A study for improving precipitation occurrences modelling with a Markov chain

Daily precipitation occurrences and their monthly wet-days' sums of precipitation-measuring stations in Greece are modelled with a Markov chain. The order of the chain is taken to be seasonally varying in accordance with the precipitation station's meteorological conditions and geographical location. The modelling efficiency of the Markov chain is significantly improved when it is conjunctively used with a second-order autoregressive stochastic model fitted on the monthly wet-days' sums.     

Stochastic calibration of an orographic precipitation model

In this study a stochastic approach to calibration of an orographic precipitation model (Rhea, 1978) was applied in the Gunnison River Basin of south-western Colorado. The stochastic approach to model calibration was used to determine: (1) the model parameter uncertainty and sensitivity; (2) the grid-cell resolution to run the model (10 or 5 km grids); (3) the model grid rotation increment; and (4) the basin subdivision by elevation band for parameter definition. Results from the stochastic calibration are location and data dependent. Uncertainty, sensitivity and range in the final parameter sets were found to vary by grid-cell resolution and elevation. Ten km grids were found to be a more robust model configuration than 5 km grids. Grid rotation increment, tested using only 10 km grids, indicated increments of less than 10 degrees to be superior. Basin subdivision into two elevation bands was found to produce ‘optimal’ results for both 10 and 5 km grids. © 1998 John Wiley & Sons, Ltd.     

Modelling point rainfall occurrences with the modified Bartlett-Lewis rectangular pulses model

A six parameter stochastic point process model, known as the modified Bartlett-Lewis Rectangular Pulses Model, is applied to fairly long hourly rainfall data recorded at Valentia (relatively a wet location) and Shannon Airport (relatively a dry location), Ireland. Five different sets of statistics of the rainfall data of each month, assuming local stationarity within the month, are used to estimate the parameters and to simulate model output. The problems of parameter stability/sensitivity and identification are discussed and it has been shown that the sensitivity of the model parameters to the choice of six statistics can be avoided by estimating the six parameters by optimization from 16 statistics namely mean, variance, lag-1 autocorrelation corfficient and proportion dry of hourly, 6-hourly, 12-hourly, and 24-hourly rainfalls. Some useful properties of the rainfall depth process are analysed using the notion of event-based statistics. The conditional distributions of rainfall depth and maximum intensity, mean event profiles, and various other features of the rainfall depth process obtained from the model simulated samples compare favourably with the historical ones.     

Numerical model for quantitative precipitation forecasting

Summary A numerical model for the quantitative precipitation forecasting has been formulated. In this model precipitation is computed as a function of the vertical velocity and humidity distribution in the atmosphere. The orographic influence on the vertical velocity was taken into consideration. Further, the relation between vertical velocity and static stability of the atmosphere has been considered and, as an important factor in the condensation process, was introduced into the equation of the model. This numerical model for the precipitation forecasting has been applied in the North Adriactic Sea region, which is characterized by a strong vertical gradient of the specific humidity and pronounced orographic influence. The results achieved show that this model could successfully be used as an objective method in the routine forecasting of the amount of precipitation.     

Rainfall uncertainty for extreme events in NWP downscaling model

Limited area numerical weather predication (NWP) models such as MM5 have become a popular method for generating rainfall estimates for hydrological analysis, particularly for catchments where rainfall data are sparse. Although several studies have been undertaken to investigate the appropriateness of MM5 parameterization schemes for hydrological applications, the size of the nested domains and the distance between them have been overlooked as a source of uncertainty in model precipitation estimates for hydrological purposes. This study examines the uncertainty of model rainfall estimates derived from MM5 by varying the domain size and the distance between the domains. The results from this study show that domain size and buffer zone have a significant impact on model rainfall estimates, which should not be overlooked by hydrologists. Copyright © 2010 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.     

Regression model for generating time series of daily precipitation amounts for climate change impact studies

The precipitation amounts on wet days at De Bilt (the Netherlands) are linked to temperature and surface air pressure through advanced regression techniques. Temperature is chosen as a covariate to use the model for generating synthetic time series of daily precipitation in a CO₂ induced warmer climate. The precipitation-temperature dependence can partly be ascribed to the phenomenon that warmer air can contain more moisture. Spline functions are introduced to reproduce the non-monotonous change of the mean daily precipitation amount with temperature. Because the model is non-linear and the variance of the errors depends on the expected response, an iteratively reweighted least-squares technique is needed to estimate the regression coefficients. A representative rainfall sequence for the situation of a systematic temperature rise is obtained by multiplying the precipitation amounts in the observed record with a temperature dependent factor based on a fitted regression model. For a temperature change of 3°C (reasonable guess for a doubled CO₂ climate according to the present-day general circulation models) this results in an increase in the annual average amount of 9% (20% in winter and 4% in summer). An extended model with both temperature and surface air pressure is presented which makes it possible to study the additional effects of a potential systematic change in surface air pressure on precipitation.     

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.     

三种下垫面温度及结冰预报模型研究

应用地表热量平衡方程,考虑太阳短波辐射、大气和地面的长波辐射、潜热、感热传输等能量之间的平衡,并考虑水汽、气溶胶、浮尘以及云等对太阳短波辐射的吸收和散射,建立了一种较实用的下垫面温度预报模型.应用湖北省恩施和金沙2009年冬季2月对土壤、水泥、沥青三种不同下垫面温度和自动气象站的常规气象要素观测进行模拟分析,并与该时段...     

A simplified stochastic model for infiltration into a heterogeneous soil forced by random precipitation

A simplified stochastic infiltration model is presented, aimed at representing the rainfall-runoff transformation in the presence of heterogeneity in the soil and with precipitation as a random variable with complex temporal evolution. Such a model is based on a simple water mass balance of a surface soil layer, considered as a non-linear reservoir. The explicit inclusion of spatial heterogeneity allows the model to be used in sub-grid parametrizations at a variety of scales, from the distributed modelling of the hydrological response of small watersheds to the representation of surface mass fluxes in General Circulation Models. An approximate solution procedure is developed, which allows the estimation of statistical moments of the soil effective saturation and runoff inside discrete time steps where the hydraulic saturated conductivity and the rainfall intensity are taken as random variables with known probability density functions. As a first test of the proposed model, two different simulations, relative to two soils with different hydraulic conductivity distributions, are presented and discussed. A year long record of hourly averaged rainfall intensities, as measured by a tipping bucket gauge in Central Italy, is taken as the main input. The main finding is that the non-linear nature of the soil filter is such that, for random precipitation intensity, the coefficient of variation of the runoff is always higher than that of precipitation. Such a non-linear variability enhancement, due mainly to the threshold character of the soil mass balance equation, tends to be slightly dampened by the variability of the hydraulic saturated conductivity.     

西藏地区复杂地形下的降水空间分布估算模型

本文提供了一个描述西藏地区年、季降水量空间分布的估算模型.利用卫星遥测数字化地形高程资料和西藏地区仅有的27个常规气象站的多年平均降水整编资料,根据地形坡向站点分为三类.再采用多元逐步回归方法,建立西藏地区的年、季降水量和经度、纬度、海拔高度、坡度、坡向、遮蔽度等6个地理、地形因子之间的关系模型,估算西藏地区降水量的空间分布.结果表明,此方法建立的关于西藏地区降水量与诸因子之间方程的相关性显著,平均绝对误差、相对误差分别为0.93mm和1.16%,对估算模型进行F检验,均通过置信度为0.95的相关检验,回归效果较显著.分析表明估算降水能够定量、定性地再现西藏地区的实际降水分布.     

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.     

Nonlinear dynamics and recurrence analysis of extreme precipitation for observed and general circulation model generated climates

A statistical framework based on nonlinear dynamics theory and recurrence quantification analysis of dynamical systems is proposed to quantitatively identify the temporal characteristics of extreme (maximum) daily precipitation series. The methodology focuses on both observed and general circulation model (GCM) generated climates for present (1961–2000) and future (2061–2100) periods which correspond to 1xCO₂ and 2xCO₂ simulations. The daily precipitation has been modelled as a stochastic process coupled with atmospheric circulation. An automated and objective classification of daily circulation patterns (CPs) based on optimized fuzzy rules was used to classify both observed CPs and ECHAM4 GCM‐generated CPs for 1xCO₂ and 2xCO₂ climate simulations (scenarios). The coupled model ‘CP‐precipitation’ was suitable for precipitation downscaling. The overall methodology was applied to the medium‐sized mountainous Mesochora catchment in Central‐Western Greece. Results reveal substantial differences between the observed maximum daily precipitation statistical patterns and those produced by the two climate scenarios. A variable nonlinear deterministic behaviour characterizes all climate scenarios examined. Transitions’ patterns differ in terms of duration and intensity. The 2xCO₂ scenario contains the strongest transitions highlighting an unusual shift between floods and droughts. The implications of the results to the predictability of the phenomenon are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

A multiscaling‐based intensity–duration–frequency model for extreme precipitation

Rainfall intensity–duration–frequency (IDF) curves are a standard tool in urban water resources engineering and management. They express how return levels of extreme rainfall intensity vary with duration. The simple scaling property of extreme rainfall intensity, with respect to duration, determines the form of IDF relationships. It is supposed that the annual maximum intensity follows the generalized extreme value (GEV) distribution. As well known, for simple scaling processes, the location parameter and scale parameter of the GEV distribution obey a power law with the same exponent. Although, the simple scaling hypothesis is commonly used as a suitable working assumption, the multiscaling approach provides a more general framework. We present a new IDF relationship that has been formulated on the basis of the multiscaling property. It turns out that the GEV parameters (location and scale) have a different scaling exponent. Next, we apply a Bayesian framework to estimate the multiscaling GEV model and to choose the most appropriate model. It is shown that the model performance increases when using the multiscaling approach. The new model for IDF curves reproduces the data very well and has a reasonable degree of complexity without overfitting on the data.     

A modified global model for predicting the tritium distribution in precipitation, 1960–2005

A modified global model for predicting the tritium concentration in precipitation has been developed using the dataset of International Atomic Energy Agency/the World Meteorological Organization (IAEA/WMO) over the period from 1960 to 2005. The tritium concentration in precipitation and its history can be estimated at any location using the model. The modified global model of tritium in precipitation (MGMTP) here presented has higher accuracy than the global model of tritium in precipitation (GMTP) developed by Doney et al. ( 1992 ). The new model is not only more appropriate for a particular station but also applicable for the un‐normalized observations directly. Another advantage of MGMTP is that it can estimate a longer history (from 1960 to 2005) of tritium content in precipitation than GMTP (from 1960 to 1986). The seasonal cycle of tritium in precipitation has also been modelled in the form of a simple cosine function with five parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

动力和统计预测信息融合预测方法及对我国夏季降水预测的检验

短期气候预测中如何将气候模式和统计方法的预测结果科学、客观的集成起来,一直是非常重要的问题.本文针对动力模式和统计方法预测结果相结合的问题,引入资料同化中信息融合的思想,采用最优内插同化方法,实现了动力模式和统计季节降水预测结果的融合.检验表明,对1982-2015年我国夏季降水百分率的回报,融合预测结果与观测的平均空间相关系数可达0.44,分别较统计预测和CFSv2模式统计降尺度订正的技巧提高了0.1左右,而均方根误差较两者可以降低5%~20%.可见,该方法可以进一步提升对我国夏季降水的预测技巧,具有显著的业务应用价值.

     

Simulation of moist mountain waves with an anelastic model

Abstract

A two-dimensional, nonlinear, time-dependent, non-hydrostatic, anelastic, numerical model is used to assess the effect of condensation on the evolution and structure of gravity waves generated by the passage of a stable, moist stream over topography. Precipation is ignored but water phase changes are taken into account explicitly.

The main effect of condensation is to damp the wave intensity and to reduce the wave drag, which can be diminished by as much as 50% compared to its value in dry simulations. This result agrees with some earlier analytical models and some more recent fully compressible numerical models.

This model also confirms that the presence of condensation delays the overturning of isentropes, and the formation of the critical layer that accompanies wave-breaking.