Multisite generalization of a daily stochastic precipitation generation model

The familiar chain-dependent-process stochastic model of daily precipitation, consisting of a two-state, first-order Markov chain for occurrences and a mixed exponential distribution for nonzero amounts, is extended to simultaneous simulation at multiple locations by driving a collection of individual models with serially independent but spatially correlated random numbers. The procedure is illustrated for a network of 25 locations in New York state, with interstation separations ranging approximately from 10 to 500 km. The resulting process reasonably reproduces various aspects of the joint distribution of daily precipitation observations at the modeled locations. The mixed exponential distributions, in addition to providing substantially better fits than the more conventional gamma distributions, are convenient for representing the tendency for smaller amounts at locations near the edges of wet areas. Means, variances, and interstation correlations of monthly precipitation totals are also well reproduced. In addition, the use of mixed exponential rather than gamma distributions yields interannual variability in the synthetic series that is much closer to the observed.     

Driving a lumped hydrological model with precipitation output from weather generators of different complexity

ABSTRACT

This paper deals with the question of whether a lumped hydrological model driven with lumped daily precipitation time series from a univariate single-site weather generator can produce equally good results compared to using a multivariate multi-site weather generator, where synthetic precipitation is first generated at multiple sites and subsequently lumped. Three different weather generators were tested: a univariate “Richardson type” model, an adapted univariate Richardson type model with an improved reproduction of the autocorrelation of precipitation amounts and a semi-parametric multi-site weather generator. The three modelling systems were evaluated in two Alpine study areas by comparing the hydrological output with respect to monthly and daily statistics as well as extreme design flows. The application of a univariate Richardson type weather generator to lumped precipitation time series requires additional attention. Established parametric distribution functions for single-site precipitation turned out to be unsuitable for lumped precipitation time series and led to a large bias in the hydrological simulations. Combining a multi-site weather generator with a hydrological model produced the least bias.     

Climate Change Projections Based on GCM-Simulated Daily Data

Three-dimensional general circulation models (GCMs) are 'state-of-the-art' tools for projecting possible changes in climate. Scenarios constructed for the Czech Republic are based on daily outputs of the ECHAM-GCM in the central European region. Essential findings, derived from validating, procedures are summarized and changes in variables between the control and perturbed experiments are examined. The resulting findings have been used in selecting the most proper methods of generating climate change projections for assessing possible hydrological and agricultural impacts of climate change in selected exposure units. The following weather variables have been studied: Daily extreme temperatures, daily mean temperature, daily sum of global solar radiation, and daily precipitation amounts. Due to some discrepancies revealed, the temperature series for changed climate conditions (2×CO ₂ ) have been created with the help of temperature differences between the control and perturbed runs, and the precipitation series have been derived from an incremental scenario based on an intercomparison of the GCMs' precipitation performance in the region. Solar radiation simulated by the ECHAM was not available and, therefore, it was generated using regression techniques relating monthly means of daily extreme temperatures and global radiation sums. The scenarios published in the paper consist of monthly means of all temperatures, their standard deviations, and monthly means of solar radiation and precipitation amounts. Daily weather series, the necessary input to impact models, are created (i) by the additive or multiplicative modification of observed weather daily series or (ii) by generating synthetic time series with the help of a weather generator whose parameters have been modified in accord with the suggested climate change scenarios.     

IMAGE: a multivariate multi-site stochastic weather generator for European weather and climate

Capturing the spatial and temporal correlation of multiple variables in a weather generator is challenging. A new massively multi-site, multivariate daily stochastic weather generator called IMAGE is presented here. It models temperature and precipitation variables as latent Gaussian variables with temporal behaviour governed by an auto-regressive model whose residuals and parameters are correlated through resampling of principle component time series of empirical orthogonal function modes. A case study using European climate data demonstrates the model’s ability to reproduce extreme events of temperature and precipitation. The ability to capture the spatial and temporal extent of extremes using a modified Climate Extremes Index is demonstrated. Importantly, the model generates events covering not observed temporal and spatial scales giving new insights for risk management purposes.     

A perfect prognosis approach for daily precipitation series in consideration of space–time correlation structure

Downscaling techniques are the required tools to link the global climate model outputs provided at a coarse grid resolution to finer scale surface variables appropriate for climate change impact studies. Besides the at-site temporal persistence, the downscaled variables have to satisfy the spatial dependence naturally observed between the climate variables at different locations. Furthermore, the precipitation spatial intermittency should be fulfilled. Because of the complexity in describing these properties, they are often ignored, which can affect the effectiveness of the hydrologic process modeling. This study is a continuation of the work by Khalili and Nguyen (Clim Dyn 49(7–8):2261–2278.  https://doi.org/10.1007/s00382-016-3443-6, 2017) regarding the multi-site statistical downscaling of daily precipitation series. Different approach of multi-site statistical downscaling based on the concept of the spatial autocorrelation is presented in this paper. This approach has proven to give effective results for multi-site multivariate statistical downscaling of daily extreme temperature time series (Khalili et al. in Int J Climatol 33:15–32.  https://doi.org/10.1002/joc.3402, 2013). However, more challenges are presented by the precipitation variable because of the high spatio-temporal variability and intermittency. The proposed approach consists of logistic and multiple regression models, linking the global climate predictors to the precipitation occurrences and amounts respectively, and using the spatial autocorrelation concept to reproduce the spatial dependence observed between the precipitation series at different sites. An empirical technique has also been involved in this approach in order to fulfill the precipitation intermittency property. The proposed approach was performed using observed daily precipitation data from ten weather stations located in the southwest region of Quebec and southeast region of Ontario in Canada, and climate predictors from the NCEP/NCAR (National Centers for Environmental Prediction/National Centre for Atmospheric Research) reanalysis dataset. The results have proven the ability of the proposed approach to adequately reproduce the observed precipitation occurrence and amount characteristics, temporal and spatial dependence, spatial intermittency and temporal variability.     

Assessment of the effectiveness of a multi-site stochastic weather generator on hydrological modelling in the Red Deer River watershed,Canada

ABSTRACT

To improve the convergence of multiple-site weather generators (SWGs) based on the brute force algorithm (MBFA), a genetic algorithm (GA) is proposed to search the overall optimal correlation matrix. Precipitation series from weather generators are used as input to the hydrological model, the soil and water assessment tool (SWAT), to generate runoff over the Red Deer watershed, Canada for further runoff analysis. The results indicate that the SWAT model using SWG-generated data accurately represents the mean monthly streamflow for most of the months. The multi-site generators were capable of better representing the monthly streamflow variability, which was notably underestimated by the single-site version. In terms of extreme flows, the proposed method reproduced the observed extreme flow with smaller bias than MBFA, while the single-site generator significantly underestimated the annual maximum flows due to its poor capability in addressing partial precipitation correlations.     

Simulation of historical temperatures using a multi‐site,multivariate block resampling algorithm with perturbation

Stochastic weather generators have evolved as tools for creating long time series of synthetic meteorological data at a site for risk assessments in hydrologic and agricultural applications. Recently, their use has been extended as downscaling tools for climate change impact assessments. Non‐parametric weather generators, which typically use a K‐nearest neighbour (K‐NN) resampling approach, require no statistical assumptions about probability distributions of variables and can be easily applied for multi‐site use. Two characteristics of traditional K‐NN models result from resampling daily values: (1) temporal correlation structure of daily temperatures may be lost, and (2) no values less than or exceeding historical observations can be simulated. Temporal correlation in simulated temperature data is important for hydrologic applications. Temperature is a major driver of many processes within the hydrologic cycle (for example, evaporation, snow melt, etc.) that may affect flood levels. As such, a new methodology for simulation of climate data using the K‐NN approach is presented (named KnnCAD Version 4). A block resampling scheme is introduced along with perturbation of the reshuffled daily temperature data to create 675 years of synthetic historical daily temperatures for the Upper Thames River basin in Ontario, Canada. The updated KnnCAD model is shown to adequately reproduce observed monthly temperature characteristics as well as temporal and spatial correlations while simulating reasonable values which can exceed the range of observations. Copyright © 2012 John Wiley & Sons, Ltd.     

Hydrological effects of climate change,groundwater withdrawal,and land use in a small Korean watershed

The effects of variability in climate and watershed (groundwater withdrawal and land use) on dry‐weather streamflows were investigated using SWAT (Soil and Water Assessment Tool). The equation to predict the total runoff (TR) using climate data was derived from simulation results for 30 years by multiple regression analysis. These may be used to estimate effects of various climate variations (precipitation during the dry period, precipitation during the previous wet period, solar radiation, and maximum temperature). For example, if daily average maximum temperature increases by 3 °C, TR during the dry period will decrease by 27·9%. Similarly, groundwater withdrawals strongly affect streamflow during the dry period. However, land use changes (increasing urbanization) within the forested watershed do not appear to significantly affect TR during the dry period. Finally, a combined equation was derived that describes the relationships between the TR during the dry period and the climate, groundwater withdrawal and urban area proportion in a small monsoon watershed. This equation will be effective to predict the water availability during the dry periods in the future since it is closely related to changes of temperature, precipitation, solar radiation, urban area ratio, and groundwater withdrawal quantity. Copyright © 2007 John Wiley & Sons, Ltd.     

Multivariate nonparametric resampling scheme for generation of daily weather variables

A nonparametric resampling technique for generating daily weather variables at a site is presented. The method samples the original data with replacement while smoothing the empirical conditional distribution function. The technique can be thought of as a smoothed conditional Bootstrap and is equivalent to simulation from a kernel density estimate of the multivariate conditional probability density function. This improves on the classical Bootstrap technique by generating values that have not occurred exactly in the original sample and by alleviating the reproduction of fine spurious details in the data. Precipitation is generated from the nonparametric wet/dry spell model as described in Lall et al. [1995]. A vector of other variables (solar radiation, maximum temperature, minimum temperature, average dew point temperature, and average wind speed) is then simulated by conditioning on the vector of these variables on the preceding day and the precipitation amount on the day of interest. An application of the resampling scheme with 30 years of daily weather data at Salt Lake City, Utah, USA, is provided.     

A hybrid stochastic-weather-generation method for temporal disaggregation of precipitation with consideration of seasonality and within-month variations

Linking atmospheric and hydrological models is challenging because of a mismatch of spatial and temporal resolutions in which the models operate: dynamic hydrological models need input at relatively fine temporal (daily) scale, but the outputs from general circulation models are usually not realistic at the same scale, even though fine scale outputs are available. Temporal dimension downscaling methods called disaggregation are designed to produce finer temporal-scale data from reliable larger temporal-scale data. Here, we investigate a hybrid stochastic weather-generation method to simulate a high-frequency (daily) precipitation sequence based on lower frequency (monthly) amounts. To deal with many small precipitation amounts and capture large amounts, we divide the precipitation amounts on rainy days (with non-zero precipitation amounts) into two states (named moist and wet states, respectively) by a pre-defined threshold and propose a multi-state Markov chain model for the occurrences of different states (also including non-rain days called dry state). The truncated Gamma and censored extended Burr XII distributions are then employed to model the precipitation amounts in the moist and wet states, respectively. This approach avoids the need to deal with discontinuity in the distribution, and ensures that the states (dry, moist and wet) and corresponding amounts in rainy days are well matched. The method also considers seasonality by constructing individual models for different months, and monthly variation by incorporating the low-frequency amounts as a model predictor. The proposed method is compared with existing models using typical catchment data in Australia with different climate conditions (non-seasonal rainfall, summer rainfall and winter rainfall patterns) and demonstrates better performances under several evaluation criteria which are important in hydrological studies.     

Modelling streamflow trends for a watershed with limited data: case of the Litani basin,Lebanon

Abstract

Streamflow variability in the Upper and Lower Litani basin, Lebanon was modelled as there is a lack of long-term measured runoff data. To simulate runoff and streamflow, daily rainfall was derived using a stochastic rainfall generation model and monthly rainfall data. Two distinct synthetic rainfall models were developed based on a two-part probabilistic distribution approach. The rainfall occurrence was described by a Markov chain process, while the rainfall distribution on wet days was represented by two different distributions (i.e. gamma and mixed exponential distributions). Both distributions yielded similar results. The rainfall data were then processed using water balance and routing models to generate daily and monthly streamflow. Compared with measured data, the model results were generally reasonable (mean errors ranging from 0.1 to 0.8?m³/s at select locations). Finally, the simulated monthly streamflow data were used to investigate discharge trends in the Litani basin during the 20th century using the Mann-Kendall and Sen slope nonparametric trend detection methods. A significant drying trend of the basin was detected, reaching a streamflow reduction of 0.8 and 0.7 m³/s per decade in January for the Upper and Lower basin, respectively.

Editor D. Koutsoyiannis; Associate editor Sheng Yue

Citation Ramadan, H.H., Beighley, R.E., and Ramamurthy, A.S., 2012. Modelling streamflow trends for a watershed with limited data: case of the Litani basin, Lebanon. Hydrological Sciences Journal, 57 (8), 1516–1529.     

Dynamic stream network intermittence explains emergent dissolved organic carbon chemostasis in headwaters

Dissolved organic carbon (DOC) concentrations vary among headwaters, with variation typically decreasing with watershed area. We hypothesized that streamflow intermittence could be an important source of variation in DOC concentrations across a small watershed, through (a) temporal legacies of drying on organic matter accumulation and biotic communities and (b) spatial patterns of connectivity with DOC sources. To test these hypotheses, we conducted three synoptic water chemistry sampling campaigns across a 25.5‐km² watershed in south‐eastern Idaho during early spring, late summer, and late fall. Using changepoint analysis, we found that DOC variability collapsed at a consistent location (watershed areas ~1.3 to ~1.8 km²) across seasons, which coincided with the watershed area where variability in streamflow intermittence collapsed (~1.5 km²). To test hypothesized mechanisms through which intermittence may affect DOC, we developed temporal, spatial, and spatio‐temporal metrics of streamflow intermittence and related these to DOC concentrations. Streamflow intermittence was a strong predictor of DOC across seasons, but different metrics predicted DOC depending on season. Seasonal changes in the effects of intermittence on DOC reflected seasonal changes from instream to flowpath controls. A metric that captured spatial connectivity to sources significantly predicted DOC during high flows, when DOC is typically controlled by transport. In contrast, a reach‐scale temporal metric of intermittence predicted DOC during the late growing season, when DOC is typically controlled by instream processes and when legacy effects of drying (e.g., diminished biological communities) would likely affect DOC. The effects of intermittence on DOC extend beyond temporal legacies at a point. Our results suggest that legacy effects of intermittence do not propagate downstream in this system. Instead, snapshots of spatial patterns of intermittence upstream of a reach are critical for understanding spatial patterns of DOC through connectivity to DOC sources, and these processes drive patterns of DOC even in perennial reaches.     

Data time step to estimate snowpack accumulation at select United States meteorological stations

When estimating the water balance for a cold region watershed, that is one that receive a substantial portion of its annual precipitation as snow, accumulation and other winter hydrological processes must be considered. For many of theses watersheds, all but the most fundamental meteorological data (temperature and precipitation), are either not measured or not measured at a reasonable time step. Of particular importance are wind data, as wind influences underestimates of precipitation due to wind undercatch and losses of snow from the snowpack, specifically, snowpack sublimation, and the occurrence and magnitude of blowing snow. Estimating snow accumulation to yield snowmelt amounts requires summing of gauged precipitation and gauge undercatch, and subtracting minus snowpack sublimation and blowing snow transport. The first two components are computed on a daily time step, while the latter two are computed on an hourly time step. From five National Weather Service meteorological stations (Pullman WA, Rawlins WY, Leadville CO, Rhinelander WI, Syracuse NY), the variations in computed snowpack mass losses minus undercatch using data at different time intervals show that at most sites it is difficult to use monthly time steps for computations derived using hourly or daily data. At the relative dry and cold Leadville, Colorado site the computations were transferable between time steps. Copyright © 2007 John Wiley & Sons, Ltd.     

On the computation of area probabilities based on a spatial stochastic model for precipitation cells and precipitation amounts

A main task of weather services is the issuing of warnings for potentially harmful weather events. Automated warning guidances can be derived, e.g., from statistical post-processing of numerical weather prediction using meteorological observations. These statistical methods commonly estimate the probability of an event (e.g. precipitation) occurring at a fixed location (a point probability). However, there are no operationally applicable techniques for estimating the probability of precipitation occurring anywhere in a geographical region (an area probability). We present an approach to the estimation of area probabilities for the occurrence of precipitation exceeding given thresholds. This approach is based on a spatial stochastic model for precipitation cells and precipitation amounts. The basic modeling component is a non-stationary germ-grain model with circular grains for the representation of precipitation cells. Then, we assign a randomly scaled response function to each precipitation cell and sum these functions up to obtain precipitation amounts. We derive formulas for expectations and variances of point precipitation amounts and use these formulas to compute further model characteristics based on available sequences of point probabilities. Area probabilities for arbitrary areas and thresholds can be estimated by repeated Monte Carlo simulation of the fitted precipitation model. Finally, we verify the proposed model by comparing the generated area probabilities with independent rain gauge adjusted radar data. The novelty of the presented approach is that, for the first time, a widely applicable estimation of area probabilities is possible, which is based solely on predicted point probabilities (i.e., neither precipitation observations nor further input of the forecaster are necessary). Therefore, this method can be applied for operational weather predictions.     

Evaluating spatio-temporal representations in daily rainfall sequences from three stochastic multi-site weather generation approaches

Many hydrological and agricultural studies require simulations of weather variables reflecting observed spatial and temporal dependence at multiple point locations. This paper assesses three multi-site daily rainfall generators for their ability to model different spatio-temporal rainfall attributes over the study area. The approaches considered consist of a multi-site modified Markov model (MMM), a reordering method for reconstructing space–time variability, and a nonparametric k-nearest neighbour (KNN) model. Our results indicate that all the approaches reproduce adequately the observed spatio-temporal pattern of the multi-site daily rainfall. However, different techniques used to signify longer time scale observed temporal and spatial dependences in the simulated sequences, reproduce these characteristics with varying successes. While each approach comes with its own advantages and disadvantages, the MMM has an overall advantage in offering a mechanism for modelling varying orders of serial dependence at each point location, while still maintaining the observed spatial dependence with sufficient accuracy. The reordering method is simple and intuitive and produces good results. However, it is primarily driven by the reshuffling of the simulated values across realisations and therefore may not be suited in applications where data length is limited or in situations where the simulation process is governed by exogenous conditioning variables. For example, in downscaling studies where KNN and MMM can be used with confidence.     

A) A. I. H. S. / A) A. I. H. S.

Abstract

A new method is presented to generate stationary multi-site hydrological time series. The proposed method can handle flexible time-step length, and it can be applied to both continuous and intermittent input series. The algorithm is a departure from standard decomposition models and the Box-Jenkins approach. It relies instead on the recent advances in statistical science that deal with generation of correlated random variables with arbitrary statistical distribution functions. The proposed method has been tested on 11 historic weekly input series, of which the first seven contain flow data and the last four have precipitation data. The article contains an extensive review of the results.

Editor D. Koutsoyiannis

Citation Ilich, N., 2014. An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series. Hydrological Sciences Journal, 59 (1), 85–98.     

Using the Climate Forecast System Reanalysis as weather input data for watershed models

Obtaining representative meteorological data for watershed‐scale hydrological modelling can be difficult and time consuming. Land‐based weather stations do not always adequately represent the weather occurring over a watershed, because they can be far from the watershed of interest and can have gaps in their data series, or recent data are not available. This study presents a method for using the Climate Forecast System Reanalysis (CFSR) global meteorological dataset to obtain historical weather data and demonstrates the application to modelling five watersheds representing different hydroclimate regimes. CFSR data are available globally for each hour since 1979 at a 38‐km resolution. Results show that utilizing the CFSR precipitation and temperature data to force a watershed model provides stream discharge simulations that are as good as or better than models forced using traditional weather gauging stations, especially when stations are more than 10 km from the watershed. These results further demonstrate that adding CFSR data to the suite of watershed modelling tools provides new opportunities for meeting the challenges of modelling un‐gauged watersheds and advancing real‐time hydrological modelling. Copyright © 2013 John Wiley & Sons, Ltd.     

Impact of number of realizations on the suitability of simulated weather data for hydrologic and environmental applications

Stochastic weather generators are widely used in hydrological, environmental, and agricultural applications to simulate weather time series. However, such stochastic models produce random outputs hence the question on how representative the generated data are if obtained from only one simulation run (realization) as is common practice. In this study, the impact of different numbers of realizations (1, 25, 50, and 100) on the suitability of generated weather data was investigated. Specifically, 50 years of daily precipitation, and maximum and minimum temperatures were generated for three weather stations in the Western Lake Erie Basin (WLEB), using three widely used weather generators, CLIGEN, LARSWG and WeaGETS. Generated results were compared with 50 years of observed data. For all three generators, the analyses showed that one realization of data for 50 years of daily precipitation, and maximum and minimum temperatures may not be representative enough to capture essential statistical characteristics of the climate. Results from the three generators captured the essential statistical characteristics of the climate when the number of realizations was increased from 1 to 25, 50 or 100. Performance did not improve substantially when realizations were increased above 25. Results suggest the need for more than a single realization when generating weather data and subsequently utilizing in other models, to obtain suitable representations of climate.     

Multi-site bias correction of climate model outputs for hydro-meteorological impact studies: An application over a watershed in China

Bias correction methods remove systematic differences in the distributional properties of climate model outputs with respect to observations, often as a means of pre-processing model outputs for use in hydrological impact studies. Traditionally, bias correction is applied at each weather station individually, neglecting the dependence that exists between different sites, which could negatively affect simulations from a distributed hydrological model. In this study, three multi-variate bias correction (MBC) methods—initially proposed to correct the inter-variable correlation or multi-variate dependence of climate model outputs—are used to correct biases in distributional properties and spatial dependence at multiple weather stations. To reveal the benefits of correcting spatial dependence, two distribution-based single-site bias correction methods are used for comparison. The effects of multi-site correction on hydro-meteorological extremes are assessed by driving a distributed hydrological model and then evaluating the model performance in terms of several meteorological and hydrological extreme indices. The results show that the multi-site bias correction methods perform well in reducing biases in spatial correlation measures of raw global climate model outputs. In addition, the multi-site methods consistently reproduce watershed-averaged meteorological variables better than single-site methods, especially for extreme values. In terms of representing hydrological extremes, the multi-site methods generally perform better than the single-site methods, although the benefits vary according to the hydrological index. However, when applying the multi-site methods, the original temporal sequence of precipitation occurrence may be altered to some extent. Overall, all multi-site bias correction methods are able to reproduce the spatial correlation of observed meteorological variables over multiple stations, which leads to better hydrological simulations, especially for extremes. This study emphasizes the necessity of considering spatial dependence when applying bias correction to ccc outputs and hydrological impact studies.     

An entropy-based investigation into the variability of precipitation

Employing the entropy concept spatial and temporal variability of precipitation time series were investigated for the State of Texas, USA. Marginal entropy was used to investigate the variability associated with monthly, seasonal and annual time series. Also, apportionment entropy and intensity entropy were used for investigating the intra-annual and decadal distributions of monthly and annual precipitation amounts and numbers of rainy days within a year and decade respectively. Finally, the Hurst exponent and the Mann–Kendall test were used to evaluate the long-term persistence and trend in the variability of precipitation. Distinct spatial patterns in annual series and different seasons were observed. The variability of precipitation amount as well as number of rainy days within a year increased from east to west of Texas. The results also indicated that highly disorderliness in the amount of precipitation and number of rainy days caused severe droughts during the 1950’s in whole of Texas.