Prediction In Ungauged Catchments Research Articles

Evaluation of regionalization parameters for stream flow prediction in ungauged catchments of Rift Valley Lakes Basin, Ethiopia

Evaluation of regionalization parameters for stream flow prediction in ungauged catchments of Rift Valley Lakes Basin, Ethiopia

Optimal Postprocessing Strategies With LSTM for Global Streamflow Prediction in Ungauged Basins

AbstractStreamflow prediction in ungauged basins (PUB) is challenging, and Long Short‐Term Memory (LSTM) is widely used to for such predictions, owing to its excellent migration performance. Traditional LSTM forced by meteorological data and catchment attribute data barely highlight the optimum data integration strategy for LSTM and its migration from data‐rich basins to ungauged ones. In this study, we experimented with 1,897 global catchments and found that LSTM‐corrected Global Hydrological Models (GHMs) outperformed uncorrected GHMs, improving the median Nash‐Sutcliff efficiency (NSE) from 0.03 to 0.66. Notably, there was a large gap between traditional LSTM modeling in ungauged basins and autoregressive modeling in data‐rich basins, and GHM‐forced LSTM were an effective way to close this gap in ungauged basins. The spatial heterogeneity of the performance of GHM‐forced LSTM was mainly influenced by three metrics (dryness, the leaf area index and latitude), which described the hydrological similarity among catchments. Weaker hydrological similarity among continental catchments results in larger variability in GHM‐forced LSTM, with the best performance in Siberia (NSE, 0.54) and the worst in North America (NSE, 0.10). However, the migration performance of GHM‐forced LSTM was significantly improved (NSE, 0.63) in ungauged basins when hydrological similarity was considered. This study stressed the advantages of GHM‐forced LSTM and due significance should be attached to hydrological similarities among catchments to improve hydrological prediction in ungauged catchments.

Streamflow prediction in ungauged catchments by using the Grunsky method

Establish a reliable rainfall-runoff relation capable of predicting runoff in ungauged basins is a matter of interest across the world for a long time and has been taking importance during the past decades. Regionalization approaches, hydrological models and machine learning techniques have been used to estimate runoff. However, returning some simplicity to the predictions might be necessary for practical uses. In this paper, we re-introduce C. E. Grunsky approach, developed in the early 1900s to predict runoff from values of precipitation on a two-equations system. Here, we analyze the Grunsky generalized method applied for 716 Brazilian catchments, on an interannual and monthly scales. First, we established the best method to find the rainfall-runoff relation coefficient for each catchment. Then, we evaluate the performance of the method on a local scale, i.e., catchment by catchment. Lastly, we analyze the method of regionalization, by grouping the catchments into six hydrologically similar classes. For local scale, the Kling-Gupta Efficiency (KGE) values range from 0.87 to 0.93 on the interannual scale and is greater than 0.50 on the monthly scale. For the regionalized approach, KGE varies from 0.60 to 0.84 on an interannual scale. We also found suitable KGE values on a monthly scale, with more than 22% of catchments with KGE greater than 0.50, being the best performances in the Non-seasonal and Extremely-wet groups, and the worst performance in the Dry group. Our findings indicate that Grunsky approach is suitable to predict streamflow for Brazilian catchments on interannual and monthly scales. This simple and easy-to-use equation presents a reliable alternative to more complex methods to compute runoff by only using rainfall data.

Sediment load estimation using a novel regionalization sediment-response similarity method for ungauged catchments

The development and application of reliable hydrological models are challenging in ungauged or poorly gauged catchments. Although several regionalization methods have been developed for predicting hydrological variables in ungauged catchments, a large uncertainty usually exists in the prediction because previous methods typically depended on several static catchment attributes or long-term mean climatic descriptors, thereby neglecting the spatiotemporal variability of the climate. In this study, we propose a new regionalization method called sediment-response similarity (SRS) using the soil and water assessment tool model and self-organizing maps to estimate sediment load in ungauged catchments, considering spatiotemporal variability and the sediment load relation to rainfall characteristics of individual catchments. The performance of SRS was evaluated by comparing it against the conventional regionalization method (i.e., physical similarity) and calibration model results, in four gauged catchments of the lower Mekong River basin. The SRS method showed improved performance over the conventional approach in estimating sediment loads, with an average Nash-Sutcliffe efficiency (NSE) and coefficient of determination (R2) of 0.75 and 0.76, respectively, which were close to the respective values of NSE and R2 = 0.77, of the calibration model. Additionally, the SRS approach showed an error reduction of up to 7 %, compared with that of the physical similarity method, indicating the potential of the proposed regionalization method in estimating catchment-wide sediment load in ungauged catchments. The findings indicate that the SRS method ideally determines the similarity of sediment loads between gauged and ungauged catchments. The SRS approach effectively tackled the main challenge of selecting catchment attributes in the conventional regionalization method and minimizing the uncertainty of sediment prediction in ungauged catchments. This novel SRS method is a promising method for estimating, not only sediment load, but also other hydrological variables and rainfall-driven phenomena in the ungauged catchments globally.

Continuous streamflow prediction in ungauged basins: long short-term memory neural networks clearly outperform traditional hydrological models

Abstract. This study investigates the ability of long short-term memory (LSTM) neural networks to perform streamflow prediction at ungauged basins. A set of state-of-the-art, hydrological model-dependent regionalization methods are applied to 148 catchments in northeast North America and compared to an LSTM model that uses the exact same available data as the hydrological models. While conceptual model-based methods attempt to derive parameterizations at ungauged sites from other similar or nearby catchments, the LSTM model uses all available data in the region to maximize the information content and increase its robustness. Furthermore, by design, the LSTM does not require explicit definition of hydrological processes and derives its own structure from the provided data. The LSTM networks were able to clearly outperform the hydrological models in a leave-one-out cross-validation regionalization setting on most catchments in the study area, with the LSTM model outperforming the hydrological models in 93 % to 97 % of catchments depending on the hydrological model. Furthermore, for up to 78 % of the catchments, the LSTM model was able to predict streamflow more accurately on pseudo-ungauged catchments than hydrological models calibrated on the target data, showing that the LSTM model's structure was better suited to convert the meteorological data and geophysical descriptors into streamflow than the hydrological models even calibrated to those sites in these cases. Furthermore, the LSTM model robustness was tested by varying its hyperparameters, and still outperformed hydrological models in regionalization in almost all cases. Overall, LSTM networks have the potential to change the regionalization research landscape by providing clear improvement pathways over traditional methods in the field of streamflow prediction in ungauged catchments.

Generalization of an Encoder-Decoder LSTM model for flood prediction in ungauged catchments

Flood prediction in ungauged catchments is usually conducted by hydrological models that are parameterized based on nearby and similar gauged catchments. As an alternative to this process-based modelling, deep learning (DL) models have demonstrated their ability for prediction in ungauged catchments (PUB) with high efficiency. Catchment characteristics, the number of gauged catchments, and their level of hydroclimatic heterogeneity in the training dataset used for model regionalization can directly affect the model’s performance. Here, we study the generalization ability of a DL model to these factors by applying an Encoder-Decoder Long Short-Term Memory neural network for a 6-hour lead-time runoff prediction in 35 mountainous catchments in China. By varying the available number of catchments and model settings with different training datasets, namely local, regional, and PUB models, we evaluated the generalization ability of our model. We found that both quantity (i.e. number of gauged catchments available) and heterogeneity of the training dataset used for the DL model are important for improving model performance in the PUB context, due to a data synergy effect. The assessment of the sensitivity to catchment characteristics showed that the model performance is mainly correlated to the local hydro-climatic conditions; the more arid the region, the more likely it is to have a poor model performance for prediction in ungauged catchments. The results suggest that the regional ED-LSTM model is a promising method to predict streamflow from rainfall inputs in PUB, and outline the need for preparing a representative training dataset.

A two-step calibration framework for hydrological parameter regionalization based on streamflow and remote sensing evapotranspiration

• We proposed a two-step calibration based parameter regionalization method. • This method combines spatial proximity method and RS ET based parameter calibration method. • The proposed regionalization method achieves the overall best model performance. • The accuracy of RS ET is the main factor affecting the performance of the proposed method. Runoff prediction in ungauged catchments is an important and challenging research topic in the field of hydrology. However, traditional parameter regionalization methods may not be applicable in regions with sparsely distributed hydrological stations. Remote sensing (RS) evapotranspiration (ET) products provide valuable information for model parameter estimations. This study aimed to improve the accuracy of hydrological modeling in ungauged catchments by combining the traditional spatial proximity (SP) method with the RS ET-based parameter calibration method to form a two-step calibration-based regionalization method (SP-bcET method using bias-corrected RS ET data and SP-rawET method using raw RS ET data). The proposed regionalization scheme is demonstrated by using the variable infiltration capacity model in the Yangtze River Basin, China, and its performance was evaluated and compared with the SP method and two RS ET-based parameter calibration schemes (bcET method using bias-corrected RS ET data and rawET method using raw RS ET data). The results indicate that the bcET method performs better than the rawET method, the SP method outperforms the RS ET-based parameter calibration method, and the SP-bcET and SP-rawET methods achieve the best overall performance among the five methods. Taking the simulated streamflow at a daily scale in the calibration period as an example, the average Nash-Sutcliffe coefficient of efficiency for the SP, bcET, rawET, SP-bcET, and SP-rawET methods were 0.69, 0.61, 0.56, 0.71, and 0.71, respectively. Moreover, the SP-bcET and SP-rawET methods improved the simulation of the temporal dynamics and spatial variability of soil moisture anomalies. The accuracy of the RS ET data was one of the most dominant factors affecting the performance of the proposed parameter regionalization scheme. The SP-bcET method is expected to perform better than the SP method in warmer catchments or when gauged catchments are sparely distributed. The findings demonstrate the great potential of combining the traditional parameter regionalization and RS ET-based parameter calibration methods in hydrological simulations in ungauged catchments.

Regionalization for Ungauged Catchments — Lessons Learned From a Comparative Large‐Sample Study

AbstractModel parameter values for ungauged catchments can be regionalized from hydrologically similar gauged catchments. Achieving reliable and robust predictions in ungauged catchments by regionalization, however, is still a major challenge. Here, we conduct a comparative assessment of 19 regionalization approaches based on previously published literature to contribute new insights into their performance in different geographic regions. The approaches use geographical information, physical catchment attributes, hydrological signatures, or a combination thereof to select donor catchments and to subsequently transfer their entire parameter sets to the ungauged receiver catchment. Each regionalization approach was tested in a leave‐one‐out cross‐validation with a bucket‐type catchment model (the HBV model) using 671 gauged catchments in the United States with a diverse hydroclimatology. We then evaluated regionalization performance for several hydrograph aspects, compared it against calibration and regionalization benchmarks, and linked it to catchment descriptors. The results of this large‐sample regionalization study can be summarized in three major lessons: (a) Catchments can benefit from a well‐chosen regionalization approach independent of their geographic region and independent of how well they can be modeled or regionalized at best. (b) Almost perfect donors exist for most catchments and an excellent relative model performance can be reached for most catchments with current regionalization approaches. This implies that there is considerable potential for improvement in the prediction in ungauged catchments. (c) The ranking of regionalization approaches depends on how the predicted hydrographs are evaluated. These findings indicate that a multi‐criteria evaluation is essential for a robust assessment of regionalization performance.

A Canberra distance-based complex network classification framework using lumped catchment characteristics

Hydrological prediction in ungauged catchments remains a challenge despite numerous attempts in the past. The well-known solution to this challenge is transfer of information from gauged catchments to ‘hydrologically-similar’ ungauged catchments, an approach known as ‘regionalization.’ The basis of regionalization is, thus, classification of catchments into hydrologically-similar groups. A major limitation of the traditional classification methods, such as the K-means clustering algorithm, is that they are not very suitable when the classes are not well separated from each other. Additionally, they cannot determine the number of classes in a dataset automatically. To overcome these limitations, some recent studies have used complex networks-based classification algorithms, widely known as community structure algorithms, for catchment classification. However, such studies have applied the community structure algorithms only to time series of hydrological variables (e.g. streamflow) and have not so far used lumped information (e.g. mean rainfall and mean slope). In this short communication, we propose a Canberra distance-based metric that can enable a community structure algorithm to exploit lumped information. For demonstration, the proposed metric is used to compute link weights for the multilevel modularity optimization algorithm. The proposed classification method is applied to lumped data from 494 basins situated in the CONtiguous United States (CONUS) for their classification, and its performance is compared with that of the K-means clustering algorithm. By and large, the proposed classification framework opens up an alternative avenue towards prediction in ungauged catchments.

A Novel Fuzzy Random Forest Model for Meteorological Drought Classification and Prediction in Ungauged Catchments

This paper presents a new tree-based model, namely Fuzzy Random Forest (FRF), for one month ahead Standardized Precipitation Evapotranspiration Index (SPEI) classification and prediction with a noteworthy application in ungauged catchments. The proposed FRF model uses global SPEI dataset as the meteorological drought quantifier and applies a fuzzy inference system to extract fuzzified and crisp SPEI values for an ungauged catchment. The evolved crisp series is then transformed into the polynomial label vector of extremely wet, wet, near normal, dry, and extremely dry categories. In the end, the state-of-the-art random forest algorithm was used to classify and predict the label vector using the lagged SPEI series of the selected global grid points. To demonstrate the development and verification process of the FRF model, the global SPEI-6 values for the period of 1961–2015 were retrieved from four global grid points around the Central Antalya Basin, Turkey. The new model was trained and validated using 70% and 30% of the data sets, respectively. The performance of the new model was examined in terms of total accuracy, misclassification, and Kappa statistics and cross-validated with the fuzzy decision tree model developed as the benchmark in this study. The results showed the promising performance of the FRF for drought classification and prediction with outstanding efficiency for extremely wet and dry events classification. According to the Kappa statistic, the proposed FRF model is 25% more accurate than the benchmark FDT model.

Hydrological signatures describing the translation of climate seasonality into streamflow seasonality

Abstract. Seasonality is ubiquitous in nature, and it is closely linked to water quality, ecology, hydrological extremes, and water resources management. Hydrological signatures aim at extracting information about certain aspects of hydrological behaviour. Commonly used seasonal hydro-climatological signatures consider climate or streamflow seasonality, but they do not consider how climate seasonality translates into streamflow seasonality. In order to analyse the translation of seasonal climate input (precipitation minus potential evapotranspiration) into seasonal catchment output (streamflow), we represent the two time series by their seasonal (annual) Fourier mode, i.e. by sine waves. A catchment alters the input sine wave by reducing its amplitude and by shifting its phase. We propose to use these quantities, the amplitude ratio and the phase shift, as seasonal hydrological signatures. We present analytical solutions describing the response of linear reservoirs to periodic forcing to interpret the seasonal signatures in terms of configurations of linear reservoirs. Using data from the UK and the US, we show that the seasonal signatures exhibit hydrologically interpretable patterns and that they are a function of both climate and catchment attributes. Wet, rather impermeable catchments hardly attenuate the seasonal climate input. Drier catchments, especially if underlain by a productive aquifer, strongly attenuate the input sine wave leading to phase shifts up to several months. As an example application, we test whether two commonly used hydrological models (Identification of unit Hydrographs and Component flows from Rainfall, Evaporation and Streamflow – IHACRES; modèle du Génie Rural à 4 paramètres Journalier – GR4J) can reproduce the observed ranges of seasonal signatures in the UK. The results show that the seasonal signatures have the potential to be useful for catchment classification, predictions in ungauged catchments, and model building and evaluation. The use of potential evapotranspiration in the input restricts the applicability of the signatures to energy-limited (humid) catchments.

Can Remotely Sensed Actual Evapotranspiration Facilitate Hydrological Prediction in Ungauged Regions Without Runoff Calibration?

AbstractRunoff prediction in ungauged catchments is a significant hydrological challenge. The common approach is to calibrate hydrological models against streamflow data from gauged catchments, and then regionalize or transfer parameter values from the gauged calibration to predict runoff in the ungauged catchments. This paper explores the potential for using parameter values from hydrological models calibrated solely against readily available remotely sensed evapotranspiration data to estimate runoff time series. The advantage of this approach is that it does not require observed streamflow data for model calibration and is therefore particularly useful for runoff prediction in poorly gauged or ungauged regions. The modeling experiments are carried out using data from 222 catchments across Australia. The results from the remotely sensed evapotranspiration runoff‐free calibration are encouraging, particularly in simulating monthly runoff and mean annual runoff in the wetter catchments. However, results for daily runoff and in the drier regions are relatively poor, and further developments are needed to realize the benefit of direct model calibration against remotely sensed data to predict runoff in ungauged catchments.

Flow Prediction in Ungauged Catchments Using Probabilistic Random Forests Regionalization and New Statistical Adequacy Tests

AbstractFlow prediction in ungauged catchments is a major unresolved challenge in scientific and engineering hydrology. This study attacks the prediction in ungauged catchment problem by exploiting advances in flow index selection and regionalization in Bayesian inference and by developing new statistical tests of model performance in ungauged catchments. First, an extensive set of available flow indices is reduced using principal component (PC) analysis to a compact orthogonal set of “flow index PCs.” These flow index PCs are regionalized under minimal assumptions using random forests regression augmented with a residual error model and used to condition hydrological model parameters using a Bayesian scheme. Second, “adequacy” tests are proposed to evaluate a priori the hydrological and regionalization model performance in the space of flow index PCs. The proposed regionalization approach is applied to 92 northern Spain catchments, with 16 catchments treated as ungauged. It is shown that (1) a small number of PCs capture approximately 87% of variability in the flow indices and (2) adequacy tests with respect to regionalized information are indicative of (but do not guarantee) the ability of a hydrological model to predict flow time series and are hence proposed as a prerequisite for flow prediction in ungauged catchments. The adequacy tests identify the regionalization of flow index PCs as adequate in 12 of 16 catchments but the hydrological model as adequate in only 1 of 16 catchments. Hence, a focus on improving hydrological model structure and input data (the effects of which are not disaggregated in this work) is recommended.

Evaluation of an instantaneous dryness index-based calibration-free continuous hydrological model in India

AbstractTraditional continuous hydrological models have a large number of free parameters whose values need to be determined through calibration, and thus their applicability is limited to gauged basins. For prediction in ungauged catchments, hydrologists generally follow regionalization methods to develop region-specific calibration-free continuous models. An alternative attempt was made recently to develop a calibration-free model by proposing an empirically derived universal ‘decay function’ that enables definition of instantaneous dryness index as a function of antecedent rainfall and solar energy. The model was earlier tested in the USA, and its performance was found to be comparable to that shown by regionalization-based models. Here, we test the instantaneous dryness index-based calibration-free model considering data from 108 Indian catchments. The medians of coefficient of determination (R2), Nash–Sutcliffe efficiency (NSE) and Kling–Gupta efficiency (KGE) values for the study catchments, respectively, are 0.50, 0.38 and 0.40. Furthermore, the model's performance significantly improved upon Box–Cox transformation (RBC2, NSEBC and KGEBC, respectively, are 0.70, 0.52 and 0.57), suggesting that the model predicts discharge quite well except during flood periods. Overall, our results suggest the model can be used as an alternative platform for predicting discharge in ungauged catchments in the USA and peninsular India, if not in every part of the world.

Runoff prediction in ungauged catchments in Norway: comparison of regionalization approaches

Abstract Runoff prediction in ungauged catchments has been a challenging topic over recent decades. Much research have been conducted including the intensive studies of the PUB (Prediction in Ungauged Basins) Decade of the International Association for Hydrological Science. Great progress has been made in the field of regionalization study of hydrological models; however, there is no clear conclusion yet about the applicability of various methods in different regions and for different models. This study made a comprehensive assessment of the strengths and limitations of existing regionalization methods in predicting ungauged stream flows in the high latitudes, large climate and geographically diverse, seasonally snow-covered mountainous catchments of Norway. The regionalization methods were evaluated using the water balance model – WASMOD (Water And Snow balance MODeling system) on 118 independent catchments in Norway, and the results show that: (1) distance-based similarity approaches (spatial proximity, physical similarity) performed better than regression-based approaches; (2) one of the combination approaches (combining spatial proximity and physical similarity methods) could slightly improve the simulation; and (3) classifying the catchments into homogeneous groups did not improve the simulations in ungauged catchments in our study region. This study contributes to the theoretical understanding and development of regionalization methods.

Catchment Morphing (CM): A Novel Approach for Runoff Modeling in Ungauged Catchments

AbstractRunoff prediction in ungauged catchments has been one of the major challenges in the past decades. However, due to the tremendous heterogeneity of the catchments, obstacles exist in deducing model parameters for ungauged catchments from gauged ones. We propose a novel approach to predict ungauged runoff with Catchment Morphing (CM) using a fully distributed model. CM is defined as by changing the catchment characteristics (area and slope here) from the baseline model built with a gauged catchment to model the ungauged ones. As a proof of concept, a case study on seven catchments in the UK has been used to demonstrate the proposed scheme. Comparing the predicted with measured runoff, the Nash‐Sutcliffe efficiency (NSE) varies from 0.03 to 0.69 in six catchments. Moreover, NSEs are significantly improved (up to 0.81) when considering the discrepancy of percentage runoff between the target and baseline catchments. A distinct advantage has been experienced by comparing the CM with a traditional method for ungauged catchments. The advantages are: (a) less demand of the similarity between the baseline catchment and the ungauged catchment, (b) less demand of available data, and (c) potentially widely applicable in varied catchments. This study demonstrates the feasibility of the proposed scheme as a potentially powerful alternative to the conventional methods in runoff predictions of ungauged catchments. Clearly, more work beyond this pilot study is needed to explore and develop this new approach further to maturity by the hydrological community.

Exploring hydrologically similar catchments in terms of the physical characteristics of upstream regions

Abstract Catchment classification strategies based on easily available physical characteristics are important for extrapolating hydrologic model parameters and improving hydrologic predictions in ungauged catchments. In this study, we conduct an experiment of catchment classification and explore the feasibility of characterizing hydrologically similar catchments using certain physical characteristics in upstream regions of the Huai River Basin. The similarity metrics of hydrologic response factors (high flow, low flow and average annual runoff) and physical factors (topography, shape, soil and vegetation) are fed into the K-means algorithm for catchment classification. All the catchments are classified into two classes regardless of the types of metrics used. By comparing the overlap coefficient (η) and Rand index (RI) between any two classification results, we found that the topography classification displays the highest concordance with the high flow classification (η = 79.2% and RI = 0.66) among all metrics. Including more metrics would not produce consistently better classification results. The optimal combination of metrics, with η = 87.5%, is the high flow metrics (Q10%, SFH and MAX90) with the topography metrics (AS and HI). The results indicate that the physical metrics adopted for hydrologic classification should be determined carefully in terms of specific hydrologic characteristics.

Process‐based hydrological modelling: The potential of a bottom‐up approach for runoff predictions in ungauged catchments

AbstractConceptual rainfall–runoff models are a valuable tool for predictions in ungauged catchments. However, most of them rely on calibration to determine parameter values. Improving the representation of runoff processes in models is an attractive alternative to calibration. Such an approach requires a straightforward, a priori parameter allocation procedure applicable on a wide range of spatial scales. However, such a procedure has not been developed yet.In this paper, we introduce a process‐based runoff generation module (RGM‐PRO) as a spin‐off of the traditional runoff generation module of the PREVAH hydrological modelling system. RGM‐PRO is able to exploit information from maps of runoff types, which are developed on the basis of field investigations and expert knowledge. It is grid based, and within each grid cell, the process heterogeneity is considered to avoid information loss due to grid resolution. The new module is event based, and initial conditions are assimilated and downscaled from continuous simulations of PREVAH, which are also available for real‐time applications. Four parameter allocation strategies were developed, on the basis of the results of sprinkling experiments on 60‐m2 hillslope plots at several grassland locations in Switzerland, and were tested on five catchments on the Swiss Plateau and Prealps. For the same catchments, simulation results obtained with the best parameter allocation strategy were compared with those obtained with different configurations of the traditional runoff generation module of PREVAH, which was also applied as an event‐based module here. These configurations include a version that avoids calibration, one that transfers calibrated parameters, and one that uses regionalised parameter values.RGM‐PRO simulated heavy events in a more realistic way than the uncalibrated traditional runoff generation module of PREVAH, and, in some instances, it even exceeded the performance of the calibrated traditional one. The use of information on the spatial distribution of runoff types additionally proved to be valuable as a regionalisation technique and showed advantages over the other regionalisation approaches, also in terms of robustness and transferability.

Runoff prediction in ungauged catchments using the gamma dimensionless time-area method

Time-area (TA), which constitutes the basis for rainfall-runoff transformation in the Clark model, is conventionally derived from the tedious procedure of delineating isochrones. In the present study, by combining the Nash instantaneous unit hydrograph (IUH), in terms of the gamma function, and the Clark model, a new TA relationship (TAR) is introduced. This equation involves the Nash models’ parameters (i.e., the number of reservoirs, n, and the storage coefficient, k). Considering that n = 5 for ungauged catchments, the following equation for estimating k was obtained: k = t c /4.24, with t c being the time of concentration of the catchment. Finally, a gamma time-area (GTA) function was derived for estimating the time-area diagram (TAD) of catchments. The TADs derived from the GTA function were compared to the GIS-based TADs and those derived from the US Army Corps of Engineers (USACE) method and the kinematic wave (KW) model in four catchments, namely, Kasilian, Ajay, Jafarabad, and Shourandika. In the Kasilian catchment, the direct runoff hydrograph (DRH) was simulated using the Clark model based on the GTA and USACE methods and compared with the observed hydrographs. Results indicate that the coefficient of efficiency (CE) in the Kasilian catchment for the two methods is approximately 0.8, while the errors in the peak discharge prediction are 9 and 11.2% in the GTA and USACE methods, respectively.

Accounting for dependencies in regionalized signatures for predictions in ungauged catchments

Abstract. A recurrent problem in hydrology is the absence of streamflow data to calibrate rainfall–runoff models. A commonly used approach in such circumstances conditions model parameters on regionalized response signatures. While several different signatures are often available to be included in this process, an outstanding challenge is the selection of signatures that provide useful and complementary information. Different signatures do not necessarily provide independent information and this has led to signatures being omitted or included on a subjective basis. This paper presents a method that accounts for the inter-signature error correlation structure so that regional information is neither neglected nor double-counted when multiple signatures are included. Using 84 catchments from the MOPEX database, observed signatures are regressed against physical and climatic catchment attributes. The derived relationships are then utilized to assess the joint probability distribution of the signature regionalization errors that is subsequently used in a Bayesian procedure to condition a rainfall–runoff model. The results show that the consideration of the inter-signature error structure may improve predictions when the error correlations are strong. However, other uncertainties such as model structure and observational error may outweigh the importance of these correlations. Further, these other uncertainties cause some signatures to appear repeatedly to be misinformative.