Probability Distributed Moisture Model Research Articles

Multi sources hydrological assessment over Vu Gia Thu Bon Basin, Vietnam

ABSTRACT The study aims to evaluate the long-term accuracy of global precipitation (Climate Prediction Center (CPC) and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks – Climate Data Record (PERSIANN-CDR)) along with raingauge datasets at multiple temporal scales in the Vu Gia Thu Bon basin, Vietnam. Since there are few rainfall stations in this basin, it is important to validate multisource data for multiple purposes. This is the first time that a lumped hydrological model (i.e. Probability Distributed Moisture (PDM)) has been used for this basin. Various statistical indicators, including the correlation coefficient, mean absolute error (MAE), root mean square error (RMSE), percent bias (BIAS) and Taylor diagram, were used to evaluate the applicability of the global precipitation data and the PDM model. The precipitation datasets showed a good correlation with the raingauge rainfall data. In contrast, CPC underestimates while PERSIANN-CDR overestimates the raingauge rainfall. In general, PERSIANN-CDR performed slightly better than CPC. The daily streamflow simulation driven by PDM and all data sources underestimates the actual flow.

Regionalisation of a PDM Model for Catchment Runoff in a Mountainous Region of Korea

This study aims to regionalize a rainfall-runoff model within the mountainous Geum River catchment, Korea. A version of the Probability Distributed Moisture model is applied to 19 gauged sub-catchments. A Monte Carlo based method is used for the calibration and validation of the model using three objective functions targeting overall performance, as well as low and high flow regimes specifically. A set of multivariate regression models linking model parameters and catchment characteristics is developed. The regionalised and locally calibrated models are compared using the leave-one-out cross-validation method. The validation results show that the regionalised model has equal or better performance than the locally calibrated model at 12 (for high flow model), 10 (for low flow model) and 10 catchments (for overall flow regime model) respectively. This study shows the potential of the regionalisation of the Probability Distributed Moisture model within the Geum River region. The results show that the suggested regionalized models for high and low flow regimes are better than a single model for the overall flow regime model. It is expected that this approach can usefully support water resource management in comparable ungauged mountainous, monsoon-affected catchments.

Prediction of Typhoon-Induced Flood Flows at Ungauged Catchments Using Simple Regression and Generalized Estimating Equation Approaches

Typhoons are the main type of natural disaster in Korea, and accurately predicting typhoon-induced flood flows at gauged and ungauged locations remains an important challenge. Flood flows caused by six typhoons since 2002 (typhoons Rusa, Maemi, Nari, Dienmu, Kompasu and Bolaven) are modeled at the outlets of 24 Geum River catchments using the Probability Distributed Moisture model. The Monte Carlo Analysis Toolbox is applied with the Nash Sutcliffe Efficiency as the criterion for model parameter estimation. Linear regression relationships between the parameters of the Probability Distributed Moisture model and catchment characteristics are developed for the purpose of generalizing the parameter estimates to ungauged locations. These generalized parameter estimates are tested in terms of ability to predict the flood hydrographs over the 24 catchments using a leave-one-out validation approach. We then test the hypothesis that a more complex generalization approach, the Generalized Estimating Equation, which includes properties of the typhoons as well as catchment characteristics as predictors of PDM model parameters, will provide more accurate predictions. The results show that the predictions of Generalized Estimating Equation are comparable to those of the simpler, conventional regression. The simpler approach is therefore recommended for practical applications; however, further refinements of the Generalized Estimating Equation approach may be explored.

Analysis of the drought recovery of Andosols on southern Ecuadorian Andean páramos

Abstract. The Neotropical Andean grasslands above 3500 m a.s.l., known as páramo, offer remarkable ecological services for the Andean region. The most important of these is the water supply of excellent quality to many cities and villages in the inter-Andean valleys and along the coast. The páramo ecosystem and especially its soils are under constant and increased threat by human activities and climate change. In this study, the recovery speed of the páramo soils after drought periods are analysed. The observation period includes the droughts of 2009, 2010, 2011, and 2012 together with intermediate wet periods. Two experimental catchments – one with and one without páramo – were investigated. The Probability Distributed Moisture (PDM) model was calibrated and validated in both catchments. Drought periods and its characteristics were identified and quantified by a threshold level approach and complemented by means of a drought propagation analysis. At the plot scale in the páramo region, the soil water content measured by time domain reflectometry (TDR) probes dropped from a normal value of about 0.84 to ∼ 0.60 cm3 cm−3, while the recovery time was 2–3 months. This did not occur at lower altitudes (Cumbe) where the soils are mineral. Although the soil moisture depletion observed in these soils was similar to that of the Andosols (27 %), decreasing from a normal value of about 0.54 to ∼ 0.39 cm3 cm−3, the recovery was much slower and took about 8 months for the drought in 2010. At the catchment scale, however, the soil water storage simulated by the PDM model and the drought analysis was not as pronounced. Soil moisture droughts occurred mainly in the dry season in both catchments. The deficit for all cases is small and progressively reduced during the wet season. Vegetation stress periods correspond mainly to the months of September, October and November, which coincides with the dry season. The maximum number of consecutive dry days were reached during the drought of 2009 and 2010 (19 and 22 days), which can be considered to be a long period in the páramo. The main factor in the hydrological response of these experimental catchments is the precipitation relative to the potential evapotranspiration. As the soils never became extremely dry nor close to the wilting point, the soil water storage capacity had a secondary influence.

Using an informational entropy-based metric as a diagnostic of flow duration to drive model parameter identification

Calibration of rainfall-runoff models is made complicated by uncertainties in data, and by the
 arbitrary emphasis placed on various magnitudes of the model residuals by most traditional
 measures of fit. Current research highlights the importance of driving model identification by
 assimilating information from the data. In this paper, we evaluate the potential use of an entropybased
 measure as an objective function or as a model diagnostic in hydrological modelling, with
 particular interest in providing an appropriate quantitative measure of fit to the flow duration curve
 (FDC). The proposed Conditioned Entropy Difference (CED) metric is capable of characterising the
 information in the flow frequency distribution and thereby constrain the model calibration to respect
 this distributional information. Four years of hourly data from the 46.6 km2 Mahurangi catchment,
 NZ, are used to calibrate the 6-parameter Probability Distributed Moisture model. Results are
 analysed using three measures: the proposed entropy-based measure, the Nash-Sutcliffe (NSE),
 and the recently proposed Kling-Gupta efficiency (KGE). We also examine a conditioned entropy
 metric that trades-off and reweights different segments of the FDC to drive model calibration in a
 way that is based on modelling objectives.
 Overall, the entropy-based measure results in good performance in terms of NSE but poor
 performance in terms of KGE. This entropy measure is strongly sensitive to the shape of the flow
 distribution and is, from some viewpoints, the single best descriptor of the FDC. By conditioning
 entropy to respect multiple segments of the FDC, we can reweight entropy to respect those parts of
 the flow distribution of most interest to the modelling application. This approach constrains the
 behavioural parameter space so as to better identify parameters that represent both the “fast” and
 “slow” runoff processes. Use of this importance-weighted, conditioned entropy metric can constrain
 high flow predictions equally well as the NSE and KGE, while simultaneously providing wellconstrained
 low flow predictions that the NSE or KGE are unable to achieve.

Bayesian conditioning of a rainfall‐runoff model for predicting flows in ungauged catchments and under land use changes

A novel method is presented for conditioning rainfall‐runoff models for ungauged catchment and land use impact applications. The method conditions the model on information from multiple regionalized response indices using a formal Bayesian approach. Two indices that hold information about soil type and land use effects are the base flow index from the Hydrology of Soil Type (HOST) classification and curve number from the U.S. Department of Agriculture's Soil Conservation Service soil and land use classification. These indices are used to constrain a five‐parameter probability distributed moisture model for subcatchments of the Wye (grazed grassland) and Severn (mainly afforested) catchments in the United Kingdom. The base flow index and curve number constrain only two of the five model parameters, indicating that ideally, other sources of information would be sought. Nevertheless, the procedure significantly reduces the prior uncertainty in runoff prediction and gives predictions close to those of the calibrated models. For the case study, the introduction of the curve number in addition to the base flow index has only a small effect on model performance and uncertainty; however, it allows a distinction between the effects of soil type and land management for the purpose of scenario analysis. The principal assumptions used in the method are the applicability of the curve number classification system and its mapping to UK soil types and the likelihood function used for Bayesian conditioning.

Flash flood warning based on rainfall thresholds and soil moisture conditions: An assessment for gauged and ungauged basins

The main objective of this paper is to evaluate a threshold-based flash flood warning method, by considering a wide range of climatic and physiographic conditions, and by focusing on ungauged basins. The method is derived from the flash flood guidance (FFG, hereafter) approach. The FFG is the depth of rain of a given duration, taken as uniform in space and time on a certain basin, necessary to cause minor flooding at the outlet of the considered basin. This rainfall depth, which is computed based on a hydrological model, is compared to either real-time-observed or forecasted rainfall of the same duration and on the same basin. If the nowcasted or forecasted rainfall depth is greater than the FFG, then flooding in the basin is considered likely. The study provides an assessment of this technique based on operational quality data from 11 mountainous basins (six nested included in five larger parent basins) located in north-eastern Italy and central France. The model used in this study is a semi-distributed conceptual rainfall–runoff model, following the structure of the PDM (probability distributed moisture) model. Two general questions are addressed: (1) How does the efficiency of the method evolve when the simulation parameters can not be calibrated but must be transposed from parent gauged basins to ungauged basins? (2) How sensitive are the results to the method used to estimate the initial soil moisture status? System performances are evaluated by means of categorical statistics, such as the critical success index (CSI). Results show that overall CSI is equal to 0.43 for the parent basins, where the hydrological model has been calibrated. CSI reduces to 0.28 for the interior basins, when model parameters are transposed from parent basins, and to 0.21, when both model parameters and soil moisture status is transposed from parent basins. Performance differences between FFG and use of time-constant soil moisture status are very high for the parent basins and decrease with decreasing the system accuracy. The percent difference amounts to 53% for the parent basins, to 25% for interior basins with parameter transposition, and to 19% for interior basins with parameter and soil moisture status transposition. These results improve our understanding of the applicability and reliability of this method at various scales and under various scenarios of data availability.

Application of Ensemble Kalman Filter for flood forecasting in Australian rivers

There is a growing interest in understanding the uncertainty in flood forecasting and the resulting flood warnings. This is borne out of the fact that the processes involved in flood forecasting have inherent uncertainties in them. The procedure used in flood forecasting consists of a number of steps. The first step is rainfall measurement and forecasting rainfall during a flood event. The rainfall is then transformed into flow using a combined water balance and runoff-routing model. There are uncertainties associated with rainfall measurement/forecasting, model (conceptualisation and parameters) and flow measurements. All these uncertainties contribute to the uncertainty in the resulting flood forecasts. The Ensemble Kalman Filter (EnKF) enables all these uncertainties to be combined in a systematic way and it has been used by a number of researchers in the past. In this paper, the EnKF with state and parameter updating is used with the Probability Distributed Moisture model to forecast flood events in six rivers located in different parts of Australia. The results showed that the quality of forecasts deteriorated with lead time greater than 6 hours and the peak discharge magnitudes were underestimated. Of the two variations used, state updating performed better than parameter updating.

Short period forecasting of catchment-scale precipitation. Part II: a water-balance storm model for short-term rainfall and flood forecasting

Abstract. A simple two-dimensional rainfall model, based on advection and conservation of mass in a vertical cloud column, is investigated for use in short-term rainfall and flood forecasting at the catchment scale under UK conditions. The model is capable of assimilating weather radar, satellite infra-red and surface weather observations, together with forecasts from a mesoscale numerical weather prediction model, to obtain frequently updated forecasts of rainfall fields. Such data assimilation helps compensate for the simplified model dynamics and, taken together, provides a practical real-time forecasting scheme for catchment scale applications. Various ways are explored for using information from a numerical weather prediction model (16.8 km grid) within the higher resolution model (5 km grid). A number of model variants is considered, ranging from simple persistence and advection methods used as a baseline, to different forms of the dynamic rainfall model. Model performance is assessed using data from the Wardon Hill radar in Dorset for two convective events, on 10 June 1993 and 16 July 1995, when thunderstorms occurred over southern Britain. The results show that (i) a simple advection-type forecast may be improved upon by using multiscan radar data in place of data from the lowest scan, and (ii) advected, steady-state predictions from the dynamic model, using "inferred updraughts", provides the best performance overall. Updraught velocity is inferred at the forecast origin from the last two radar fields, using the mass-balance equation and associated data and is held constant over the forecast period. This inference model proves superior to the buoyancy parameterisation of updraught employed in the original formulation. A selection of the different rainfall forecasts is used as input to a catchment flow forecasting model, the IH PDM (Probability Distributed Moisture) model, to assess their effect on flow forecast accuracy for the 135 km2 Brue catchment in Somerset. Keywords: rainfall forecasting, flood forecasting, weather radar, satellite, storm model

An elevation-dependent snowmelt model for upland Britain

An elevation-dependent snowmelt forecasting model, combining a rainfall-runoff model with a snowmelt module, is developed for use in upland Britain. Here, the dynamic nature of snow cover, and the occurrence of heavy rain along with melt, can exert a considerable influence on major floods. The model comprises the PACK snowmelt model linked to a lumped conceptual rainfall-runoff model, the PDM (Probability Distributed Moisture) model. The PACK snowmelt module conceptualizes the lying snow as being made up of dry snow that has yet to melt and wet snow which has melted but is still held in the snowpack. When the temperature is above the melt threshold the dry snow melts and contributes to the wet snow store. Water is released from the wet snow store at a rate dependent on the proportion of the pack that is melted snow, and is transformed into flow at the basin outlet by the rainfall-runoff model. The variation of temperature with elevation in a catchment and its effect on melt can be incorporated into the model by partitioning the catchment into a finite number of elevation zones. Model performance is generally improved through the use of more zones. This result prompted the development of a snowmelt model that can use either a near-continuous distribution or a finite number of elevation zones derived from a digital terrain model. The new snowmelt model is tested on two upland catchments, Monachyle Burn in Scotland and Trout Beck in northern England. Flow simulation accuracy is compared for a range of choices of elevation zone number in order to determine the optimum number to use for a given catchment. Visual observations of the position of the snowline are also compared with model predictions. Daily snow survey and hourly snow pillow measurements are compared with point model predictions of snow water equivalent. They are also assimilated into the linked snowmelt and rainfall-runoff model so as to improve the accuracy of the flow forecasts. Copyright © 1999 John Wiley & Sons, Ltd.

A grid-based distributed flood forecasting model for use with weather radar data: Part 2. Case studies

Abstract. A simple distributed rainfall-runoff model, configured on a square grid to make best use of weather radar data, was developed in Part 1 (Bell and Moore, 1998). The simple form of the basic model, referred to as the Simple Grid Model or SGM, allows a number of model variants to be introduced, including probability-distributed storage and topographic index representations of runoff production and formulations which use soil survey and land use data. These models are evaluated here on three catchments in the UK: the Rhondda in south Wales, the Wyre in north-west England and the Mole in the Thames Basin near London. Assessment is initially carried out in simulation mode to focus on the conversion of rainfall to runoff as influenced by (i) use of radar or raingauge input, (ii) choice of model variant, and (iii) use of a lumped or distributed model formulation. Weather radar data, in grid square and catchment average form, and raingauge data are used as alternative estimates of rainfall input to the model. Results show that when radar data are of good quality, significant model improvement may be obtained by replacing data from a single raingauge by 2 km grid square radar data. The performance of the Simple Grid Model with optimised isochrones is only marginally improved through the use of different model variants and is generally preferred on account of its simplicity. A more traditional lumped rainfall-runoff model, the Probability-Distributed Moisture model or PDM, is used as a benchmark against which to assess the performance of the distributed models. This proves hard to better, although the distributed formulation of the Grid model proves more reliable for some storm and catchment combinations where spatial effects on runoff response are evident. Assessment is then carried out in updating mode to emulate a real-time forecasting environment. First, a state updating form of the Grid Model is developed and then assessed against an ARMA error-prediction technique. Both state updating and error prediction give much improved model performance when compared with simulation mode results. No one updating technique is superior, with the simulation model formulation having greatest impact on forecast accuracy. However, when the results from the different catchments are considered together it is apparent that in the rapidly responding Rhondda catchment state updating gives slightly better results, while in the slower responding Wyre and Mole catchments, error prediction is slightly superior. This is attributed to the greater difficulty of reliably adjusting states when there are significant time delays associated with the catchment response. In general, the influence of rainfall input type, model variant and distributed versus lumped model reflect the results obtained in simulation mode. Updating doesn't fully compensate for a poor rainfall input or a deficient rainfall-runoff model formulation, especially for longer forecast lead times.