Assessment of radar-based locally varying anisotropy on daily rainfall interpolation

ABSTRACT

Spatial variability of rainfall has been recognised as an important factor controlling the hydrological response of catchments. However, gauged daily rainfall data are often available at scattered locations over the catchments. This paper looks into how to capitalise on the spatial structure of radar rainfall data for improving kriging interpolation of limited gauge data over catchments at the 1-km² grid scale, using for the case study 117 gauged stations within the 128 km × 128 km region of the Mt Stapylton weather radar field (near Brisbane, Australia). Correlograms were developed using a Fast Fourier Transform method on the Gaussianised radar and gauged data. It is observed that the correlograms vary from day to day and display significant anisotropy. For the radar data, locally varying anisotropy (LVA) was examined by developing the correlogram centred on each pixel and for different radial distances. Cross-validation was carried out using the empirical correlogram tables, as well as different fitting strategies of a two-dimensional exponential distribution for both the gauged and the radar data. The results indicate that the correlograms based on the radar data outperform the gauged ones as judged by statistical measures including root mean square error, mean bias, mean absolute bias, mean standard deviation and mean inter-quartile range. While the radar data display significant LVA, it was observed that LVA did not significantly improve the estimates compared with the global anisotropy. This was also confirmed by conditional simulation of 120 rainfields using different options of correlogram development.

EDITOR M.C. Acreman; ASSOCIATE EDITOR Q. Zhang     

Spatio-temporal interpolation of precipitation during monsoon periods in Pakistan

Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space–time heterogeneity of rainfall observations make space–time estimation of precipitation a challenging task. In this paper we propose a Box–Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space–time monthly precipitation in the monsoon periods during 1974–2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space–time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method.     

Intra‐event intermittency of rainfall: an analysis of the metrics of rain and no‐rain periods

The metric or ‘observable’ properties of intra‐event rainfall intermittency (IERI) are quantified using a 10‐year record from arid Fowlers Gap, Australia. Rainfall events were delineated using the minimum inter‐event time (MIT) criterion, using eight values in the range of 1 h – 24 h. Within events, no‐rain periods were defined as corresponding to rainfall rates R < 0.1 mm/h or R < 0.2 mm/h (both less than typical wet‐canopy evaporation rates during rainfall). In this way, rainfall events were subdivided into rain and no‐rain periods. Intermittency was characterised using two measures: the fraction of rainless time within an event, and the duration of the longest rainless period. Events identified using a minimum inter‐event time (MIT) of 24 h included on average 9.4 h of contiguous no‐rain time (47.5% of the mean event duration), and only 6.8 h of contiguous rain. Total IERI averaged 51.1% for these events. Events defined with MIT = 6 h (a value commonly adopted in the literature) exhibited a mean of 1.53 h of no‐rain and 9.04 h of contiguous rain. Total IERI averaged 13.9% for these events for R < 0.1 mm/h, but reached 39.2% if no‐rain periods were taken as those of <0.2 mm/h. The maximum contiguous no‐rain period for events defined using MIT = 6 h was 10.9 h from an event of 12.6 h duration, and this represents 86.5% of the event duration. Results demonstrate that smaller, shorter, and less intense rainfall events tend to exhibit higher IERI than larger, longer, and more intense events. IERI is relevant to the understanding of land surface processes. Information on the metric properties of IERI in different rainfall types (convective and stratiform) and rainfall climates (arid, maritime, and wet tropical) may prove to have significance for diverse studies in land surface hydrology. Copyright © 2015 John Wiley & Sons, Ltd.     

Bilinear surface smoothing for spatial interpolation with optional incorporation of an explanatory variable. Part 2: Application to synthesized and rainfall data

ABSTRACT

The non-parametric mathematical framework of bilinear surface smoothing (BSS) methodology provides flexible means for spatial (two dimensional) interpolation of variables. As presented in a companion paper, interpolation is accomplished by means of fitting consecutive bilinear surface into a regression model with known break points and adjustable smoothing terms defined by means of angles formed by those bilinear surface. Additionally, the second version of the methodology (BSSE) incorporates, in an objective manner, the influence of an explanatory variable available at a considerably denser dataset. In the present study, both versions are explored and illustrated using both synthesized and real world (hydrological) data, and practical aspects of their application are discussed. Also, comparison and validation against the results of commonly used spatial interpolation methods (inverse distance weighted, spline, ordinary kriging and ordinary cokriging) are performed in the context of the real world application. In every case, the method’s efficiency to perform interpolation between data points that are interrelated in a complicated manner was confirmed. Especially during the validation procedure presented in the real world case study, BSSE yielded very good results, outperforming those of the other interpolation methods. Given the simplicity of the approach, the proposed mathematical framework’s overall performance is quite satisfactory, indicating its applicability for diverse tasks of scientific and engineering hydrology and beyond.

Editor Z. W. Kundzewicz; Associate editor A. Carsteanu     

A spatial disaggregation procedure for precipitation

Abstract

A disaggregation procedure is presented to render forecast values of precipitation from an atmospheric model with spatial resolution of 11 × 11 km suitable as input for a distributed hydrological model with spatial resolution of 1.1 × 1.1 km. Statistical and morphological properties of the input field, such as spatial mean, variance, correlation structure and intermittency, are respected in the disaggregated field. The adopted approach is a combination of interpolation and simulation. The four nodal points of the atmospheric model grid cell are used both for determining the parameters of the exponential distribution for simulating precipitation values, and in a simple interpolation procedure to determine the spatial location of the precipitation values. A shifted distribution with two parameters is used in the case of full coverage of the grid cell, and a one-parameter distribution with a theoretically derived intermittency parameter is used if intermittency is present. The results are promising with respect to the statistical and morphological properties of the disaggregated field.     

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.     

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.     

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 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.     

Spatiotemporal dynamics of aboveground primary productivity along a precipitation gradient in Chinese temperate grassland

Investigating the spatial and temporal variance in productivity along natural precipitation gradients is one of the most efficient approaches to improve understanding of how ecosystems respond to climate change. In this paper, by using the natural precipitation gradient of the Inner Mongolian Plateau from east to west determined by relatively long-term observations, we analyzed the temporal and spatial dynamics of aboveground net primary productivity (ANPP) of the temperate grasslands covering this region. Across this grassland transect, ANPP increased exponentially with the increase of mean annual precipitation (MAP) (ANPP=24.47e0.005MAP, R2=0.48). Values for the three vegetation types desert steppe, typical steppe, and meadow steppe were: 60.86 gm-2a-1, 167.14 gm-2a-1 and 288.73 gm-2a-1 respectively. By contrast, temperature had negative effects on ANPP. The moisture index (K ), which takes into ac- count both precipitation and temperature could explain the spatial variance of ANPP better than MAP alone (ANPP=2020.34K1.24, R2=0.57). Temporally, we found that the inter-annual variation in ANPP (cal- culated as the coefficient of variation, CV) got greater with the increase of aridity. However, this trend was not correlated with the inter-annual variation of precipitation. For all of the three vegetation types, ANPP had greater inter-annual variation than annual precipitation (PPT). Their difference (ANPP CV/PPT CV) was greatest in desert steppe and least in meadow steppe. Our results suggest that in more arid regions, grasslands not only have lower productivity, but also higher inter-annual variation of production. Climate change may have significant effects on the productivity through changes in precipitation pattern, vegetation growth potential, and species diversity.     

Multivariate interpolation and information entropy for optimizing raingauge network in the Mekong River Basin

ABSTRACT

The applicability of multivariate interpolation and information entropy to optimize the raingauge network in the Mekong River Basin (MRB) is investigated. Three different spatial interpolation methods are tested: inverse distance squared (IDS), ordinary kriging (OK) and gradient plus inverse distance squared (GIDS). The validated results confirm that the GIDS method outperformed IDS and OK. The application of information entropy together with GIDS on a network of 57 gauges provided the same information content (7.34 nat) as could be obtained using all 6788 gauges in the MRB. Combining this result with meteorological and hydrological indicators revealed that the number of gauges for the optimum raingauge network could be reduced to 40. The results imply good applicability of the proposed method, which may be used to help prioritize efforts and funds to maintain the raingauge network in a given river basin.     

Geostatistical interpolation of space–time rainfall on Tamshui River basin,Taiwan

Taiwan suffers from heavy storm rainfall during the typhoon season. This usually causes large river runoff, overland flow, erosion, landslides, debris flows, loss of power, etc. In order to evaluate storm impacts on the downstream basin, a real‐time hydrological modelling is used to estimate potential hazard areas. This can be used as a decision‐support system for the Emergency Response Center, National Fire Agency Ministry, to make ‘real‐time’ responses and minimize possible damage to human life and property. This study used 34 observed events from 14 telemetered rain‐gauges in the Tamshui River basin, Taiwan, to study the spatial–temporal characteristics of typhoon rainfall. In the study, regionalized theory and cross‐semi‐variograms were used to identify the spatial‐temporal structure of typhoon rainfall. The power form and parameters of the cross‐semi‐variogram were derived through analysis of the observed data. In the end, cross‐validation was used to evaluate the performance of the interpolated rainfall on the river basin. The results show the derived rainfall interpolator represents the observed events well, which indicates the rainfall interpolator can be used as a spatial‐temporal rainfall input for real‐time hydrological modelling. Copyright © 2007 John Wiley & Sons, Ltd.     

Missing precipitation data estimation using optimal proximity metric-based imputation,nearest-neighbour classification and cluster-based interpolation methods

Abstract

New optimal proximity-based imputation, K-nearest neighbour (K-NN) classification and K-means clustering methods are proposed and developed for estimation of missing daily precipitation records. Mathematical programming formulations are developed to optimize the weighting, classification and clustering schemes used in these methods. Ten different binary and real-valued distance metrics are used as proximity measures. Two climatic regions, Kentucky and Florida, (temperate and tropical) in the USA, with different gauge density and network structure, are used as case studies to evaluate the new methods. A comprehensive exercise is undertaken to compare the performances of the new methods with those of several deterministic and stochastic spatial interpolation methods. The results from these comparisons indicate that the proposed methods performed better than existing methods. Use of optimal proximity metrics as weights, spatial clustering of observation sites and classification of precipitation data resulted in improvement of missing data estimates.

Editor D. Koutsoyiannis; Associate editor C. Onof     

Spatial and temporal variations in summer precipitation in Japanese mountain areas

We examined spatial and temporal variations in precipitation measured during summer season between 1976 and 2007 for 28 stations located in mountain areas across Japan using the amount of precipitation (Pr), the mean depth of precipitation events (η), and the inverse of the mean interval times (λ). We obtained positive correlations between the period mean Pr (Pr ) and the period mean η ( ) and between Pr and the period mean λ ( ) for the 28 stations. Pr was more strongly related to than to , indicating the spatial variations in Pr that are primarily related to the variations in . In addition, Pr was more strongly related to η than to λ for most stations on the basis of data for 1976–2007, indicating that the year‐to‐year variations in Pr are primarily related to η. We also examined temporal trends in Pr, η and λ for 1976–2007 and found no systematic trends for 23 of the 28 stations, suggesting long‐term trends that are not common in mountain areas of Japan. The relationships between Pr and and between Pr and η presented in this study enable us to generate a temporal precipitation distribution pattern based on only Pr and Pr data, respectively. Furthermore, probabilistic stochastic hydrological models require precipitation characteristics as input; thus, this study contributes to the determination of hydrological cycles and their possible future changes in Japanese mountain areas and therefore to water resource management. Copyright © 2010 John Wiley & Sons, Ltd.     

基于地质统计方法与DEM的地震灾情空间插值研究

历次破坏性地震的震害调查和强震观测资料显示, 地形地貌对地震灾害有着显著的影响. 地震发生后, 为了能够及时、 准确地为地震救灾指挥提供灾情分布信息, 该文借鉴了地质统计学方法, 利用灾情速报人员上报的地震现场离散点灾情短信对灾区进行灾情空间模拟的同时, 将数学高程模型(DEM)中所包含的高程、 坡度等地形地貌信息作为影响因素引入协克里金(Co-Kriging)插值; 并以汶川M_S8.0地震灾情短信数据为例, 分别对确定性插值、 地质统计学插值结果与有无考虑坡度因素的地质统计学插值结果进行了交叉检验. 结果表明, 考虑坡度影响因素的协克里金插值在合适的模型和参数下取得了最优的灾情模拟效果. 该方法为地震应急期间进行较高精度的灾情模拟提供了一种新的可行思路.     

Consistency of precipitation products over the Arabian Peninsula and interactions with soil moisture and water storage

The regional-scale consistency between four precipitation products from the GPCC, TRMM, WM, and CMORPH datasets over the Arabian Peninsula was assessed. Their macroscale relationships were inter-compared with soil moisture and total water storage (TWS) estimates from AMSR-E and GRACE. The consistency analysis was studied with multivariate statistical hypothesis testing and Pearson correlation metrics for the period from January 2000 to December 2010. The products and GRACE estimates were assessed over a representative sub-domain (United Arab Emirates) with available in situ well observations. Next, geographically temporally weighted regression (GTWR) was employed to examine the interdependencies among the peninsula’s hydrological components. The results showed GPCC-TRMM recording the highest correlation (0.85) with insignificant mean differences over more than 90% of the peninsula. The highest GTWR predictive performance of TWS (R² = 0.84) was achieved with TRMM forcing, which indicates its potential to monitor changes in TWS over the arid peninsular region.     

分形插值地震数据重建方法研究

对分形插值方法作了较详细的探讨,给出了分形插值函数的显式表达方式,同时给出了垂直比例因子的局部显式表达式,旨在提高地震道插值重建的精度及突出局部信息,并从单道地震图的角度分析其在地震道插值重建中的应用效果.利用该方法对理论模型和济阳坳陷实际地震台站资料进行了重建处理,结果表明,分形插值重建的地震道是原始地震道的良好近似,缺失道的振幅和相位都得到了很好的恢复.该法克服了随机分形插值方法必须进行多步迭代的弱点,提高了计算效率.通过对单道地震图插值重建结果的分析,说明了本文分形插值方法具有较高的精度和较高的效率,有深入研究的潜力.本文提出的显式分形插值方法既能够突出地震道数据的局部信息,又较好地保持了地震道数据的总体变化趋势.     

A watershed rainfall data recovery approach with application to distributed hydrological models

Watershed areal rainfall estimation, which is one of the most important and fundamental aspects in hydrological forecasting and various kinds of catchment‐scale hydrological models, is widely used in the analysis of hydrological regime change, and its precision has a direct influence on the accuracy of hydrological forecasting and hydrological simulation. In China, it is difficult to obtain the watershed areal rainfall estimate with reliable precision and avoid the phenomenon of ‘the same effect of different parameters’ because of the low density of the rain gauge network. Therefore, a watershed rainfall data recovery approach of improving the precision of watershed areal rainfall estimation is proposed here. This approach is to build new observatories, establish the time–space relations of rainfall between newly built observatories and previously built observatories in a relatively short interval and then recover the rainfall data of newly built observatories prior to their construction through simulating the relations over a longer time. As a result, watershed rainfall information could be elaborated to improve the precision of watershed areal rainfall estimate and avoid the phenomenon of ‘the same effect of different parameters’ to a certain degree in the process of hydrological simulation. The approach is used in the hydrological simulation of Hali River catchment. In combination with the Soil Water Assessment Tool model, a better result can be obtained in the hydrological simulation. Therefore, the approach can be used in other similar catchments. Copyright © 2011 John Wiley & Sons, Ltd.     

Statistical approach to inverse distance interpolation

Inverse distance interpolation is a robust and widely used estimation technique. Variants of kriging are often proposed as statistical techniques with superior mathematical properties such as minimum error variance; however, the robustness and simplicity of inverse distance interpolation motivate its continued use. This paper presents an approach to integrate statistical controls such as minimum error variance into inverse distance interpolation. The optimal exponent and number of data may be calculated globally or locally. Measures of uncertainty and local smoothness may be derived from inverse distance estimates.     

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.