SHORT-TERM FORECASTING OF SNOWMELT RUNOFF USING ARMAX MODELS1

ABSTRACT: Time series models of the ARMAX class were investigated for use in forecasting daily riverflow resulting from combined snowmelt/rainfall. The Snowmelt Runoff Model (Martinec-Rango Model) is shown to have a form similar to the ARMAX model. The advantage of the ARMAX approach is that analytical model identification and parameter estimation techniques are available. In addition, previous forecast errors can be included to improve forecasts and confidence limits can be estimated for the forecasts. Diagnostic checks are available to determine if the model is performing properly. Finally, Kalman filtering can be used to allow the model parameters to vary continuously to reflect changing basin runoff conditions. The above advantages result in improved flow forecasts with fewer model parameters.     

Defining the Diurnal Pattern of Snowmelt Using a Beta Distribution Function

Snow is an important component of the hydrologic cycle for many regions worldwide. In addition to vital water resources, snowmelt can be important for forest ecosystem dynamics and flood risk. However, standard design events in the United States lack a design snowmelt event, including only precipitation events, though snowmelt has been shown to be larger than rainfall. In this article, we present a method using hourly snow water equivalent data to develop and test a function for representing the diurnal pattern of snowmelt. A two‐parameter beta distribution function is modified for the purposes of this study and found to fit the pattern of snowmelt well with a root mean squared error of 0.008. Soil moisture sensors were additionally utilized to assess the timing of the snowmelt water outflow from the base of the snowpack that supports the shape of the function, but suggests that the timing of losses recorded on snow pillows lag as much as 3 h. Further testing of the function showed the shape of the function to be accurate. The methods developed and tested in this paper can be applied for design purposes comparing snowmelt and rainfall events or to improve hydrological models investigating processes such as streamflow or groundwater recharge.     

Use of Predictive Weather Uncertainties in an Irrigation Scheduling Tool Part II: An Application of Metrics and Adjoints

We apply predictive weather metrics and land model sensitivities to improve the Colorado State University Water Irrigation Scheduler for Efficient Application (WISE). WISE is an irrigation decision aid that integrates environmental and user information for optimizing water use. Rainfall forecasts and verification performance metrics are used to estimate predictive rainfall probabilities that are used as input data within the irrigation decision aid. These input data errors are also used within a land model sensitivity study to diagnose important prognostic water movement behaviors for irrigation tool development purposes simultaneously performing the analysis in space and time. Thus, important questions such as “how long can a crop water application be delayed while maintaining crop yield production?” are addressed by evaluating crop growth stage interactions as a function of soil depth (i.e., space), rainfall events (i.e., time), and their probabilistic uncertainties. Editor’s note : This paper is part of the featured series on Optimizing Ogallala Aquifer Water Use to Sustain Food Systems. See the February 2019 issue for the introduction and background to the series.     

BAYESIAN MODELS OF FORECASTED TIME SERIES1

Bayesian Processor of Forecasts (BPF) combines a prior distribution, which describes the natural uncertainty about the realization of a hydrologic process, with a likelihood function, which describes the uncertainty in categorical forecasts of that process, and outputs a posterior distribution of the process, conditional upon the forecasts. The posterior distribution provides a means of incorporating uncertain forecasts into optimal decision models. We present fundamentals of building BPF for time series. They include a general formulation, stochastic independence assumptions and their interpretation, computationally tractable models for forecasts of an independent process and a first-order Markov process, and parametric representations for normal-linear processes. An example is shown of an application to the annual time series of seasonal snowmelt runoff volume forecasts.     

Development and Operational Testing of a Super‐Ensemble Artificial Intelligence Flood‐Forecast Model for a Pacific Northwest River

Coastal catchments in British Columbia, Canada, experience a complex mixture of rainfall‐ and snowmelt‐driven contributions to flood events. Few operational flood‐forecast models are available in the region. Here, we integrated a number of proven technologies in a novel way to produce a super‐ensemble forecast system for the Englishman River, a flood‐prone stream on Vancouver Island. This three‐day‐ahead modeling system utilizes up to 42 numerical weather prediction model outputs from the North American Ensemble Forecast System, combined with six artificial neural network‐based streamflow models representing various slightly different system conceptualizations, all of which were trained exclusively on historical high‐flow data. As such, the system combines relatively low model development times and costs with the generation of fully probabilistic forecasts reflecting uncertainty in the simulation of both atmospheric and terrestrial hydrologic dynamics. Results from operational testing by British Columbia's flood forecasting agency during the 2013‐2014 storm season suggest that the prediction system is operationally useful and robust.     

Simulation of Temperature Mitigation by a Stormwater Detention Pond1

Abstract: A numerical model has been developed to simulate the hydraulic and heat transfer properties of a stormwater detention pond, as part of a simulation tool to evaluate thermal pollution of coldwater streams from stormwater runoff. The model is dynamic (unsteady) and based on principles of fluid mechanics and heat transfer. It is driven by hourly weather data, and specified inflow rates and temperatures. To calibrate and validate the pond model field data were collected on a commercial site in Woodbury, Minnesota. The relationship between pond inflow and outflow rates to precipitation was effectively calibrated using continuously recorded pond levels. Algorithms developed for surface heat transfer in lakes were found to be applicable to the pond with some modification, resulting in agreement of simulated and observed pond surface temperature within 1.0°C root mean square error. The use of an unshaded pond for thermal mitigation of runoff from paved surfaces was evaluated using the pond model combined with simulated runoff from an asphalt parking lot for six years of observed rainfall events. On average, pond outflow temperature was 1.2°C higher than inflow temperature, but with significant event‐to‐event variation. On average, the pond added heat energy to runoff from an asphalt parking lot. Although the pond added total heat energy to runoff, it did reduce the rate of heat outflow from the pond by an order of magnitude due to reductions in volumetric outflow rate compared with the inflow rate. By reducing the rate of heat flow, the magnitude of temperature impacts in a receiving stream were also reduced, but the duration of impacts was increased.     

Regional scale flood modeling using NEXRAD rainfall, GIS, and HEC-HMS/RAS: a case study for the San Antonio River Basin Summer 2002 storm event

This paper develops a framework for regional scale flood modeling that integrates NEXRAD Level III rainfall, GIS, and a hydrological model (HEC-HMS/RAS). The San Antonio River Basin (about 4000 square miles, 10,000 km2) in Central Texas, USA, is the domain of the study because it is a region subject to frequent occurrences of severe flash flooding. A major flood in the summer of 2002 is chosen as a case to examine the modeling framework. The model consists of a rainfall-runoff model (HEC-HMS) that converts precipitation excess to overland flow and channel runoff, as well as a hydraulic model (HEC-RAS) that models unsteady state flow through the river channel network based on the HEC-HMS-derived hydrographs. HEC-HMS is run on a 4 x 4 km grid in the domain, a resolution consistent with the resolution of NEXRAD rainfall taken from the local river authority. Watershed parameters are calibrated manually to produce a good simulation of discharge at 12 subbasins. With the calibrated discharge, HEC-RAS is capable of producing floodplain polygons that are comparable to the satellite imagery. The modeling framework presented in this study incorporates a portion of the recently developed GIS tool named Map to Map that has been created on a local scale and extends it to a regional scale. The results of this research will benefit future modeling efforts by providing a tool for hydrological forecasts of flooding on a regional scale. While designed for the San Antonio River Basin, this regional scale model may be used as a prototype for model applications in other areas of the country.     

Evaluation of Gauge‐Radar Merging Methods Using a Semi‐Distributed Hydrological Model in the Upper Thames River Basin,Canada

Gauge‐radar merging methods combine rainfall estimates from rain gauges and radar to capitalize on the strengths of the individual instruments. The performance of four well‐known gauge‐radar merging methods, including mean field bias correction, Brandes spatial adjustment, local bias correction using kriging, and conditional merging, are examined using Environment Canada radar and the Upper Thames River Basin in southwestern Ontario, Canada, as a case study. The analysis assesses the effect of gauge‐radar merging methods on: (1) the accuracy of predicted rainfall accumulations; and (2) the accuracy of predicted streamflows using a semi‐distributed hydrological model. In addition, several influencing factors (i.e., gauge density, storm type, basin type, proximity to the radar tower, and time‐step of adjustment) are analyzed to determine their effect on the performance of the rainfall estimation techniques. Confirming results of previous studies, the merging methods provide an increase in the accuracy of both rainfall accumulation estimations and predicted streamflows. The results also indicate specific factors such as gauge density, rainfall intensity, and time‐step of adjustment can reduce the accuracy of merging methods and play a key role in the examination of its use for operational purposes. Results provide guidance for hydrologists and engineers assessing how best to apply corrected radar products to improve rainfall estimation and hydrological modeling accuracy.     

A MULTICOMPONENT MODEL OF PHOSPHORUS DYNAMICS IN RESERVOIRS1

The models available for simulating phosphorus dynamics and trophic state in impoundments vary widely. The simpler empirically derived phosphorus models tend to be appropriate for long-term, steady or near steady state analyses. The more complex ecosystem models, because of computational expense and the importance of input parameter uncertainty, are impractical for very long-term simulation and most applicable for time-variable water quality simulations generally of short to intermediate time frames. An improved model for time variable, long-term simulation of trophic state in reservoirs with fluctuating inflow and outflow rates and volume is needed. Such a model is developed in this paper representing the phosphorus cycle in two-layer (i.e., epilimnion and hypolimnion) reservoirs. The model is designed to simulate seasonally varying reservoir water quality and eutrophication potential by using the phosphorus state variable as the water quality indicator. Long-term simulations with fluctuating volumes and variable influent and effluent flow rates are feasible and practical. The model utility is demonstrated through application to a pumped storage reservoir characteristic of these conditions.     

APPLICATION OF GREY MODEL AND ARTIFICIAL NEURAL NETWORKS TO FLOOD FORECASTING1

The main focus of this study was to compare the Grey model and several artificial neural network (ANN) models for real time flood forecasting, including a comparison of the models for various lead times (ranging from one to six hours). For hydrological applications, the Grey model has the advantage that it can easily be used in forecasting without assuming that forecast storm events exhibit the same stochastic characteristics as the storm events themselves. The major advantage of an ANN in rainfall‐runoff modeling is that there is no requirement for any prior assumptions regarding the processes involved. The Grey model and three ANN models were applied to a 2,509 km² watershed in the Republic of Korea to compare the results for real time flood forecasting with from one to six hours of lead time. The fifth‐order Grey model and the ANN models with the optimal network architectures, represented by ANN1004 (34 input nodes, 21 hidden nodes, and 1 output node), ANN1010 (40 input nodes, 25 hidden nodes, and 1 output node), and ANN1004T (14 input nodes, 21 hidden nodes, and 1 output node), were adopted to evaluate the effects of time lags and differences between area mean and point rainfall. The Grey model and the ANN models, which provided reliable forecasts with one to six hours of lead time, were calibrated and their datasets validated. The results showed that the Grey model and the ANN1010 model achieved the highest level of performance in forecasting runoff for one to six lead hours. The ANN model architectures (ANN1004 and ANN1010) that used point rainfall data performed better than the model that used mean rainfall data (ANN1004T) in the real time forecasting. The selected models thus appear to be a useful tool for flood forecasting in Korea.     

A Streamflow Forecasting Framework using Multiple Climate and Hydrological Models1

Abstract: Water resources planning and management efficacy is subject to capturing inherent uncertainties stemming from climatic and hydrological inputs and models. Streamflow forecasts, critical in reservoir operation and water allocation decision making, fundamentally contain uncertainties arising from assumed initial conditions, model structure, and modeled processes. Accounting for these propagating uncertainties remains a formidable challenge. Recent enhancements in climate forecasting skill and hydrological modeling serve as an impetus for further pursuing models and model combinations capable of delivering improved streamflow forecasts. However, little consideration has been given to methodologies that include coupling both multiple climate and multiple hydrological models, increasing the pool of streamflow forecast ensemble members and accounting for cumulative sources of uncertainty. The framework presented here proposes integration and offline coupling of global climate models (GCMs), multiple regional climate models, and numerous water balance models to improve streamflow forecasting through generation of ensemble forecasts. For demonstration purposes, the framework is imposed on the Jaguaribe basin in northeastern Brazil for a hindcast of 1974‐1996 monthly streamflow. The ECHAM 4.5 and the NCEP/MRF9 GCMs and regional models, including dynamical and statistical models, are integrated with the ABCD and Soil Moisture Accounting Procedure water balance models. Precipitation hindcasts from the GCMs are downscaled via the regional models and fed into the water balance models, producing streamflow hindcasts. Multi‐model ensemble combination techniques include pooling, linear regression weighting, and a kernel density estimator to evaluate streamflow hindcasts; the latter technique exhibits superior skill compared with any single coupled model ensemble hindcast.     

Comparison of the Performance of Statistical Models in Forecasting Monthly Total Dissolved Solids in the Rio Grande1

Abudu, S., J.P. King, Z. Sheng, 2011. Comparison of the Performance of Statistical Models in Forecasting Monthly Total Dissolved Solids in the Rio Grande. Journal of the American Water Resources Association (JAWRA) 48(1): 10‐23. DOI: 10.1111/j.1752‐1688.2011.00587.x Abstract: This paper presents the application of autoregressive integrated moving average (ARIMA), transfer function‐noise (TFN), and artificial neural networks (ANNs) modeling approaches in forecasting monthly total dissolved solids (TDS) of water in the Rio Grande at El Paso, Texas. Predictability analysis was performed between the precipitation, temperature, streamflow rates at the site, releases from upstream reservoirs, and monthly TDS using cross‐correlation statistical tests. The chi‐square test results indicated that the average monthly temperature and precipitation did not show significant predictability on monthly TDS series. The performances of one‐ to three‐month‐ahead model forecasts for the testing period of 1984‐1994 showed that the TFN model that incorporated the streamflow rates at the site and Caballo Reservoir release improved monthly TDS forecasts slightly better than the ARIMA models. Except for one‐month‐ahead forecasts, the ANN models using the streamflow rates at the site as inputs resulted in no significant improvements over the TFN models at two‐month‐ahead and three‐month‐ahead forecasts. For three‐month‐ahead forecasts, the simple ARIMA showed similar performance compared to all other models. The results of this study suggested that simple deseasonalized ARIMA models could be used in one‐ to three‐month‐ahead TDS forecasting at the study site with a simple, explicit model structure and similar model performance as the TFN and ANN models for better water management in the Basin.     

PCN BASED METAL PARTITIONING IN URBAN SNOWMELT,RAINFALL/RUNOFF,AND RIVER FLOW SYSTEMS1

ABSTRACT: Drawing an analogy between the popular Soil Conservation Service curve number (SCS‐CN) method based infiltration and metal sorption processes, a new partitioning curve number (PCN) approach is suggested for partitioning of heavy metals into dissolved and particulate bound forms in urban snowmelt, rainfall/runoff, and river flow environments. The parameters, the potential maximum desorption, ψ, and the PCN analogous to the SCS‐CN parameters S and CN, respectively, are introduced. Under the condition of snowmelt, PCN (or ψ) is found to generally rely on temperature, relative humidity, pH, and chloride content; during a rainstorm, ψ is found to depend on the alkalinity and the pH of the rainwater; and in the river flow situation, PCN is found to generally depend on the temperature, pH, and chloride content. The advantage of using PCN instead of the widely used partitioning parameter, K_d, is found to lie in the PCN's efficacy to distinguish the adsorption (or sorption) behavior of metals in the above snowmelt, rainfall/runoff, and river flow situations, analogous to the hydrological behavior of watersheds.     

REVISITING THE DEGREE-DAY METHOD FOR SNOWMELT COMPUTATIONS1

ABSTRACT: The simple, empirical degree-day approach for calculating snowmelt and runoff from mountain basins has been in use for more than 60 years. It is frequently suggested that the degree-day method be replaced by the more physically-based energy balance approach. The degree-day approach, however, maintains its popularity, applicability, and effectiveness. It is shown that the degree-day method is reliable for computing total snowmelt depths for periods of a week to the entire snowmelt season. It can also be used for daily snowmelt depths when utilized in connection with an adequate snowmelt runoff model for computing the basin runoff. The degree-day ratio is shown to vary seasonally as opposed to being constant as is often assumed. Additionally, in order to evaluate the degree-day ratio correctly, the changing snow cover extent in a basin during the snowmelt season must be taken into account. It is also possible to combine the degree-day approach with a radiation component so that short time interval (<24 hours) computations of snowmelt depth can be made. When snowmelt input is transformed to basin output (runoff) by a snowmelt runoff model, there is little difference between the degree-day approach and a radiation-based approach. This is fortuitous because the physically-based energy balance models will not soon displace the degree-day methods because of their excessive data requirements.     

Effect of Snow Cover Conditions on the Hydrologic Regime: Case Study in a Pluvial‐Nival Watershed,Japan1

Abstract: Hydrologic monitoring in a small forested and mountainous headwater basin in Niigata Prefecture has been undertaken since 2000. An important characteristic of the basin is that the hydrologic regime contains pluvial elements year‐round, including rain‐on‐snow, in addition to spring snowmelt. We evaluated the effect of different snow cover conditions on the hydrologic regime by analyzing observed data in conjunction with model simulations of the snowpack. A degree‐day snow model is presented and applied to the study basin to enable estimation of the basin average snow water equivalent using air temperature at three representative elevations. Analysis of hydrological time series data and master recession curves showed that flow during the snowmelt season was generated by a combination of ground water flow having a recession constant of 0.018/day and diurnal melt water flow having a recession constant of 0.015/hour. Daily flows during the winter/snowmelt season showed greater persistence than daily flows during the warm season. The seasonal water balance indicated that the ratio of runoff to precipitation during the cold season (December to May) was about 90% every year. Seasonal snowpack plays an important role in defining the hydrologic regime, with winter precipitation and snowmelt runoff contributing about 65% of the annual runoff. The timing of the snowmelt season, indicated by the date of occurrence of the first significant snowmelt event, was correlated with the occurrence of low flow events. Model simulations showed that basin average snow water equivalent reached a peak around mid‐February to mid‐March, although further validation of the model is required at high elevation sites.     

AI-based runoff simulation based on remote sensing observations: A case study of two river basins in the United States and Canada

Data-driven techniques are used extensively for hydrologic time-series prediction. We created various data-driven models (DDMs) based on machine learning: long short-term memory (LSTM), support vector regression (SVR), extreme learning machines, and an artificial neural network with backpropagation, to define the optimal approach to predicting streamflow time series in the Carson River (California, USA) and Montmorency (Canada) catchments. The moderate resolution imaging spectroradiometer (MODIS) snow-coverage dataset was applied to improve the streamflow estimate. In addition to the DDMs, the conceptual snowmelt runoff model was applied to simulate and forecast daily streamflow. The four main predictor variables, namely snow-coverage (S-C), precipitation (P), maximum temperature (T_max), and minimum temperature (T_min), and their corresponding values for each river basin, were obtained from National Climatic Data Center and National Snow and Ice Data Center to develop the model. The most relevant predictor variable was chosen using the support vector machine-recursive feature elimination feature selection approach. The results show that incorporating the MODIS snow-coverage dataset improves the models' prediction accuracies in the snowmelt-dominated basin. SVR and LSTM exhibited the best performances (root mean square error = 8.63 and 9.80) using monthly and daily snowmelt time series, respectively. In summary, machine learning is a reliable method to forecast runoff as it can be employed in global climate forecasts that require high-volume data processing.     

A COMPARATIVE STUDY OF A SWEDISH AND A CHINESE HYDROLOGICAL MODEL1

ABSTRACT: There are a large number of conceptual hydrological models available today. It is not easy to immediately identify the similarities and differences between the different models. The Swedish HBV model and the Chinese Xinanjiang model are two examples of conceptual, semi-distributed, rainfall-runoff models. The Xinanjiang model was designed for use in humid and semi-humid regions, with no routine for the snowmelt runoff, whereas the snow routine is an important part of the HBV model in many applications. The model structures of the two models may be described in four routines, compared in this paper. The integral structures of them are similar, but there are some differences, especially in the runoff production routine. The physical significance and physical definitions of some model parameters were analyzed. Both models were tested in two basins. Both models gave similar results, and both models performed well in the application. The similarity of the results obtained by different model structures leads to the following two conclusions. First, more effort should probably be spent on the improvement of input data quality and coverage than on the development of more detailed model structures only. Second, inference about basin behavior and characteristics from the values of calibrated model parameters must be made with great caution.     

ANN OUTPUT UPDATING OF LUMPED CONCEPTUAL RAINFALL/RUNOFF FORECASTING MODELS1

ABSTRACT: Artificial neural networks (ANNs) are tested for the output updating of one‐day‐ahead and three‐day‐ahead streamflow forecasts derived from three lumped conceptual rainfall/runoff (R‐R) models: the GR4J, the IHAC, and the TOPMO. ANN output updating proved superior to a parameter updating scheme and to the ‘simple’ output updating scheme, which always replicates the last observed forecast error. In fact, ANN output updating was able to compensate for large differences in the initial performance of the three tested lumped conceptual R‐R models, which the other tested updating approaches were not able to achieve. This is done mainly by incorporating input vectors usually exploited for ANN R‐R modeling such as previous rainfall and streamflow observations, in addition to the previous observed error. For one‐day‐ahead forecasts, the performance of all three lumped conceptual R‐R models, used in conjunction with ANN output updating, was equivalent to that of the ANN R‐R model. For three‐day‐ahead forecasts, the performance of the ANN‐output‐updated conceptual models was even superior to that of the ANN R‐R model, revealing that the conceptual models are probably performing some tasks that the ANN R‐R model cannot map. However, further testing is needed to substantiate the last statement.     

Generation of Ensemble Streamflow Forecasts Using an Enhanced Version of the Snowmelt Runoff Model1

Harshburger, Brian J., Von P. Walden, Karen S. Humes, Brandon C. Moore, Troy R. Blandford, and Albert Rango, 2012. Generation of Ensemble Streamflow Forecasts Using an Enhanced Version of the Snowmelt Runoff Model. Journal of the American Water Resources Association (JAWRA) 48(4): 643‐655. DOI: 10.1111/j.1752‐1688.2012.00642.x Abstract: As water demand increases in the western United States, so does the need for accurate streamflow forecasts. We describe a method for generating ensemble streamflow forecasts (1‐15 days) using an enhanced version of the snowmelt runoff model (SRM). Forecasts are produced for three snowmelt‐dominated basins in Idaho. Model inputs are derived from meteorological forecasts, snow cover imagery, and surface observations from Snowpack Telemetry stations. The model performed well at lead times up to 7 days, but has significant predictability out to 15 days. The timing of peak flow and the streamflow volume are captured well by the model, but the peak‐flow value is typically low. The model performance was assessed by computing the coefficient of determination (R²), percentage of volume difference (Dv%), and a skill score that quantifies the usefulness of the forecasts relative to climatology. The average R² value for the mean ensemble is >0.8 for all three basins for lead times up to seven days. The Dv% is fairly unbiased (within ±10%) out to seven days in two of the basins, but the model underpredicts Dv% in the third. The average skill scores for all basins are >0.6 for lead times up to seven days, indicating that the ensemble model outperforms climatology. These results validate the usefulness of the ensemble forecasting approach for basins of this type, suggesting that the ensemble version of SRM might be applied successfully to other basins in the Intermountain West.     

Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool

Traditionally, the multiple linear regression technique has been one of the most widely used models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, neuro-fuzzy systems have gained much popularity for calibrating the nonlinear relationships. This study evaluated the potential of a neuro-fuzzy system as an alternative to the traditional statistical regression technique for the purpose of predicting flow from a local source in a river basin. The effectiveness of the proposed identification technique was demonstrated through a simulation study of the river flow time series of the Citarum River in Indonesia. Furthermore, in order to provide the uncertainty associated with the estimation of river flow, a Monte Carlo simulation was performed. As a comparison, a multiple linear regression analysis that was being used by the Citarum River Authority was also examined using various statistical indices. The simulation results using 95% confidence intervals indicated that the neuro-fuzzy model consistently underestimated the magnitude of high flow while the low and medium flow magnitudes were estimated closer to the observed data. The comparison of the prediction accuracy of the neuro-fuzzy and linear regression methods indicated that the neuro-fuzzy approach was more accurate in predicting river flow dynamics. The neuro-fuzzy model was able to improve the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of the multiple linear regression forecasts by about 13.52% and 10.73%, respectively. Considering its simplicity and efficiency, the neuro-fuzzy model is recommended as an alternative tool for modeling of flow dynamics in the study area.