Topological Kriging Research Articles

Geospatial tools effectively estimate nonexceedance probabilities of daily streamflow at ungauged and intermittently gauged locations in Ohio

Study regionThe state of Ohio in the United States, a humid, continental climate. Study focusThe estimation of nonexceedance probabilities of daily streamflows as an alternative means of establishing the relative magnitudes of streamflows associated with hydrologic and water-quality observations. New hydrological insights for the regionSeveral methods for estimating nonexceedance probabilities of daily mean streamflows are explored, including single-index methodologies (nearest-neighboring index) and geospatial tools (kriging and topological kriging). These methods were evaluated by conducting leave-one-out cross-validations based on analyses of nearly 7 years of daily streamflow data from 79 unregulated streamgages in Ohio and neighboring states. The pooled, ordinary kriging model, with a median Nash–Sutcliffe performance of 0.87, was superior to the single-site index methods, though there was some bias in the tails of the probability distribution. Incorporating network structure through topological kriging did not improve performance. The pooled, ordinary kriging model was applied to 118 locations without systematic streamgaging across Ohio where instantaneous streamflow measurements had been made concurrent with water-quality sampling on at least 3 separate days. Spearman rank correlations between estimated nonexceedance probabilities and measured streamflows were high, with a median value of 0.76. In consideration of application, the degree of regulation in a set of sample sites helped to specify the streamgages required to implement kriging approaches successfully.

Spatial prediction of water quality variables along a main river channel, in presence of pollution hotspots

In order to treat and evaluate the available data of water quality and fully exploit monitoring results (e.g. characterize regional patterns, optimize monitoring networks, infer conditions at unmonitored locations, etc.), it is crucial to develop improved and efficient methodologies. Accordingly, estimation of water quality along fluvial ecosystems is a frequent task in environment studies. In this work, a particular case of this problem is examined, namely, the estimation of water quality along a main stem of a large basin (where most anthropic activity takes place), from observational data measured along this river channel. We adapted topological kriging to this case, where each watershed contains all the watersheds of the upstream observed data (“nested support effect”). Data analysis was additionally extended by taking into account the upstream distance to the closest contamination hotspot as an external drift. We propose choosing the best estimation method by cross-validation. The methodological approach in spatial variability modeling may be used for optimizing the water quality monitoring of a given watercourse. The methodology presented is applied to 28 water quality variables measured along the Santiago River in Western Mexico.

Combining streamflow observations and hydrologic simulations for the retrospective estimation of daily streamflow for ungauged rivers in southern Quebec (Canada)

Retrospective estimation of daily streamflow for all rivers within a territory is of practical interest for sustainable and optimal water management. This implies, however, the availability of methods for providing accurate estimations of flow for ungauged rivers. This study compares the potential of statistical interpolation (SI)—a simple data assimilation technique that combines observations and simulations from hydrological modelling—with four other approaches: nearest neighbour, direct use of outputs from hydrological modelling, ordinary and topological kriging. Through subsampling cross-validation analyses based on the modified Kling-Gupta efficiency indicator, we show that SI compares favourably with these other approaches. While the performance of other methods depends on the configuration of the ungauged site in regards to the neighbouring reference sites, SI is less affected by these configurations. SI outperforms the other approaches particularly where the ungauged site is relatively distant from observation sites. In these cases, SI performance depends on the performance of the background model that relies on simulations of hydrological processes forced by precipitation and temperature observations. Our findings offer the potential for heightened performance estimates through an improvement of hydrological modelling and the use of more complex assimilation techniques for exploiting the model.

Ordinary kriging as a tool to estimate historical daily streamflow records

Abstract. Efficient and responsible management of water resources relies on accurate streamflow records. However, many watersheds are ungaged, limiting the ability to assess and understand local hydrology. Several tools have been developed to alleviate this data scarcity, but few provide continuous daily streamflow records at individual streamgages within an entire region. Building on the history of hydrologic mapping, ordinary kriging was extended to predict daily streamflow time series on a regional basis. Pooling parameters to estimate a single, time-invariant characterization of spatial semivariance structure is shown to produce accurate reproduction of streamflow. This approach is contrasted with a time-varying series of variograms, representing the temporal evolution and behavior of the spatial semivariance structure. Furthermore, the ordinary kriging approach is shown to produce more accurate time series than more common, single-index hydrologic transfers. A comparison between topological kriging and ordinary kriging is less definitive, showing the ordinary kriging approach to be significantly inferior in terms of Nash–Sutcliffe model efficiencies while maintaining significantly superior performance measured by root mean squared errors. Given the similarity of performance and the computational efficiency of ordinary kriging, it is concluded that ordinary kriging is useful for first-order approximation of daily streamflow time series in ungaged watersheds.

Regional prediction of basin-scale brown trout habitat suitability

Abstract. In this study we propose a novel method for the estimation of ecological indices describing the habitat suitability of brown trout (Salmo trutta). Traditional hydrological tools are coupled with an innovative regional geostatistical technique, aiming at the prediction of the brown trout habitat suitability index where partial or totally ungauged conditions occur. Several methods for the assessment of ecological indices are already proposed in the scientific literature, but the possibility of exploiting a geostatistical prediction model, such as Topological Kriging, has never been investigated before. In order to develop a regional habitat suitability model we use the habitat suitability curve, obtained from measured data of brown trout adult individuals collected in several river basins across the USA. The Top-kriging prediction model is then employed to assess the spatial correlation between upstream and downstream habitat suitability indices. The study area is the Metauro River basin, located in the central part of Italy (Marche region), for which both water depth and streamflow data were collected. The present analysis focuses on discharge values corresponding to the 0.1-, 0.5-, 0.9-empirical quantiles derived from flow-duration curves available for seven gauging stations located within the study area, for which three different suitability indices (i.e. ψ10, ψ50 and ψ90) are evaluated. The results of this preliminary analysis are encouraging showing Nash-Sutcliffe efficiencies equal to 0.52, 0.65, and 0.69, respectively.

Topological and canonical kriging for design flood prediction in ungauged catchments: an improvement over a traditional regional regression approach?

Abstract. In the United States, estimation of flood frequency quantiles at ungauged locations has been largely based on regional regression techniques that relate measurable catchment descriptors to flood quantiles. More recently, spatial interpolation techniques of point data have been shown to be effective for predicting streamflow statistics (i.e., flood flows and low-flow indices) in ungauged catchments. Literature reports successful applications of two techniques, canonical kriging, CK (or physiographical-space-based interpolation, PSBI), and topological kriging, TK (or top-kriging). CK performs the spatial interpolation of the streamflow statistic of interest in the two-dimensional space of catchment descriptors. TK predicts the streamflow statistic along river networks taking both the catchment area and nested nature of catchments into account. It is of interest to understand how these spatial interpolation methods compare with generalized least squares (GLS) regression, one of the most common approaches to estimate flood quantiles at ungauged locations. By means of a leave-one-out cross-validation procedure, the performance of CK and TK was compared to GLS regression equations developed for the prediction of 10, 50, 100 and 500 yr floods for 61 streamgauges in the southeast United States. TK substantially outperforms GLS and CK for the study area, particularly for large catchments. The performance of TK over GLS highlights an important distinction between the treatments of spatial correlation when using regression-based or spatial interpolation methods to estimate flood quantiles at ungauged locations. The analysis also shows that coupling TK with CK slightly improves the performance of TK; however, the improvement is marginal when compared to the improvement in performance over GLS.

Smooth regional estimation of low-flow indices: physiographical space based interpolation and top-kriging

Abstract. Recent studies highlight that spatial interpolation techniques of point data can be effectively applied to the problem of regionalization of hydrometric information. This study compares two innovative interpolation techniques for the prediction of low-flows in ungauged basins. The first one, named Physiographical-Space Based Interpolation (PSBI), performs the spatial interpolation of the desired streamflow index (e.g., annual streamflow, low-flow index, flood quantile, etc.) in the space of catchment descriptors. The second technique, named Topological kriging or Top-kriging, predicts the variable of interest along river networks taking both the area and nested nature of catchments into account. PSBI and Top-kriging are applied for the regionalization of Q355 (i.e., a low-flow index that indicates the streamflow that is equalled or exceeded 355 days in a year, on average) over a broad geographical region in central Italy, which contains 51 gauged catchments. The two techniques are cross-validated through a leave-one-out procedure at all available gauges and applied to a subregion to produce a continuous estimation of Q355 along the river network extracted from a 90m elevation model. The results of the study show that Top-kriging and PSBI present complementary features. Top-kriging outperforms PSBI at larger river branches while PSBI outperforms Top-kriging for headwater catchments. Overall, they have comparable performances (Nash-Sutcliffe efficiencies in cross-validation of 0.89 and 0.83, respectively). Both techniques provide plausible and accurate predictions of Q355 in ungauged basins and represent promising opportunities for regionalization of low-flows.

Spatiotemporal topological kriging of runoff time series

This paper proposes a geostatistical method for estimating runoff time series in ungauged catchments. The method conceptualizes catchments as space‐time filters and exploits the space‐time correlations of runoff along the stream network topology. We hence term the method topological kriging or top kriging. It accounts for hydrodynamic and geomorphologic dispersion as well as routing and estimates runoff as a weighted average of the observed runoff in neighboring catchments. Top kriging is tested by cross validation on 10 years of hourly runoff data from 376 catchments in Austria and separately for a subset of these data, the Innviertel region. The median Nash‐Sutcliffe efficiency of hourly runoff in the Innviertel region is 0.87 but decreases to 0.75 for the entire data set. For a subset of 208 catchments, the median efficiency of daily runoff estimated by top kriging is 0.87 as compared to 0.67 for estimates of a deterministic runoff model that uses regionalized model parameters. The much better performance of top kriging is because it avoids rainfall data errors and avoids the parameter identifiability issues of traditional runoff models. The analyses indicate that the kriging variance can be used for identifying catchments with potentially poor estimates. The Innviertel region is used to examine the kriging weights for nested and nonnested catchments and to compare various variants of top kriging. The spatial kriging variant generally performs better than the more complex spatiotemporal kriging and spatiotemporal cokriging variants. It is argued that top kriging may be preferable to deterministic runoff models for estimating runoff time series in ungauged catchments, provided stream gauge density is high and there is no need to account for causal rainfall‐runoff processes. Potential applications include the estimation of flow duration curves in a region and near–real time mapping of runoff.

Top-kriging - geostatistics on stream networks

Abstract. We present Top-kriging, or topological kriging, as a method for estimating streamflow-related variables in ungauged catchments. It takes both the area and the nested nature of catchments into account. The main appeal of the method is that it is a best linear unbiased estimator (BLUE) adapted for the case of stream networks without any additional assumptions. The concept is built on the work of Sauquet et al. (2000) and extends it in a number of ways. We test the method for the case of the specific 100-year flood for two Austrian regions. The method provides more plausible and, indeed, more accurate estimates than Ordinary Kriging. For the variable of interest, Top-kriging also provides estimates of the uncertainty. On the main stream the estimated uncertainties are smallest and they gradually increase as one moves towards the headwaters. The method as presented here is able to exploit the information contained in short records by accounting for the uncertainty of each gauge. We suggest that Top-kriging can be used for spatially interpolating a range of streamflow-related variables including mean annual discharge, flood characteristics, low flow characteristics, concentrations, turbidity and stream temperature.