Daily Weather Generator Research Articles

Application of Synthetic Meteorological Time Series in BROOK90: A Case Study for the Tharandt Forest in Saxony, Germany

This study presents an extended version of a single site daily weather generator after Richardson. The model is driven by daily precipitation series derived by a first-order two-state Markov chain and considers the annual cycle of each meteorological variable. The evaluation of its performance was done by deploying its synthetic time series into the physical based hydrological model BROOK90. The weather generator was applied and tested for data from the Anchor Station at the Tharandt Forest, Germany. Additionally its results were compared to the output of another weather generator with spell-length approach for the precipitation series (LARS-WG). The comparison was distinguished into a meteoro-logical and a hydrological part in terms of extremes, monthly and annual sums and averages. Extreme events could be preserved adequately by both models. Nevertheless a general underestimation of rare events was observed. Natural correlations between vapour pressure and minimum temperature could be conserved as well as annual cycles of the hydro-logical and meteorological regime. But the simulated spectrums of extremes, especially, of precipitation and temperature, are more limited than the observed spectrums. While LARS-WG already finds application in practice, the results show that the data derived from the presented weather generator is as useful and reliable as those from the established model for the simulation of the water balance.

Monthly Weather Forecasts in a Pest Forecasting Context: Downscaling, Recalibration, and Skill Improvement

AbstractMonthly weather forecasts (MOFCs) were shown to have skill in extratropical continental regions for lead times up to 3 weeks, in particular for temperature and if weekly averaged. This skill could be exploited in practical applications for implementations exhibiting some degree of memory or inertia toward meteorological drivers, potentially even for longer lead times. Many agricultural applications fall into these categories because of the temperature-dependent development of biological organisms, allowing simulations that are based on temperature sums. Most such agricultural models require local weather information at daily or even hourly temporal resolution, however, preventing direct use of the spatially and temporally aggregated information of MOFCs, which may furthermore be subject to significant biases. By the example of forecasting the timing of life-phase occurrences of the codling moth (Cydia pomonella), which is a major insect pest in apple orchards worldwide, the authors investigate the application of downscaled weekly temperature anomalies of MOFCs for use in an impact model requiring hourly input. The downscaling and postprocessing included the use of a daily weather generator and a resampling procedure for creating hourly weather series and the application of a recalibration technique to correct for the original underconfidence of the forecast occurrences of codling moth life phases. Results show a clear skill improvement of up to 3 days in root-mean-square error over the full forecast range when incorporating MOFCs as compared with deterministic benchmark forecasts using climatological information for predicting the timing of codling moth life phases.

Stochastic weather generators for climate‐change downscaling, part II: multivariable and spatially coherent multisite downscaling

AbstractThis paper continues Part I (Wilks DS. Use of stochastic weather generators for precipitation downscaling. WIRES Clim Change 2010, 1(6):898–907) of a two‐part review on statistical downscaling of climate changes using parametric ‘weather generators’, which treated only precipitation downscaling at individual locations. Here the review is extended to include also downscaling of nonprecipitation variables at individual locations, and spatially coherent precipitation and nonprecipitation downscaling. Parametric weather generators are explicitly stochastic models that usually operate on the daily timescale. The use of stochastic methods for climate downscaling is natural and logically consistent because of the inherent indeterminacy of the problem: any number of small‐scale weather sequences may be associated with a given set of larger‐scale values. Downscaled climate changes are simulated by adjusting or varying the parameters of the weather generators, in a manner consistent with dynamically simulated or otherwise assumed larger‐scale climate changes. Two main approaches for such parametric adjustments have been developed, namely changes in the daily weather generator parameters based on imposed or assumed changes in the corresponding monthly statistics, and day‐by‐day changes to the generator parameters that are controlled by daily variations in simulated atmospheric circulation. These methods are reviewed here, and perspectives on their relative merits are offered. WIREs Clim Change 2012 DOI: 10.1002/wcc.167This article is categorized under: Assessing Impacts of Climate Change > Representing Uncertainty

Climate change impact on development rates of the codling moth (Cydia pomonella L.) in the Wielkopolska region, Poland

The main goal of this paper is to estimate how the observed and predicted climate changes may affect the development rates and emergence of the codling moth in the southern part of the Wielkopolska region in Poland. In order to simulate the future climate conditions one of the most frequently used A1B SRES scenarios and two different IPCC climate models (HadCM3 and GISS modelE) are considered. A daily weather generator (WGENK) was used to generate temperature values for present and future climate conditions (time horizons 2020–2040 and 2040–2060). Based on the generated data set, the degree-days values were then calculated and the emergence dates of the codling moth at key stages were estimated basing on the defined thresholds. Our analyses showed that the average air surface temperature in the Wielkopolska region may increase from 2.8°C (according to GISS modelE) even up to 3.3°C (HadCM3) in the period of 2040–2060. With the warming climate conditions the cumulated degree-days values may increase at a rate of about 142 DD per decade when the low temperature threshold (T low) of 0°C is considered and 91 DD per decade when T low = 10°C. The key developmental stages of the codling moth may occur much earlier in the future climate conditions than currently, at a rate of about 3.8–6.8 days per decade, depending on the considered GCM model and the pest developmental stage. The fastest changes may be observed in the emergence dates of 95% of larvae of the second codling moth generation. This could increase the emergence probability of the pest third generation that has not currently occurred in Poland.

WeaGETS – a Matlab-based daily scale weather generator for generating precipitation and temperature

This paper describes a versatile stochastic daily weather generator (WeaGETS) for producing daily precipitation, maximum and minimum temperatures (Tmax and Tmin). The performance of WeaGETS is demonstrated with respect to the generation of precipitation, Tmax and Tmin for two Canadian meteorological stations. The results show that the widely used first-order Markov model is adequate for producing precipitation occurrence, but it underestimates the longest dry spell for dry station. The higher-order models have positive effects. The gamma distribution is consistently better than the exponential distribution at generating precipitation quantity. The conditional scheme is good at simulating Tmax and Tmin. The spectral correction approach built in WeaGETS successfully preserves the observed low-frequency variability and autocorrelation functions of precipitation and temperatures.

A Versatile Weather Generator for Daily Precipitation and Temperature

Stochastic daily weather generators are often used to generate long time series of weather variables to drive hydrological and agricultural models. More recently, they have also been used as a downscaling tool for studying the impacts of climate change. This article describes a versatile stochastic weather generator (WeaGETS) for producing daily precipitation, and maximum and minimum temperatures (Tmax and Tmin). WeaGETS regroups several options of other weather generators into one package, such as three Markov models to produce precipitation occurrence, four distributions to generate wet day precipitation amount, and two methods to simulate Tmax and Tmin. More importantly, a spectral correction approach is included in WeaGETS for correcting the underestimation of interannual variability, which is a problem common to all weather generators. The performance of WeaGETS is demonstrated through a comparison against two well-known weather generators (WGEN and CLIGEN) with respect to the generation of precipitation, Tmax, and Tmin for two Canadian meteorological stations. The results show that the widely used first-order Markov model is adequate for producing precipitation occurrence, but it underestimates the longest dry spell for the low-precipitation station. The higher-order models have positive effects. The mixed exponential and skewed normal Pearson III distributions are consistently better than the exponential and gamma distributions at generating precipitation amounts. The two-component mixed exponential distribution is better at representing extreme precipitation events than the other three distributions. WeaGETS is consistently better than WGEN and CLIGEN at producing Tmax and Tmin. Both WGEN and CLIGEN underestimate the monthly and interannual variances of precipitation and temperatures. However, WeaGETS successfully preserves the observed low-frequency variability and autocorrelation functions of precipitation and temperatures. Overall, WeaGETS is consistently better than the other two weather generators (WGEN and CLIGEN) for producing precipitation, Tmax, and Tmin. The Matlab freeware allows for easy modification of all routines, making it easy to add additional weather variables to simulate.

The potential impact of climate change on groundwater‐fed wetlands in eastern England

ABSTRACTWetlands are fragile ecosystems that provide a range of useful functions. However, such ecosystems have been experiencing persistent pressures and stresses from a range of socio‐economic drivers in the last few centuries. In the 21st century, changes in global climate are expected to have impacts on hydrological and water supply regimes, which will in turn impose additional pressures on wetlands. Consequently, the need for quantitative methods to evaluate the likely impact of climate change is essential if appropriate conservation strategies and integrated water management regimes are to be developed. In this paper, a methodology is presented to evaluate the implications of potential climate change on groundwater‐fed wetlands underlain by an unconfined limestone (Chalk) aquifer in eastern England, one of the most vulnerable regions to climate change in the UK. A daily weather generator, a recharge model and a groundwater model have been coupled to investigate the most extreme consequences of future climate change as described by the UKCIP02 ‘high’ greenhouse gas emissions scenario. Simulations showed that a declining trend in wetland water levels could result in loss of species with a small tolerance to dry conditions by the end of the 21st century. Copyright © 2011 John Wiley & Sons, Ltd.

Use of stochastic weathergenerators for precipitation downscaling

AbstractDownscaling coarse‐resolution model representations of climate is a disaggregation problem, in which any number of small‐scale weather sequences can be associated with a given set of large‐scale values. Because of this intrinsic indeterminacy it is natural and logically consistent for downscaling methods to include explicitly random elements. Weather generators are stochastic models for (usually) daily weather time series, which can be used for climate‐change downscaling through appropriate adjustments to their parameters. Two main approaches for such parametric adjustments have been developed, namely changes in the daily weather generator parameters based on imposed or assumed changes in the corresponding monthly statistics, and day‐by‐day changes to the generator parameters that are controlled by daily variations in simulated atmospheric circulation. This paper reviews and compares these two methods for weather‐generator‐based downscaling, focusing on the downscaling of precipitation. WIREs Clim Change 2010 1 898–907 DOI: 10.1002/wcc.85This article is categorized under: Assessing Impacts of Climate Change > Evaluating Future Impacts of Climate Change Assessing Impacts of Climate Change > Representing Uncertainty

A stochastic daily weather generator for skewed data

To simulate multivariate daily time series (minimum and maximum temperatures, global radiation, wind speed, and precipitation intensity), we propose a weather state approach with a multivariate closed skew‐normal generator, WACS‐Gen, that is able to accurately reproduce the statistical properties of these five variables. Our weather generator construction takes advantage of two elements. We first extend the classical wet and dry days dichotomy used in most past weather generators to the definition of multiple weather states using clustering techniques. The transitions among weather states are modeled by a first‐order Markov chain. Second, the vector of our five daily variables of interest is sampled, conditionally on these weather states, from a closed skew‐normal distribution. This class of distribution allows us to handle nonsymmetric behaviors. Our method is applied to the 20 years of daily weather measurements from Colmar, France. This example illustrates the advantages of our approach, especially improving the simulation of radiation and wind distributions.

A daily stochastic weather generator for preserving low-frequency of climate variability

Weather generators are computer models that produce time series of meteorological data that have similar statistical properties as that of observed data. The past decade has seen a sharp and renewed increase in interest in weather generators, linked to their potential use in climate change studies. One appealing property of weather generators is their ability to rapidly produce time series of unlimited length, thus permitting impact studies of rare occurrences of meteorological variables. However, one problem with daily weather generators is that they underestimate monthly and inter-annual variances because they do not take into account the low-frequency component of climate variability. This research aims to present an approach for correcting the low-frequency variability of weather variables for weather generator and to assess its ability to reproduce key statistical parameters at the daily, monthly and yearly scales. The approach is applied to precipitation which is usually the variable displaying the largest inter-annual variability. The daily stochastic precipitation model is a Richardson-based weather generator that uses a first-order two-state Markov chain for precipitation occurrence and a gamma distribution for precipitation amounts. Low-frequency variability was modeled based on observed power spectra of monthly and annual time series. Generation of synthetic monthly and yearly precipitation data was achieved by assigning random phases for each spectral component. This preserved the power spectra, variances and the autocorrelation functions at the monthly and annual scales. The link to daily parameters was established through linear functions. The quality of these corrections was assessed through direct and indirect validation tests, with the direct validation focusing on comparing the means, standard deviations and autocorrelations of different weather series. The results showed that standard deviations of both monthly and annual precipitations were produced almost exactly. The proposed method also preserved the autocorrelation of annual precipitation. The indirect validation involved modelling the discharge of a river basin using a hydrological model driven by different precipitation series. The results showed that the corrected weather series significantly improved the variability of simulated flow discharges at the monthly and annual scales compared to those simulated using the data generated by the standard weather generator.

A gridded multisite weather generator and synchronization to observed weather data

Procedures are described for constructing a daily multisite weather generator at a collection of arbitrary (e.g., gridded) locations and for synchronizing the gridded generator to observed weather series at a set of reference stations. The gridded generator is constructed by interpolating conventional single‐station weather generator parameters using locally weighted regressions and producing coherent simulations of daily weather from them using spatial correlation functions. When implemented, the synchronization algorithm results in simulated spatial weather fields at the grid points that are consistent with daily weather observations at nearby locations for particular years. The synchronization is achieved by exploiting the latent multivariate Gaussian structure of the spatially distributed weather generator and making use of well‐known statistical results that define conditional multivariate Gaussian distributions given known values for a subset of variables from the larger joint distribution. The primary focus is on precipitation, but the nonprecipitation variables in the weather generator are also amenable to gridding and to synchronization with nearby observed weather series. The motivating idea is to allow calibration of spatially distributed hydrological models consistent with the climate of the spatial weather generator, potentially allowing more realistic hydrological simulation, but the procedure may also be useful for interpolation of missing daily weather data.

A daily weather generator based on a two-stage resampling algorithm

A two-stage time-series resampling algorithm is presented that is capable of generating daily values of weather variables outside their historical ranges. In this algorithm the simulated daily values are composed of an expected value and a sampled historical residual. The residuals broaden the range of the simulated daily values. Both the estimation of the expected value and the sampling of the residuals are based on the nearest-neighbours concept. In particular the influence of the neighbourhood sizes in both nearest-neighbour searches was studied. The algorithm was tested with data generated by two theoretical time-series models. Using observed precipitation and temperature data, a 12,000-year series of precipitation and temperature for the Ourthe catchment (Belgium) was simulated and used as input for a rainfall–runoff model to produce a long synthetic sequence of daily discharge. The two-stage algorithm correctly reproduces the mean, standard deviation and lag 1 autocorrelation of daily precipitation. The simulated distributions of 4-day and 10-day precipitation maxima in winter also show good correspondence with those observed, while the largest daily amounts substantially exceed those in the original data. However, the widened range of daily precipitation amounts has no discernible effect on the simulated discharge maxima in winter.

A daily weather generator for use in climate change studies

This paper describes the development of a weather generator for use in climate impact assessments of agricultural and water system management. The generator produces internally consistent series of meteorological variables including: rainfall, temperature, humidity, wind, sunshine, as well as derivation of potential evapotranspiration. The system produces series at a daily time resolution, using two stochastic models in series: first, for rainfall which produces an output series which is then used for a second model generating the other variables dependent on rainfall. The series are intended for single sites defined nationally across the UK at a 5 km resolution, but can be generated to be representative across small catchments (<1000 km 2). Scenarios can be generated for the control period (1961–1990) based on observed data, as well as for the UK Climate Impacts Programme (UKCIP02) scenarios for three time slices (2020s, 2050s and 2080s). Future scenarios are generated by fitting the models to observations which have been perturbed by application of change factors derived from the UKCIP02 mean projected changes in that variable. These change factors are readily updated, as new scenarios become available, and with suitable calibration data the approach could be extended to any geographical region.

Using monthly weather statistics to generate daily data in a SWAT model application to West Africa

Most hydrologic models require daily weather data to run. While this information may be abundant in some parts of the world, in most parts such data is not available on daily basis. Distributed hydrologic models are particularly adversely affected by the lack of daily data or the existence of very inaccurate data as they impart large uncertainties to the model prediction. In this study we developed a daily weather generator algorithm (dGen) that uses the currently available 0.5° monthly weather statistics from the Climatic Research Unit (CRU). We tested dGen in two ways. First, we made a direct comparison of the measured and generated precipitation and maximum–minimum temperatures by looking at some long-term statistics in a few stations in West Africa. Second, we ran the model “Soil and Water Assessment Tool” (SWAT) with dGen-generated and measured daily weather data to simulate 25 years of annual and monthly river discharges at some gauging stations. The simulated river discharges were then compared with the measured ones. It was seen that using the dGen-simulated daily weather data resulted in a much better match with the measured discharge data than the measured daily weather data in combination with the SWAT internal weather generator WXGEN. WXGEN is used in SWAT to fill missing data using monthly statistics, which must be calculated from the existing daily data. For annual and monthly hydrological simulations, dGen-generated daily rainfall and temperature data appears to have a high degree of reliability.

Neural network based daily precipitation generator (NNGEN-P)

Daily weather generators are used in many applications and risk analyses. The present paper explores the potential of neural network architectures to design daily weather generator models. Focusing this first paper on precipitation, we design a collection of neural networks (multi-layer perceptrons in the present case), which are trained so as to approximate the empirical cumulative distribution (CDF) function for the occurrence of wet and dry spells and for the precipitation amounts. This approach contributes to correct some of the biases of the usual two-step weather generator models. As compared to a rainfall occurrence Markov model, NNGEN-P represents fairly well the mean and standard deviation of the number of wet days per month, and it significantly improves the simulation of the longest dry and wet periods. Then, we compared NNGEN-P to three parametric distribution functions usually applied to fit rainfall cumulative distribution functions (Gamma, Weibull and double-exponential). A data set of 19 Argentine stations was used. Also, data corresponding to stations in the United States, in Europe and in the Tropics were included to confirm the results. One of the advantages of NNGEN-P is that it is non-parametric. Unlike other parametric function, which adapt to certain types of climate regimes, NNGEN-P is fully adaptive to the observed cumulative distribution functions, which, on some occasions, may present complex shapes. On-going works will soon produce an extended version of NNGEN to temperature and radiation.

A Heuristic Method for Time Disaggregation of Seasonal Climate Forecasts

Abstract To be immediately useful in practical applications that employ daily weather generators, seasonal climate forecasts issued for overlapping 3-month periods need to be disaggregated into a sequence of 1-month forecasts. Direct linear algebraic approaches to disaggregation produce physically unrealistic sequences of monthly forecasts. As an alternative, a heuristic method has been developed to disaggregate the NOAA/Climate Prediction Center (CPC) probability of exceedance seasonal precipitation forecasts, and tested on observed precipitation data for 1971–2000 for the 102 forecast divisions covering the contiguous United States. This simple method produces monthly values that replicate the direction and amplitude of variations on the 3-month time scale, and approach the amplitude of variations on the 1-month scale, without any unrealistic behavior. Root-mean-square errors between the disaggregated values and the actual precipitation over the 30-yr test period and all forecast divisions averaged 0.94 in., which is 39% of the mean monthly precipitation, and 58% of the monthly standard deviation. This method performs equally well across widely different precipitation regimes and does a reasonable job reproducing the sudden onset of strong seasonal variations such as the southwest U.S. monsoon.

Simulation of extreme temperature events by a stochastic weather generator: effects of interdiurnal and interannual variability reproduction

A WGEN-like four-variate (maximum and minimum temperature, precipitation and solar radiation) stochastic daily weather generator Met&Roll is used to provide synthetic weather series for models simulating crop growth and hydrological regime in present and changed climate conditions. Since impacts of climate change will be largely affected by changes in climate variability and extreme events, present climate models should satisfactorily reproduce both interdiurnal and interannual variability of the weather series and the occurrence of extremes. Three improvements of Met&Roll aiming at a better reproduction of interdiurnal and interannual variability have been introduced: (i) lag-0 and lag-1 correlations among solar radiation and daily extreme temperatures are allowed to vary during a year; (ii) a Markov chain of the third order (instead of the first order) is used to model precipitation occurrence; (iii) the synthetic daily weather series is adjusted to fit the series of the monthly means, which is generated using the four-variate first-order autoregressive (AR) model. Model performance regarding the simulation of extreme temperature events is evaluated against observations at 83 stations covering most of Europe. None of the improvements of the generator lead to a generally better reproduction of extreme high and low temperatures (1 day extremes); the basic version of the generator performs best for annual maxima, whereas the inclusion of the annual cycle of correlations slightly enhances the simulation of annual minima. For multiday extremes, the incorporation of the monthly generator tends to improve heat- and cold-wave characteristics, mainly the chaining of hot and cold days in spells; in western and central Europe, it improves (worsens) the simulation of heat waves (cold waves). Bad reproduction of most extreme event characteristics out of western and central Europe indicates a limited applicability of a generator based on the first-order AR model for temperature outside the mild climate zone and in areas with a high degree of continentality. The validity of assumptions of the generator should be tested using weather series related to a given area before its application in impact studies, and, if necessary, adjustments must be made. Copyright © 2005 Royal Meteorological Society

High-Frequency and Low-Frequency Variability in Stochastic Daily Weather Generator and Its Effect on Agricultural and Hydrologic Modelling

The high-frequency and low-frequency variabilities, which are often misreproduced by the daily weather generators, have a significant effect on modelling weather-dependent processes. Three modifications are suggested to improve the reproduction of the both variabilities in a four-variate daily weather generator Met&Roll: (i) inclusion of the annual cycle of lag-0 and lag-1 correlations among solar radiation, maximum temperature and minimum temperature, (ii) use of the 3rd order Markov chain to model precipitation occurrence, (iii) applying the monthly generator (based on a first-order autoregressive model) to fit the low-frequency variability. The tests are made to examine the effects of the three new features on (i) a stochastic structure of the synthetic series, and on (ii) outputs from CERES-Wheat crop model (crop yields) and SAC-SMA rainfall-runoff model (monthly streamflow characteristics, distribution of 5-day streamflow) fed by the synthetic weather series. The results are compared with those obtained with the observed weather series. Results: (i) The inclusion of the annual cycle of the correlations has rather ambiguous effect on the temporal structure of the weather characteristics simulated by the generator and only insignificant effect on the output from either simulation model. (ii) Increased order of the Markov chain improves modelling of precipitation occurrence series (especially long dry spells), and correspondingly improves reliability of the output from either simulation model. (iii) Conditioning the daily generator on monthly generator has the most positive effect, especially on the output from the hydrological model: Variability of the monthly streamflow characteristics and the frequency of extreme streamflows are better simulated. (iv) Of the two simulation models, the improvements related to the three modifications are more pronounced in the hydrological simulations. This may be also due to the fact that the crop growth simulations were less affected by the imperfections of the unmodified version of Met&Roll.

Stochastic generation of annual, monthly and daily climate data: A review

Abstract. The generation of rainfall and other climate data needs a range of models depending on the time and spatial scales involved. Most of the models used previously do not take into account year to year variations in the model parameters. Long periods of wet and dry years were observed in the past but were not taken into account. Recently, Thyer and Kuczera (1999) developed a hidden state Markov model to account for the wet and dry spells explicitly in annual rainfall. This review looks firstly at traditional time series models and then at the more complex models which take account of the pseudo-cycles in the data. Monthly rainfall data have been generated successfully by using the method of fragments. The main criticism of this approach is the repetitions of the same yearly pattern when only a limited number of years of historical data are available. This deficiency has been overcome by using synthetic fragments but this brings an additional problem of generating the right number of months with zero rainfall. Disaggregation schemes are effective in obtaining monthly data but the main problem is the large number of parameters to be estimated when dealing with many sites. Several simplifications have been proposed to overcome this problem. Models for generating daily rainfall are well developed. The transition probability matrix method preserves most of the characteristics of daily, monthly and annual characteristics and is shown to be the best performing model. The two-part model has been shown by many researchers to perform well across a range of climates at the daily level but has not been tested adequately at monthly or annual levels. A shortcoming of the existing models is the consistent underestimation of the variances of the simulated monthly and annual totals. As an alternative, conditioning model parameters on monthly amounts or perturbing the model parameters with the Southern Oscillation Index (SOI) result in better agreement between the variance of the simulated and observed annual rainfall and these approaches should be investigated further. As climate data are less variable than rainfall, but are correlated among themselves and with rainfall, multisite-type models have been used successfully to generate annual data. The monthly climate data can be obtained by disaggregating these annual data. On a daily time step at a site, climate data have been generated using a multisite type model conditional on the state of the present and previous days. The generation of daily climate data at a number of sites remains a challenging problem. If daily rainfall can be modelled successfully by a censored power of normal distribution then the model can be extended easily to generate daily climate data at several sites simultaneously. Most of the early work on the impacts of climate change used historical data adjusted for the climate change. In recent studies, stochastic daily weather generation models are used to compute climate data by adjusting the parameters appropriately for the future climates assumed.

Stochastic daily solar irradiance for biological modeling applications

Stochastic daily weather generators commonly used for biological modeling applications do not adequately reproduce empirical distributions of global solar irradiance. The daily clearness index, the ratio of daily global-to-extraterrestrial irradiance, captures the stochastic component of solar irradiance due to atmospheric conditions. Three alternative models of daily solar irradiance (truncated Gaussian distributions, a proposed modification based on logit-transformed relative clearness, and a family of empirically derived distributions) conditioned on the occurrence of rain are described and evaluated using data from 10 U.S. locations. These models are presented in terms of monthly cumulative distributions and density functions of clearness. Strong non-normality of distributions of clearness, and improved fits obtained with a logit transformation, are demonstrated. The proposed model, based on a logit transformation of relative clearness, was superior to the other two in terms of Akaike's information criterion, and generally superior to the standard model based on truncated Gaussian distributions in terms of goodness of fit between observed and generated irradiances. Based on this evidence, the proposed model is recommended for stochastic generation of daily irradiance conditioned on daily rainfall occurrence and temperature extremes.