relationship between the standardized flood peak and the event flood volume, is shown using data from six rivers flowing into the Gippsland Lakes in southeast Australia. The results indicate that the steepness index unit volume flood hydrograph approach can be used to disaggregate modelled daily flood flows satisfactorily, but its reliability is dependent on a model's ability to simulate the standardized daily flood hydrograph rising‐limb steepness index and the event flood volume. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of daily space–time precipitation series for macroscale hydrological modelling

An important problem in modelling macroscale basins, especially for sparsely observed regions, is the lack of precipitation information. Alternatives to using straightforward interpolated surface observations include the utilization of more advanced interpolation techniques and the use of additional precipitation information from atmospheric models. Conventional and geostatistical methods are applied for optimal interpolation and assimilation of observed and model precipitation. Various time-series of daily areal precipitation distributions are produced and compared using not only an internal precipitation validation, but also an objective verification based on stream flow simulations. The Mackenzie River Basin in north-western Canada is used as the study area and hydrological simulations are carried out with the model SLURP. It was found that better interpolation techniques and the use of combined precipitation data can improve the hydrological simulations and that the enhancements are related to the relative size of the simulation units used. © 1998 John Wiley & Sons, Ltd.     

Spatiotemporal characteristics of precipitation and extreme events on the Loess Plateau of China between 1957 and 2009

Spatiotemporal trends in precipitation may influence vegetation restoration, and extreme precipitation events profoundly affect soil erosion processes on the Loess Plateau. Daily data collected at 89 meteorological stations in the area between 1957 and 2009 were used to analyze the spatiotemporal trends of precipitation on the Loess Plateau and the return periods of different types of precipitation events classified in the study. Nonparametric methods were employed for temporal analysis, and the Kriging interpolation method was employed for spatial analysis. The results indicate a small decrease in precipitation over the Loess Plateau in last 53 years (although a Mann–Kendall test did not show this decrease to be significant), a southward shift in precipitation isohyets, a slightly delayed rainy season, and prolonged return periods, especially for rainstorm and heavy rainstorm events. Regional responses to global climate change have varied greatly. A slightly increasing trend in precipitation in annual and sub‐annual series, with no obvious shift of isohyets, and an evident decreasing trend in extreme precipitation events were detected in the northwest. In the southeast, correspondingly, a more seriously decreasing trend occurred, with clear shifts of isohyets and a slightly decreasing trend in extreme precipitation events. The result suggests that a negative trend in annual precipitation may have led to decreased soil erosion but an increase in sediment yield during several extreme events. These changes in the precipitation over the Loess Plateau should be noted, and countermeasures should be taken to reduce their adverse impacts on the sustainable development of the region. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of zero measurements on the spatial correlation structure of rainfall

In this study, the effect of zero measurements on the spatial correlation function of rainfall is analyzed for the quantification of a rainfall field. The use of a bivariate mixed distribution function made it possible to analyze and compare the spatial correlation functions for these three different data sets: only the positive measurements at both gauge locations, positive measurements at either one or both gauge locations, and all measurements including zero at both locations. As an example, the spatial correlation functions are derived for the Geum River Basin, Korea and evaluated for the wet and dry seasons, respectively. Results show that the effect of zero measurements on spatial correlation structures is significant during the wet season, when the inter-station correlations were estimated significantly lower than those during the dry season. It was also found that only the case considering positive measurements are valid for the quantification of rainfall field. Even during the wet season, the inter-station correlation coefficients derived by considering the zero measurements show their high variability along with many abnormally looking high estimates, which made the quantification of the spatial correlation function become very ambiguous.     

An approach for the determination of precipitation input for worst-case flood modelling

ABSTRACT

There is a lack of suitable methods for creating precipitation scenarios that can be used to realistically estimate peak discharges with very low probabilities. On the one hand, existing methods are methodically questionable when it comes to physical system boundaries. On the other hand, the spatio-temporal representativeness of precipitation patterns as system input is limited. In response, this paper proposes a method of deriving spatio-temporal precipitation patterns and presents a step towards making methodically correct estimations of infrequent floods by using a worst-case approach. A Monte Carlo approach allows for the generation of a wide range of different spatio-temporal distributions of an extreme precipitation event that can be tested with a rainfall–runoff model that generates a hydrograph for each of these distributions. Out of these numerous hydrographs and their corresponding peak discharges, the physically plausible spatio-temporal distributions that lead to the highest peak discharges are identified and can eventually be used for further investigations.

Editor A. Castellarin; Associate editor E. Volpi