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.     

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.     

A two steps disaggregation method for highly seasonal monthly rainfall

 The need for high resolution rainfall data at temporal scales varying from daily to hourly or even minutes is a very important problem in hydrology. For many locations of the world, rainfall data quality is very poor and reliable measurements are only available at a coarse time resolution such as monthly. The purpose of this work is to apply a stochastic disaggregation method of monthly to daily precipitation in two steps: 1. Initialization of the daily rainfall series by using the truncated normal model as a reference distribution. 2.␣Restructuring of the series according to various time series statistics (autocorrelation function, scaling properties, seasonality) by using a Markov chain Monte Carlo based algorithm. The method was applied to a data set from a rainfall network of the central plains of Venezuela, in where rainfall is highly seasonal and data availability at a daily time scale or even higher temporal resolution is very limited. A detailed analysis was carried out to study the seasonal and spatial variability of many properties of the daily rainfall as scaling properties and autocorrelation function in order to incorporate the selected statistics and their annual cycle into an objective function to be minimized in the simulation procedure. Comparisons between the observed and simulated data suggest the adequacy of the technique in providing rainfall sequences with consistent statistical properties at a daily time scale given the monthly totals. The methodology, although highly computationally intensive, needs a moderate number of statistical properties of the daily rainfall. Regionalization of these statistical properties is an important next step for the application of this technique to regions in where daily data is not available.     

Prediction of hydrological drought durations based on Markov chains: case of the Canadian prairies

Abstract

Hydrological drought durations (lengths) in the Canadian prairies were modelled using the standardized hydrological index (SHI) sequences derived from the streamflow series at annual, monthly and weekly time scales. The rivers chosen for the study present high levels of persistence (as indicated by values exceeding 0.95 for lag-1 autocorrelation in weekly SHI sequences), because they encompass large catchment areas (2210–119 000 km²) and traverse, or originate in, lakes. For such rivers, Markov chain models were found to be simple and efficient tools for predicting the drought duration (year, month, or week) based on annual, monthly and weekly SHI sequences. The prediction of drought durations was accomplished at threshold levels corresponding to median flow (Q50) (drought probability, q?=?0.5) to Q95 (drought probability, q?=?0.05) exceedence levels in the SHI sequences. The first-order Markov chain or the random model was found to be acceptable for the prediction of annual drought lengths, based on the Hazen plotting position formula for exceedence probability, because of the small sample size of annual streamflows. On monthly and weekly time scales, the second-order Markov chain model was found to be satisfactory using the Weibull plotting position formula for exceedence probability. The crucial element in modelling drought lengths is the reliable estimation of parameters (conditional probabilities) of the first- and second-order persistence, which were estimated using the notions implicit in the discrete autoregressive moving average class of models. The variance of drought durations is of particular significance, because it plays a crucial role in the accurate estimation of persistence parameters. Although, the counting method of the estimation of persistence parameters was found to be unsatisfactory, it proved useful in setting the initial values and also in subsequent adjustment of the variance-based estimates of persistence parameters. At low threshold levels corresponding to q < 0.20, even the first-order Markov chain can be construed as a satisfactory model for predicting drought durations based on monthly and weekly SHI sequences.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Sharma, T.C. and Panu, U.S., 2012. Prediction of hydrological drought durations based on Markov chains in the Canadian prairies. Hydrological Sciences Journal, 57 (4), 705–722.     

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.     

Simulated changes due to global warming in the variability of precipitation, and their interpretation using a gamma-distributed stochastic model

The interannual variability of monthly mean January and July precipitation and its possible change due to global warming are assessed using a five-member ensemble of climate for the period 1871–2100, simulated by the CSIRO Mark 2 global coupled atmosphere–ocean model. In the 1961–1990 climate, for much of the middle to high latitudes the standard deviation of precipitation for both months is roughly proportional to the mean, with the coefficient of variation (C) typically 0.3–0.5. The variability there is shown to be largely consistent with that from a first-order Markov chain model of the daily rainfall occurrence, with the distribution of wet-day amounts approximated by a gamma distribution. Global distributions of Mark 2-based parameters of this stochastic model, commonly used in weather generators, are presented. In low latitudes, however, the variability from the coupled model is typically double that anticipated by the stochastic model, as quantified by an ‘overdispersion ratio’. C often exceeds one at subtropical locations, where rain is less frequent, but sometimes relatively heavy.The standard deviation of monthly mean precipitation S generally increases as the global model warms, with the global mean S in 2071–2100 in January (July) being 9.0% (11.5%) larger than in 1961–1990. Decreases in some subtropical locations occur, particularly where mean precipitation decreases. The global pattern of overdispersion is largely unchanged, however, and the changes in S can be related to those in the stochastic model parameters. Much of the increase in S is associated with increases in the scale parameter of the gamma distribution of wet-day amounts. Changes in C, which is unaffected by this parameter, are generally small. Increases in C in several subtropical bands and over northern midlatitude land in July are related to a decreased frequency of precipitation, and (to a lesser degree) changes in the gamma shape parameter. Some potential applications of the results to downscaling are discussed, and illustrated using observed rainfall from southeast Australia.     

Combined analysis of precipitation and water deficit for drought hazard assessment

Abstract

The combined analysis of precipitation and water scarcity was done with the use of the Standardized Precipitation Index (SPI) and the Standardized Runoff Index (SRI), developed as a monthly, two-variable SPI-SRI indicator to identify different classes of hydrometeorological conditions. Stochastic analysis of a long-term time series (1966–2005) of monthly SPI-SRI indicator values was performed using a first-order Markov chain model. This provided characteristics of regional features of drought formation, evolution and persistence, as well as tools for statistical long-term drought hazard prediction. The study was carried out on two subbasins of the Odra River (Poland) of different orography and land use: the mountainous Nysa K?odzka basin and the lowland, agricultural Prosna basin. Classification obtained with the SPI-SRI indicator was compared with the output from the NIZOWKA model that provided identification of hydrological drought events including drought duration and deficit volume. Severe and long-duration droughts corresponded to SPI-SRI Class 3 (dry meteorological and dry hydrological), while severe but short-term droughts (lasting less than 30 days) corresponded to SPI-SRI Class 4 (wet meteorological and dry hydrological). The results confirm that, in Poland, meteorologically dry conditions often shift to hydrologically dry conditions within the same month, droughts rarely last longer than 2 months and two separate drought events can be observed within the same year.     

Significance of AIC differences for precipitation intensity distributions

Chain dependent models for daily precipitation typically model the occurrence process as a Markov chain and the precipitation intensity process using one of several probability distributions. It has been argued that the mixed exponential distribution is a superior model for the rainfall intensity process, since the value of its information criterion (Akaike information criterion or Bayesian information criterion) when fit to precipitation data is usually less than the more commonly used gamma distribution. The differences between the criterion values of the best and lesser models are generally small relative to the magnitude of the criterion value, which raises the question of whether these differences are statistically significant. Using a likelihood ratio statistic and nesting the gamma and mixed exponential distributions in a parent distribution, we show indirectly that generally the superiority of the mixed exponential distribution over the gamma distribution for modeling precipitation intensity is statistically significant. Comparisons are also made with a common-a gamma model, which are less informative.     

Relation between the monthly sums of sunshine and global radiation

Summary The statistical treatment of the dependence of monthly sums of global radiation on the monthly sums of sunshine at the stations of Hradec Králové, Bratislava — Koliba and Hurbanovo is presented. The parameters of linear and quadratic regression are derived for the said stations and for the individual months of the year. Drawing on the statistical analysis of the initial data sets, the accuracy and reliability of the mentioned regression relations are critically evaluated.     

Über die Bestimmung des Schneeanteils am Niederschlag

Zusammenfassung Der nach verschiedenen Verfahren berechnete Schneeantei am Gesamtniederschlag wird mit dem nach Registrierungen der winterlichen Niederschläge ermittelten wahrscheinlichen Schneeanteil verglichen. Ausgehend von den Niederschlagssummen ergibt sich gute Uebereinstimmung, wenn bei Mischniederschlägen die Hälfte dem Schneeanteil zugerechnet wird. Ausgehend von der Neuschneehöhe zeigt sich die geringste Abweichung, wenn der Anteil aus reinem Schnee der Niederschlagsmessung, der Anteil aus Mischniederschlägen dem Wasserwert der Neuschneedecke gleichgesetzt wird, für dessen Errechnung neue Monatsmittel der Schneedichte aus Mischniederschlägen mitgeteilt werden.

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Summary The part of snow of the total precipitation is finding out by different former methods and compounded with the probable part of snow according the records of the winter precipitations. Using the precipitation sums of every part it results a good concordance when the half of sleet is attributed to the part of snow. Going out from the depth of new snowcover the least deviation is demonstrated, if the part of pure new snow is taken from the precipitation measurement in the rain gage, and the part of sleet is equalized to the water equivalent of new snow cover. For these calculations new monthly means of density of snow from sleet are given to information.

     

Einfluss korrelativer Abhängigkeiten auf simulierte Zeitreihen: Empfindlichkeit des Fiering-Modells gegenüber Veränderungen der Korrelationsstruktur

The simulation of time series is based on estimated statistical parameters of the empirical time series. The Fiering Model generating monthly sums of streamflows is used as an example for the simulation in order to account for the error of the model, theoretically and practically, caused by statistically inprecise parameter estimation. The sensitivity of this model, especially to the correlation coefficients, is analyzed by means of systematic variations of the correlation coefficients, since these are most affected by the error of estimation. No significant dependency could be found comparing the empirical and simulated parameters mean, standard deviation, and skewness. From this follows, that the importance of the correlation coefficients in the Fiering Model is generally overestimated. The results are given for monthly sums of streamflows at four stations with different hydrological characteristics.      

Precipitation as a proxy for climate variables: application for hydrological modelling

It has been proposed that linear regression curves can be used to estimate monthly climate variables from observed precipitation. This approach was explored by applying the MGB hydrological model to the Paraná Basin (Brazil). Linear regressions were obtained for 54 climate gauges, and most of them showed at least six months of significant correlation between monthly climate variables (sunlight hours and relative humidity) and precipitation. The regression equations were applied to 5201 raingauges to estimate monthly climate variables and evapotranspiration, and the results were compared with a scenario using long-term climate averages only. The main differences occurred in wetter periods, where negative correlations between monthly precipitation and evapotranspiration were obtained when using precipitation as a proxy. Long-term changes in the hydrological regime were assessed and showed that the effect of precipitation on relative humidity and sunlight hours seems to have a minor effect on the alterations observed in river discharge in the Paraná Basin.     

Semi-empirical prediction method for monthly precipitation prediction based on environmental factors and comparison with stochastic and machine learning models

ABSTRACT

Precipitation prediction is central in hydrology and water resources planning and management. This paper introduces a semi-empirical predictive model to predict monthly precipitation and compares its predictive skill with those of machine learning (ML) methods. The stochastic method presented herein estimates monthly precipitation with one-step-ahead prediction properties. The ML predictive skill of the algorithms is evaluated by predicting monthly precipitation relying on the statistical association between precipitation and environmental and topographic factors. The semi-empirical predictive model features non-negative matrix factorization (NMF) for investigating the influence of multiple predictor variables on precipitation. The semi-empirical predictive model’s parameters are optimized with the hybrid genetic algorithm (GA) and Levenberg-Marquardt algorithm (LM), or GALMA, yielding a validated model with high predictive skill. The methodologies are illustrated with data from Hubei Province, China, which comprise 27 meteorological station datasets from 1988–2017. The empirical results provide valuable insights for developing semi-empirical rainfall prediction models.     

Analysis of hydrological seasonality across northern catchments using monthly precipitation–runoff polygon metrics

Abstract

Seasonality is an important hydrological signature for catchment comparison. Here, the relevance of monthly precipitation–runoff polygons (defined as scatter points of 12 monthly average precipitation–runoff value pairs connected in the chronological monthly sequence) for characterizing seasonality patterns was investigated to describe the hydrological behaviour of 10 catchments spanning a climatic gradient across the northern temperate region. Specifically, the research objectives were to: (a) discuss the extent to which monthly precipitation–runoff polygons can be used to infer active hydrological processes in contrasting catchments; (b) test the ability of quantitative metrics describing the shape, orientation and surface area of monthly precipitation–runoff polygons to discriminate between different seasonality patterns; and (c) examine the value of precipitation–runoff polygons as a basis for catchment grouping and comparison. This study showed that some polygon metrics were as effective as monthly average runoff coefficients for illustrating differences between the 10 catchments. The use of precipitation–runoff polygons was especially helpful to look at the dynamics prevailing in specific months and better assess the coupling between precipitation and runoff and their relative degree of seasonality. This polygon methodology, linked with a range of quantitative metrics, could therefore provide a new simple tool for understanding and comparing seasonality among catchments.

Editor Z.W. Kundzewicz; Associate editor K. Heal

Citation Ali, G., Tetzlaff, D., Kruitbos, L., Soulsby, C., Carey, S., McDonnell, J., Buttle, J., Laudon, H., Seibert, J., McGuire, K., and Shanley, J., 2013. Analysis of hydrological seasonality across northern catchments using monthly precipitation–runoff polygon metrics. Hydrological Sciences Journal, 59 (1), 56–72.     

Detection of ENSO‐influence on the monthly precipitation in South Korea

During the latest several decades, there has been considerable interest in revealing the relationship between El Niño–southern oscillation (ENSO) and hydro‐meteorological variables. The oscillation is characterized by a simple index, the southern oscillation index (SOI). However, thus far, there is little evidence for the influence of ENSO in Korea and Japan. The influence of ENSO has also been studied in South Korea, but the estimated results are still qualitative and show an indirect relationship between ENSO and hydro‐meteorological variables. In this study we use simple approaches to reveal the quantitative and direct correlation between SOI and the monthly precipitation at five stations distributed over South Korea. The monthly precipitation data are transformed into nonexceedance probability time series because the data cannot be normally distributed by applying the usual transformations. The SOI is classified into five categories according to their values. Additionally, to detect the nonlinear relationship between categorized SOI and nonexceedance probability of the monthly precipitation, we use Kendall's τ, a nonparametric test. Significant correlations between the categorized SOI and the transformed precipitation are detected. Generally, the monthly precipitation is influenced by a La Niña event with a lag time of 4 months for southern coastal areas and a lag time of 5 months for middle to high regions in South Korea. Copyright © 2005 John Wiley & Sons, Ltd.     

Precipitation,temperature and runoff analysis from 1950 to 2002 in the Yangtze basin,China / Analyse des précipitations,températures et débits de 1950 à 2002 dans le bassin du Yangtze,en Chine

Abstract

Abstract Monthly precipitation and temperature trends of 51 stations in the Yangtze basin from 1950–2002 were analysed and interpolated. The Mann-Kendall trend test was applied to examine the monthly precipitation and temperature data. Significant positive and negative trends at the 90, 95 and 99% significance levels were detected. The monthly mean temperature, precipitation, summer precipitation and monthly mean runoff at Yichang, Hankou and Datong stations were analysed. The results indicate that spatial distribution of precipitation and temperature trends is different. The middle and lower Yangtze basin is dominated by upward precipitation trend but by somewhat downward temperature trend; while downward precipitation trend and upward temperature trend occur in the upper Yangtze basin. This is because increasing precipitation leads to increasing cloud coverage and, hence, results in decreasing ground surface temperature. Average monthly precipitation and temperature analysis for the upper, middle and lower Yangtze basin, respectively, further corroborate this viewpoint. Analysis of precipitation trend for these three regions and of runoff trends for the Yichang, Hankou and Datong stations indicated that runoff trends respond well to the precipitation trends. Historical flood trend analysis also shows that floods in the middle and lower Yangtze basin are in upward trend. The above findings indicate that the middle and lower Yangtze basin is likely to face more serious flood disasters. The research results help in further understanding the influence of climatic changes on floods in the Yangtze basin, providing scientific background for the flood control activities in large catchments in Asia.     

Probabilistic forecasting of drought: a hidden Markov model aggregated with the RCP 8.5 precipitation projection

The creeping characteristics of drought make it possible to mitigate drought’s effects with accurate forecasting models. Drought forecasts are inevitably plagued by uncertainties, making it necessary to derive forecasts in a probabilistic framework. In this study, we proposed a new probabilistic scheme to forecast droughts that used a discrete-time finite state-space hidden Markov model (HMM) aggregated with the Representative Concentration Pathway 8.5 (RCP) precipitation projection (HMM-RCP). The standardized precipitation index (SPI) with a 3-month time scale was employed to represent the drought status over the selected stations in South Korea. The new scheme used a reversible jump Markov chain Monte Carlo algorithm for inference on the model parameters and performed an RCP precipitation projection transformed SPI (RCP-SPI) weight-corrected post-processing for the HMM-based drought forecasting to perform a probabilistic forecast of SPI at the 3-month time scale that considered uncertainties. The point forecasts which were derived as the HMM-RCP forecast mean values, as measured by forecasting skill scores, were much more accurate than those from conventional models and a climatology reference model at various lead times. We also used probabilistic forecast verification and found that the HMM-RCP provided a probabilistic forecast with satisfactory evaluation for different drought categories, even at long lead times. In a drought event analysis, the HMM-RCP accurately predicted about 71.19 % of drought events during the validation period and forecasted the mean duration with an error of less than 1.8 months and a mean severity error of <0.57. The results showed that the HMM-RCP had good potential in probabilistic drought forecasting.     

Probability distribution of annual,seasonal and monthly precipitation in Japan

Abstract

The method of L-moment ratio diagrams and the average weighted distance (AWD) are used to determine the probability distribution type of annual, seasonal and monthly precipitation in Japan. For annual precipitation, the log-Pearson type III (LP3) distribution provides the best fit to the observations with the generalized-extreme value (GEV), three-parameter lognormal (LN3) and Pearson type III (P3) distributions as potential alternatives. For seasonal precipitation, the P3 distribution shows the best fit to the observations of spring precipitation; the LP3 the best fit for summer and winter precipitation; and the LN3 the best fit for autumn precipitation with the LP3 as a potential alternative. For monthly precipitation, the P3 distribution fits the precipitation best for January, February, March, May, July, October and December; the LP3 for June; and the LN3 for April, August, September and November. The identified probability distribution types of annual, seasonal and monthly precipitation are basically consistent. Overall, the P3 and LP3 distributions are acceptable distribution types for representing statistics of precipitation in Japan with the LN3 distribution as a potential alternative.     

Topographical effects on the distributions of rainfall and 18O distributions: a case in Miyake Island,Japan

In this paper, we try to calculate precipitation in Miyake Island, Japan. In order to know the temporal and spatial variations of precipitation, we have set 15 rain gauges randomly in the island to collect the monthly precipitation data since June 1994. It is found that the precipitation is very different from point to point. First, we used statistical methods to get the correlations between the monthly precipitation at our survey points and that at the weather station. Next, regression analyses were used to establish formulae to calculate precipitation as a function of altitude, aspect of the geomorphological surface and wind direction. Based on these results, distributions of monthly and yearly precipitation and δ¹⁸O over the island were assessed. The results show that landscape patterns strongly influence precipitation distribution over the island, with the highest precipitation being found on the windward side, about 400–600 m above sea level. Even at places at the same altitude, the precipitation was different because of the aspect of the landscape. At the same time, altitude effects for δ¹⁸O on both the windward and leeward sides were −0·10‰/100 m and −0·15‰/100 m, respectively. Comparing with the distribution of precipitation distribution, it was also found that δ¹⁸O for the windward and leeward sides was different from that for precipitation, which means that both topographical effects must be considered separately. © 1998 John Wiley & Sons, Ltd.