Rainfall-runoff Model Structure Research Articles

Bridging the gap from hydrological to biogeochemical processes using tracer-aided hydrological models in a tropical montane ecosystem

How simple or complex catchment models need to be is still unclear particularly for tracer-aided models that go beyond hydrograph fitting. Here, we take advantage of a sub-daily hydrometric and tracer data set from a tropical montane (páramo) experimental catchment to fill this knowledge gap. We evaluated six conceptual rainfall-runoff model structures with different complexity that represent the perceptual understanding of the catchment's hydrological functioning. The models solved conservative and reactive tracer mass balances to simulate streamflow, stable isotopes, and DOC concentrations and were assessed for performance and parsimony using three calibration targets (discharge only, discharge and stable isotopes, and discharge and DOC), resulting in 18 model configurations. Although all models satisfied the discharge calibration (KGE > 0.8), differences arose when considering tracer transport. The more complex models outperformed the simpler ones in terms of goodness-of-fit and parsimony, indicating that the catchment streamflow response consisted of quick near-surface flow and tracer contributions, more mixed flow through the two main soil types (Andosols and Histosols), as well as flow from the well-mixed shallow fractured rock (up to 20 m depth). The bedrock flow pathway contributed up to ∼25% of total flow during baseflow conditions. This study provides a benchmark experiment to identify hydrological and biogeochemical behavior in tropical montane catchments using relatively parsimonious tracer-aided hydrological models.

On the application of rainfall projections from a convection-permitting climate model to lumped catchment models

Climate change is predicted to increase rainfall intensity in tropical regions. Convection permitting (CP) climate models have been developed to address deficiencies in conventional climate models that use parameterised convection. However, to date, precipitation projections from CP climate models have not been used in conjunction with hydrological models to explore potential impacts of explicit modelling of convective rainfall on river flows in the tropics. Here we apply the outputs of a continental scale CP climate model as inputs to lumped rainfall-runoff models in Africa for the first time. Applied to five catchments in the Lake Victoria Basin, we show that the CP climate model produces greater river flows than an equivalent model using parameterised convection in both the current and future (c. 2100) climate. However, the location of the catchments near to Lake Victoria results in limited changes in extreme rainfall and river flows relative to changes in mean rainfall and river flows. Application of CP model rainfall data from an area where rainfall extremes change more than the change in mean rainfall to the rainfall-runoff model does not result in significant changes in river flows. Instead, this is shown to be a result of the rainfall-runoff model structure and parameterisation, which we posit is due to large-scale storage in the catchments associated with wetland cover, that buffers the impact of rainfall extremes. Based on an assessment of hydrological attributes (wetland coverage, water table depth, topography, precipitation, evapotranspiration and river flow) using global-scale datasets for the catchments in this research, this buffering may be extensive across humid regions. Application of CP climate model data to lumped catchment models in these areas are unlikely to result in significant increases in extreme river flows relative to increases in mean flows.

Exploring parsimonious daily rainfall-runoff model structure using the hyperbolic tangent function and Tank model

Mathematical models with small numbers of parameters are useful for hydrological analyses and water resources planning as they are easier to prepare, use, and interpret compared to more complex models. Many simple model structures and simulation strategies have been developed, but there is still substantial room for improvement in the efficiency of daily rainfall-runoff modeling. This study proposes daily rainfall-runoff models that require only two to four parameters yet are capable of predicting peak discharge and baseflow. Parsimonious model structures were obtained using the hyperbolic tangent function and combining it with one subsurface layer and two parameters of a Tank model. The daily rainfall-runoff models proposed based on the Two-Parameter Hyperbolic Model (TPHM) and Tank model were applied to 41 watersheds throughout South Korea. Model accuracy was evaluated by comparing observed and simulated watershed streamflow and compared with that of a nine-parameter Tank model. The original TPHM and its variants yielded slightly better efficiency with a smaller number of parameters than the Tank model when reproducing high flows on a daily basis. The accuracy of low flow and flow duration curve predictions provided by the TPHM-based models was higher in watersheds with relatively large baseflow temporal variability. The results suggested that the TPHM-based structures be alternative parsimonious daily rainfall-runoff simulation models. This study demonstrates that daily high streamflow can be efficiently simulated using a two-parameter hydrological model, and daily baseflow simulation can be improved by adding two additional parameters to the model.

A Spatial–Dynamical Framework for Evaluation of Satellite Rainfall Products for Flood Prediction

Abstract Rainfall maps that are derived from satellite observations provide hydrologists with an unprecedented opportunity to forecast floods globally. However, the limitations of using these precipitation estimates with respect to producing reliable flood forecasts at multiple scales are not well understood. To address the scientific and practical question of applicability of space-based rainfall products for global flood forecasting, a data evaluation framework is developed that allows tracking the rainfall effects in space and time across scales in the river network. This provides insights on the effects of rainfall product resolution and uncertainty. Obtaining such insights is not possible when the hydrologic evaluation is based on discharge observations from single gauges. The proposed framework also explores the ability of hydrologic model structure to answer questions pertaining to the utility of space-based rainfall observations for flood forecasting. To illustrate the framework, hydrometeorological data collected during the Iowa Flood Studies (IFloodS) campaign in Iowa are used to perform a hydrologic simulation using two different rainfall–runoff model structures and three rainfall products, two of which are radar based [stage IV and Iowa Flood Center (IFC)] and one satellite based [TMPA–Research Version (RV)]. This allows for exploring the differences in rainfall estimates at several spatial and temporal scales and provides improved understanding of how these differences affect flood predictions at multiple basin scales. The framework allows for exploring the differences in peak flow estimation due to nonlinearities in the hydrologic model structure and determining how these differences behave with an increase in the upstream area through the drainage network. The framework provides an alternative evaluation of precipitation estimates, based on the diagnostics of hydrological model results.

Non-stationarity driven by long-term change in catchment storage: possibilities and implications

Abstract. "Non-stationarity" with reference to hydrology is a term applied to many situations (Milly et al., 2008). While climate change non-stationarity is often examined, these effects can provide a test for assumptions of runoff generation process impliedin rainfall–runoff (RR) models. Observations from South-western Australia (SWA) over the past 40 years show a decline in rainfall and reductions in runoff. Runoff and rainfall relationships in SWA show a significant shift over the past 40 years suggesting a change in runoff generation and catchment state. This has challenged the nature of assumed runoff generation process in SWA as well as the veracity of conceptual RR model structure. We expand on some of the lessons learned from SWA and discuss the climatic and geomorphic conditions that may make reasonable predictions of runoff very difficult with RR models calibrated in traditional ways. Catchment storage has a significant interaction with runoff generation and we examine the situations where these may change in the longer term. We suggest some strategies in terms of model structure and calibration that may improve predictive performance in such situations.

On hydrological model complexity, its geometrical interpretations and prediction uncertainty

Knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models. Optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk. This may be considered equivalent to minimizing an upper bound on prediction error, defined here as the mathematical expectation of empirical risk. In this paper, we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time. We demonstrate that hydrological model complexity, as defined in the presented theoretical framework, plays an important role in determining the upper bound. The model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill-posed. We provide an algorithm for computing complexity of any arbitrary hydrological model. We also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space. The presented theory is applied to quantify complexities of two hydrological model structures: SAC-SMA and SIXPAR. It detects that SAC-SMA is indeed more complex than SIXPAR. We also develop an algorithm to estimate the upper bound on prediction error, which is applied on five different rainfall-runoff model structures that vary in complexity. We show that a model selection problem is stabilized by regularizing it with model complexity. Complexity regularized model selection yields models that are robust in predicting future but yet unseen data.

A framework to assess the realism of model structures using hydrological signatures

Abstract. The use of flexible hydrological model structures for hypothesis testing requires an objective and diagnostic method to identify whether a rainfall-runoff model structure is suitable for a certain catchment. To determine if a model structure is realistic, i.e. if it captures the relevant runoff processes, both performance and consistency are important. We define performance as the ability of a model structure to mimic a specific part of the hydrological behaviour in a specific catchment. This can be assessed based on evaluation criteria, such as the goodness of fit of specific hydrological signatures obtained from hydrological data. Consistency is defined as the ability of a model structure to adequately reproduce several hydrological signatures simultaneously while using the same set of parameter values. In this paper we describe and demonstrate a new evaluation Framework for Assessing the Realism of Model structures (FARM). The evaluation framework tests for both performance and consistency using a principal component analysis on a range of evaluation criteria, all emphasizing different hydrological behaviour. The utility of this evaluation framework is demonstrated in a case study of two small headwater catchments (Maimai, New Zealand, and Wollefsbach, Luxembourg). Eight different hydrological signatures and eleven model structures have been used for this study. The results suggest that some model structures may reveal the same degree of performance for selected evaluation criteria while showing differences in consistency. The results also show that some model structures have a higher performance and consistency than others. The principal component analysis in combination with several hydrological signatures is shown to be useful to visualise the performance and consistency of a model structure for the study catchments. With this framework performance and consistency are evaluated to identify which model structure suits a catchment better compared to other model structures. Until now the framework has only been based on a qualitative analysis and not yet on a quantitative analysis.

제주도 유출분석을 위한 한계유출 모의기법 개발

In Jeju island, runoff has frequently happened when the rainfall depth is over a threshold value. To simulated this characteristic rainfall-runoff model structure has to be modified. In this study, the TRSM (Threshold Runoff Simulation Method) was developed to overcome the limitations of SWAT in applying to the hydrologic characteristics of Jeju island. When the precipitation and soil water are less than threshold value, we revised the SWAT routine not to make surface/lateral or groundwater discharge. For Hancheon watershed, the threshold value was set as 80% of soil water through the analysis of rainfall-runoff relationship. Through the simulation of test watershed, it was proven that TRSM performed much better in simulating pulse type stream flow for the Hancheon watershed.

Analysis and development of conceptual rainfall-runoff model structures for regionalisation purposes

This paper attempts to investigate, in detail, the behaviour of the selected conceptual rainfall runoff model structures (a Pen manbased model and a probability distribution-based model) by using a novel method of dynamic parameter identifiability analysis (DYNIA). Two UK catchments were used as case studies. This paper shows that potential weaknesses of model structures are uncovered by this analysis; a) the optimum parameter shifts over the time domain, and b) insensitive model parameters shift over the wet period and dry period. However, attempting to interpret these results, and use them as a basis for improving the model structure proved difficult. The dynamic relationships between the model parameter and the variable soil moisture state in the model have been considered based on these analyses. Possible model modifications have been suggested: a) Making the proportion of rainfall that bypasses the soil stores responsive to soil wetness, rather than a constant, and b) Directing this bypassed rain fall to the fas trouting reservoirs rather than splitting it between fast and slow reservoirs. However, substantial and well-founded changes in the model structures had marginal effect on the time-series output. The lack of improved performance raises a number of questions and points the way forward for more research. The results may suggest that improvement of the model performance depends more on the quality of data (or catchment information) rather than the hydrological representation of the different catchments.

Impact of biased and randomly corrupted inputs on the efficiency and the parameters of watershed models

In this paper, we use a sample of 12 US watersheds with various characteristics to investigate the influence of both random and systematic errors in input data (rainfall and potential evapotranspiration—PE) on the performance and parameter values of rainfall-runoff models. Two different rainfall-runoff model structures were tested to get a more general overview on this issue. A dynamic sensitivity analysis approach was adopted (i.e. with re-calibration of model parameters). Results indicate that watershed models use their different functions (and corresponding parameters) to absorb input errors and muffle their impact on streamflow simulations. The main conclusions are: (1) models are almost insensitive to random errors in PE series, which comes from the inherent low pass filter properties of rainfall-runoff models; (2) random errors in rainfall series significantly affect model performances and parameter values; (3) systematic errors in PE series have a greater impact than random errors, but they are partly buffered by Soil Moisture Accounting (SMA) stores; (4) systematic errors in rainfall time series, when large enough, can be very detrimental to model performances but their impact can be reduced if the model structure includes a procedure other than evapotranspiration to adapt water balance.

Selection of conceptual models for regionalisation of the rainfall-runoff relationship

This study attempts to identify relationships between suitable conceptual rainfall-runoff model structures and catchment types, and demonstrates an objective procedure for selection of model structures for use in model regionalisation studies. 12 conceptual model structures have been tested on 28 UK catchments. The model structures are combinations of three soil moisture accounting modules (the catchment wetness index model structure, a modified Penman model structure, and a probability distributed soil moisture model), and four routing models (two linear reservoirs in parallel, an adaptation that represents macropore flow, three linear reservoirs in parallel, and a model that includes leakage from the groundwater store). The 28 catchments were selected to cover a range of hydrological types based on known catchment characteristics (designed combinations of catchment size, baseflow index, and annual rainfall are used). The important points in objectively selecting model structures for regionalisation are proposed as: performance in calibration and validation, trade-off between high and low flow performance, and model complexity (here represented as the number of parameters). Although, the results in this study provide no evidence of relationships between catchment type and preferred model structure, the study indicates that out of the 12 trial model structures, the following four may be the most suitable for regionalisation across UK catchments: the modified Penman model with two parallel linear routing reservoirs, and the probability distributed soil moisture model with two parallel linear routing reservoirs, three parallel linear routing reservoirs, or the macropore adaptation.

Improved unit hydrograph characterisation of the daily flow regime (including low flows) for the River Teifi, Wales: towards better rainfall-streamflow models for regionalisation

Abstract. An established rainfall-streamflow modelling methodology employing a six-parameter unit hydrograph-based rainfall-runoff model structure is developed further to give an improved model-fit to daily flows for the River Teifi at Glan Teifi. It is shown that a previous model of this type for the Teifi, which (a) accounted for 85% of the variance in observed streamflow, (b) incorporated a pure time delay of one day and (c) was calibrated using a trade-off between two model-fit statistics (as recommended in the original methodology), systematically over-estimates low flows. Using that model as a starting point the combined application of a non-integer pure time delay and further adjustment of a temperature modulation parameter in the loss module, using the flow duration curve as an additional model-fit criterion, gives a much improved model-fit to low flows, while leaving the already good model-fit to higher flows essentially unchanged. The further adjustment of the temperature modulation loss module parameter in this way is much more effective at improving model-fit to low flows than the introduction of the non-integer pure time delay. The new model for the Teifi accounts for 88% of the variance in observed streamflow and performs well over the 5 percentile to 95 percentile range of flows. Issues concerning the utility and efficacy of the new model selection procedure are discussed in the context of hydrological studies, including regionalisation. Keywords: unit hydrographs, rainfall-runoff modelling, low flows, regionalisation.

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.

Development of confidence interval estimates for predictions from a rainfall-runoff model

In any rainfall-runoff model, there is uncertainty associated to prediction of runoff. The stochastic integral equation method is used in this paper to represent the history of the rainfall-runoff modeling error as a convolution of model input (effective rainfall in this paper) with a frequency-distribution of transfer function realizations. In prediction, the expected runoff estimate is quantified by use of a distribution of runoff error estimates, each estimate of error based upon a previous experience using the subject rainfall-runoff model. Although this paper focuses upon a simple unit-hydrograph rainfall-runoff model, the principles discussed apply, in generality, to other rainfall-runoff model structures.