Advanced Search
Article Contents

Temporal Statistical Downscaling of Precipitation and Temperature Forecasts Using a Stochastic Weather Generator


doi: 10.1007/s00376-015-5115-6

  • Statistical downscaling is based on the fact that the large-scale climatic state and regional/local physiographic features control the regional climate. In the present paper, a stochastic weather generator is applied to seasonal precipitation and temperature forecasts produced by the International Research Institute for Climate and Society (IRI). In conjunction with the GLM (generalized linear modeling) weather generator, a resampling scheme is used to translate the uncertainty in the seasonal forecasts (the IRI format only specifies probabilities for three categories: below normal, near normal, and above normal) into the corresponding uncertainty for the daily weather statistics. The method is able to generate potentially useful shifts in the probability distributions of seasonally aggregated precipitation and minimum and maximum temperature, as well as more meaningful daily weather statistics for crop yields, such as the number of dry days and the amount of precipitation on wet days. The approach is extended to the case of climate change scenarios, treating a hypothetical return to a previously observed drier regime in the Pampas.
  • 加载中
  • Apipattanavis S., 2008: Stochastic nonparametric methods for multi-site weather generation and flood frequency estimation: applications to construction delay,hydrology and agricultural modeling. PhD dissertation, University of Colorado,199 pages.
    Apipattanavis S., G. P. Podest谩, B. Rajagopalan, and R. W. Katz, 2007: A semiparametric multivariate and multisite weather generator. Water Resour. Res., 43,W11401, doi: 10.1029/ 2006WR005 714.10.1029/2006WR005714b759c5039097ef55476c11b32c619242http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F2006WR005714%2Ffullhttp://onlinelibrary.wiley.com/doi/10.1029/2006WR005714/full[1] We propose a semiparametric multivariate weather generator with greater ability to reproduce the historical statistics, especially the wet and dry spells. The proposed approach has two steps: (1) a Markov Chain for generating the precipitation state (i.e., no rain, rain, or heavy rain), and (2) a k -nearest neighbor ( k -NN) bootstrap resampler for generating the multivariate weather variables. The Markov Chain captures the spell statistics while the k -NN bootstrap captures the distributional and lag-dependence statistics of the weather variables. Traditional k -NN generators tend to under-simulate the wet and dry spells that are keys to watershed and agricultural modeling for water planning and management; hence the motivation for this research. We demonstrate the utility of the proposed approach and its improvement over the traditional k -NN approach through an application to daily weather data from Pergamino in the Pampas region of Argentina. We show the applicability of the proposed framework in simulating weather scenarios conditional on the seasonal climate forecast and also at multiple sites in the Pampas region.
    Apipattanavis S., F. Bert, G. P. Podest谩, and B. Rajagopalan, 2010a: Linking weather generators and crop models for assessment of climate forecast outcomes. Agriculture and Forest Meteorology, 150, 166- 174.10.1016/j.agrformet.2009.09.0122313aad8-3abd-4fac-96a3-b073a7fd4d7cf8d3cc50142c093a44f6093a61f58e21http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0168192309002287refpaperuri:(67dfeb34cd99b40a9720e4bbde318492)http://www.sciencedirect.com/science/article/pii/S0168192309002287Agricultural production responses to climate variability require salient information to support decisions. We coupled a new hybrid stochastic weather generator (combining parametric and nonparametric components) with a crop simulation model to assess yields and economic returns relevant to maize production in two contrasting regions (Pergamino and Pilar) of the Pampas of Argentina. The linked models were used to assess likely outcomes and production risks for seasonal forecasts of dry and wet climate. Forecasts involving even relatively small deviations from climatological probabilities of precipitation may have large impacts on agricultural outcomes. Furthermore, yield changes under alternative scenarios have a disproportionate effect on economic risks. Additionally, we show that regions receiving the same seasonal forecast may experience fairly different outcomes: a forecast of dry conditions did not change appreciably the expected distribution of economic margins in Pergamino (a climatically optimal location) but modified considerably economic expectations (and thus production risk) in Pilar (a more marginal location).
    Apipattanavis S., K. Sabol, K. Molenaar, B. Rajagopalan, Y. Xi, B. Blackard, and S. Patil, 2010b: Integrated framework for quantifying and predicting weather-related highway construction delays. Journal of Construction Engineering and Management, 136, 1160- 1168.
    Barnston A. G., S. H. Li, S. J. Mason, D. G. DeWitt, L. Goddard, and X. F. Gong, 2010: Verification of the first 11 years of IRI's seasonal climate forecasts. Journal of Applied Meteorology and Climatology, 49, 493- 520.10.1175/2009JAMC2325.1b5be6b0351c18c2641f3369338aa3e4bhttp%3A%2F%2Fwww.researchgate.net%2Fpublication%2F249603814_Verification_of_the_First_11_Years_of_IRI%27s_Seasonal_Climate_Forecastshttp://www.researchgate.net/publication/249603814_Verification_of_the_First_11_Years_of_IRI's_Seasonal_Climate_ForecastsAbstract This paper examines the quality of seasonal probabilistic forecasts of near-global temperature and precipitation issued by the International Research Institute for Climate and Society (IRI) from late 1997 through 2008, using mainly a two-tiered multimodel dynamical prediction system. Skill levels, while modest when globally averaged, depend markedly on season and location and average higher in the tropics than extratropics. To first order, seasons and regions of useful skill correspond to known direct effects as well as remote teleconnections from anomalies of tropical sea surface temperature in the Pacific Ocean (e.g., ENSO related) and in other tropical basins. This result is consistent with previous skill assessments by IRI and others and suggests skill levels beneficial to informed clients making climate risk management decisions for specific applications. Skill levels for temperature are generally higher, and less seasonally and regionally dependent, than those for precipitation, partly because of correct forecasts of enhanced probabilities for above-normal temperatures associated with warming trends. However, underforecasting of above-normal temperatures suggests that the dynamical forecast system could be improved through inclusion of time-varying greenhouse gas concentrations. Skills of the objective multimodel probability forecasts, used as the primary basis for the final forecaster-modified issued forecasts, are comparable to those of the final forecasts, but their probabilistic reliability is somewhat weaker. Automated recalibration of the multimodel output should permit improvements to their reliability, allowing them to be issued as is. IRI is currently developing single-tier prediction components.
    Beersma J. J., T. Adri Buishand, 2003: Multi-site simulation of daily precipitation and temperature conditional on the atmospheric circulation. Climate Research, 25, 121- 134.10.3354/cr0251215b9ed9a3b8ffefa8eef3b5d7b329ef31http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F250220884_Multi-site_simulation_of_daily_precipitation_and_temperature_conditional_on_the_atmospheric_circulationhttp://www.researchgate.net/publication/250220884_Multi-site_simulation_of_daily_precipitation_and_temperature_conditional_on_the_atmospheric_circulationABSTRACT Nearest-neighbour resampling was used to generate multi-site sequences of daily precipitation and temperature in the Rhine basin. The simulation is conditional on the values of 3 continuous indices of the atmospheric circulation, An advantage of nearest-neighbour resampling is that the spatial correlations of the daily precipitation and temperature data are automatically preserved in the simulated data. Comparison of different resampling models showed that the simulation of the precipitation and temperature for a new day should not only be conditioned on the circulation characteristics of that day but also on the simulated precipitation and temperature for the previous day, in order to achieve the appropriate level of persistence and variability in the generated data. With a hydrological application in mind, 980 yr multi-site simulations of daily precipitation and temperature were performed conditional on a simulated time series of circulation indices that was obtained with a second resampling model. The distribution of the extreme 10 d area-average precipitation amounts in these long-duration simulations was compared with the distribution of the historical 10 d area averages. Again, the models in which the precipitation and temperature of the previously simulated day were taken into account performed best, but even these models somewhat underestimate the quantiles of the distribution of the 10 d area-average precipitation. The long-duration simulations demonstrate that nearest-neighbour resampling is capable of producing much larger 10 d area-average precipitation amounts than the historical maximum.
    Benestad R. E., I. Hanssen-Bauer, and D. L. Chen, 2008: Empirical Statistical Downscaling. World Scientific,228 pps.10.1029/2004EO420002ccfe1c8aab43c45e14e70569577e439fhttp%3A%2F%2Fwww.worldscientific.com%2Fdoi%2Fpdf%2F10.1142%2F9789812819147_bmatterhttp://www.worldscientific.com/doi/pdf/10.1142/9789812819147_bmatterABSTRACT Publisher’s description: Empirical-statistical downscaling (ESD) is a method for estimating how local climatic variables are affected by large-scale climatic conditions. ESD has been applied to local climate/weather studies for years, but there are few – if any – textbooks on the subject. It is also anticipated that ESD will become more important and commonplace in the future, as anthropogenic global warming proceeds. Thus, a textbook on ESD will be important for next-generation climate scientists. Contents: 61 Downscaling strategies 61 Predictors and preprocessing 61 Linear techniques 61 Nonlinear techniques 61 Predictions and diagnostics 61 Shortcomings and limitations 61 Reducing uncertainties 61 Downscaling extremes and PDFs 61 Weather generator 61 Implementing ESD
    Briggs W. M., D. S. Wilks, 1996: Extension of the Climate Prediction Center long-lead temperature and precipitation outlooks to general weather statistics. J.Climate, 9, 3496- 3504.10.1175/1520-0442(1996)0092.0.CO;20b1efd88a77cb9bd7dc3592aeb3e636dhttp%3A%2F%2Fwww.researchgate.net%2Fpublication%2F253795108_Extension_of_the_Climate_Prediction_Center_Long-Lead_Temperature_and_Precipitation_Outlooks_to_General_Weather_Statisticshttp://www.researchgate.net/publication/253795108_Extension_of_the_Climate_Prediction_Center_Long-Lead_Temperature_and_Precipitation_Outlooks_to_General_Weather_StatisticsAbstract The long-lead monthly and seasonal forecasts issued by the Climate Prediction Center literally pertain only to average temperature and total precipitation outcomes, but implicitly contain information regarding other quantities that are correlated with these two variables. This paper presents a method for estimating the conditional probability distribution for any such quantity that is a computable statistic of available daily climatological data, through weighted bootstrap resampling conditional on particular joint (temperature and precipitation) forecast probabilities. Examples illustrating implementation and particular results are provided.
    Buishand, T. A., 1978: Some remarks on the use of daily rainfall models. J. Hydrol., 36, 295- 308.10.1016/0022-1694(78)90150-62c0b613fc49037e400411d299f756900http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2F0022169478901506http://www.sciencedirect.com/science/article/pii/0022169478901506Features of daily rainfall processes are described using data from different sites of the world. The process of rainfall occurrence is modelled by an alternating renewal process or by a Markov chain. It is shown that rainfall amounts within a wet spell are often neither independent nor identically distributed.There are, however, features of the rainfall process which are hardly sensitive to the choice of the process for the occurrence of wet days or to some assumptions about the behaviour of the rainfall amounts, for example the distribution of 30-day totals and the distribution of monthly extremes.
    Caldwell J., B. Rajagopalan, and E. Danner, 2014: Statistical modeling of daily water temperature attributes on the Sacramento River. Journal of Hydrologic Engineering, 20,04014065, doi: 10.1061/(ASCE)HE.1943-5584.0001023.\clearpage10.1061/,DanaInfo=dx.doi.org+(ASCE)HE.1943-5584.0001023995630cd9d106eda249b974015daca02http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F266373690_Statistical_Modeling_of_Daily_Water_Temperature_Attributes_on_the_Sacramento_Riverhttp://www.researchgate.net/publication/266373690_Statistical_Modeling_of_Daily_Water_Temperature_Attributes_on_the_Sacramento_RiverABSTRACT Abstract The Sacramento River is the largest river in California, and an important source of water for agricultural, municipal, and industrial users. Input to the Sacramento River comes from Shasta Lake and is controlled by operators of Shasta Dam, who are challenged with ...
    Cleveland, W. S., 1979: Robust locally-weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74, 829- 836.10.2307/2286407ddae677d-3812-49c5-884b-9ab2e4e6dfcce1bd4dfc9921c84aac321c7dbbafd513http%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Fabs%2F10.1080%2F01621459.1979.10481038refpaperuri:(32841f08be6d1618288965dd41b045c0)http://www.tandfonline.com/doi/abs/10.1080/01621459.1979.10481038and small if it is not. A robust fitting procedure is used that guards against deviant points distorting the smoothed points. Visual, computational, and statistical issues of robust locally weighted regression are discussed. Several examples, including data on lead intoxication, are used to illustrate the methodology.
    Furrer E. M., R. W. Katz, 2007: Generalized linear modeling approach to stochastic weather generators. Climate Research, 34, 129- 144.10.3354/cr0341293e467321dbfb248a564851bf1c9e5cd5http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F250221852_Generalized_linear_modeling_approach_to_stochastic_weather_generatorshttp://www.researchgate.net/publication/250221852_Generalized_linear_modeling_approach_to_stochastic_weather_generatorsStochastic weather generators are a popular method for producing synthetic sequences of daily weather. We demonstrate that generalized linear models (GLMs) can-provide a general modeling framework, allowing the straightforward incorporation of annual cycles and other covariates (e.g. an index of the El Nino-Southern Oscillation, ENSO) into stochastic weather generators. We apply the GLM technique to daily time series of weather variables (i.e. precipitation and minimum and maximum temperature) from Pergamino, Argentina. Besides annual cycles, the fit is significantly improved by permitting both the transition probabilities of the first-order Markov chain for daily precipitation occurrence, as well as the means of both daily minimum and maximum temperature, to depend on the ENSO state. Although it is more parsimonious than typical weather generators, the GLM-based weather generator performs comparably, particularly in terms of extremes and overdispersion.
    Giorgi F., L. O. Mearns, 1991: Approaches to the simulation of regional climate change: A review. Rev. Geophys., 29, 191- 216.10.1029/90RG02636a144800f03cdaf6c8275ba6a055b19a2http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F90RG02636%2Ffullhttp://onlinelibrary.wiley.com/doi/10.1029/90RG02636/fullThe increasing demand by the scientific community, policy makers, and the public for realistic projections of possible regional impacts of future climate changes has rendered the issue of regional climate simulation critically important. The problem of projecting regional climate changes can be identified as that of representing effects of atmospheric forcings on two different spatial scales: large-scale forcings, i.e., forcings which modify the general circulation and determine the sequence of weather events which characterize the climate regime of a given region (for example, greenhouse gas abundance), and mesoscale forcings, i.e., forcings which modify the local circulations, thereby regulating the regional distribution of climatic variables (for example, complex mountainous systems). General circulation models (GCMs) are the main tools available today for climate simulation. However, they are run and will likely be run for the next several years at resolutions which are too coarse to adequately describe mesoscale forcings and yield accurate regional climate detail. This paper presents a review of these approaches. They can be divided in three broad categories: (1) Purely empirical approaches, in which the forcings are not explicitly accounted for, but regional climate scenarios are constructed by using instrumental data records or paleoclimatic analogues; (2) semiempirical approaches, in which GCMs are used to describe the atmospheric response to large-scale forcings of relevance to climate changes, and empirical techniques account for the effect of mesoscale forcings; and (3) modeling approaches, in which mesoscale forcings are described by increasing the model resolution only over areas of interest. Since they are computationally inexpensive, empirical and semiempirical techniques have been so far more widely used. Their application to regional climate change projection is, however, limited by their own empiricism and by the availability of data sets of adequate quality. More recently, a nested GCM-limited area model methodology for regional climate simulation has been developed, with encouraging preliminary results. As it is physically, rather than empirically, based, the nested modeling framework has a wide range of applications.
    Hansen J. W., T. Mavromatis, 2001: Correcting low-frequency variability bias in stochastic weather generators. Agricultural and Forest Meteorology, 109, 297- 310.10.1016/S0168-1923(01)00271-4f1d604a527f3b7582a512982088a30a1http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0168192301002714http://www.sciencedirect.com/science/article/pii/S0168192301002714ABSTRACT Stochastic weather generators used with agricultural simulation models tend to under predict interannual variability of generated climate, often resulting in distortion of simulated agricultural or hydrological variables. This study presents a stochastic weather generator that attempts to improve interannual variability characteristics by perturbing monthly parameters using a low-frequency stochastic model, and evaluates the effectiveness of the low-frequency component on interannual variability of generated monthly climate and simulated crop variables. Effectiveness of the low-frequency correction was tested by comparing results based on observed weather sequences to those generated from the same underlying stochastic model without and with the low-frequency component. For monthly precipitation and maximum and minimum temperatures at 25 locations in the continental USA, the low-frequency correction reduced total error and eliminated negative bias of interannual variability, and reduced the number of station-months with significant differences between observed and generated interannual variability, but over-represented variability of precipitation frequency. For 11 crop scenarios, the low-frequency correction reduced the number of instances in which mean simulated yields and development times differed for observed and generated weather, and improved all measures of interannual variability of simulated yields and development times. We conclude that the approach presented here to disaggregate and separately model the high- and low-frequency components of weather variability can effectively address the negative bias of interannual variability of monthly climatic means found in some stochastic weather generators, and improve crop simulation applications of stochastically-generated weather. Further refinement is needed to better represent interannual variability of both precipitation occurrence and intensity processes, and to rectify over-correction of interannual temperature variability.
    Hastie T. J., R. J. Tibshirani, 1990: Generalized Additive Models. Chapman andHall.10.1002/0471667196.ess0297.pub28ad3ce4302b0a35837caba9fc0e0f294http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2F0470011815.b2a09018%2Fpdfhttp://onlinelibrary.wiley.com/doi/10.1002/0470011815.b2a09018/pdfLikelihood based regression models, such as the normal linear regression model and the linear logistic model, assume a linear (or some other parametric) form for the covariate effects. We introduce the Local Scotinq procedure which replaces the liner form C Xjpj by a sum of smooth functions C Sj(Xj)a The Sj(.) ‘s are unspecified functions that are estimated using scatterplot smoothers. The technique is applicable to any likelihood-based regression model: the class of Generalized Linear Models contains many of these. In this class, the Locul Scoring procedure replaces the linear predictor VI = C Xj@j by the additive predictor C ai ( hence, the name Generalized Additive Modeb. Local Scoring can also be applied to non-standard models like Cox’s proportional hazards model for survival data. In a number of real data examples, the Local Scoring procedure proves to be useful in uncovering non-linear covariate effects. It has the advantage of being completely automatic, i.e. no “detective work ” is needed on the part of the statistician. In a further generalization, the technique is modified to estimate the form of the link function for generalized linear models. The Local Scoring procedure is shown to be asymptotically equivalent to Local Likelihood estimation, another technique for estimating smooth covariate functions. They are seen to produce very similar results with real data, with Local Scoring being considerably faster. As a theoretical underpinning, we view Local Scoring and Local Likelihood as empirical maximizers of the ezpected log-likelihood, and this makes clear their connection to standard maximum likelihood estimation. A method for estimating the “degrees of freedom” of the procedures is also given.
    Hostetler S. W., J. R. Alder, and A. M. Allan, 2011: Dynamically downscaled climate simulations over North America: Methods, evaluation, and supporting documentation for users. U.S. Geological Survey Open-File Report 2011-1238, 64 pp.
    Katz R. W., M. B. Parlange, 1998: Overdispersion phenomenon in stochastic modeling of precipitation. J.Climate, 11, 591- 601.10.1175/1520-0442(1998)011<0591:OPISMO>2.0.CO;27622c4937ae65878b21cf9acb18cc1a7http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F37421916_Overdispersion_phenomenon_in_stochastic_modeling_of_precipitationhttp://www.researchgate.net/publication/37421916_Overdispersion_phenomenon_in_stochastic_modeling_of_precipitationSimple stochastic models fit to time series of daily precipitation amount have a marked tendency to under-estimate the observed (or interannual) variance of monthly (or seasonal) total precipitation. By considering extensions of one particular class of stochastic model known as a chain-dependent process, the extent to which this "overdispersion" phenomenon is attributable to an inadequate model for high-frequency variation of pre-cipitation is examined. For daily precipitation amount in January at Chico, California, fitting more complex stochastic models greatly reduces the underestimation of the variance of monthly total precipitation. One source of overdispersion, the number of wet days, can be completely eliminated through the use of a higher-order Markov chain for daily precipitation occurrence. Nevertheless, some of the observed variance remains unexplained and could possibly be attributed to low-frequency variation (sometimes termed "potential predictability"). Of special interest is the fact that these more complex stochastic models still underestimate the monthly variance, more so than does an alternative approach, in which the simplest form of chain-dependent process is conditioned on an index of large-scale atmospheric circulation.
    Kim Y., R. W. Katz, B. Rajagopalanc, G. P. Podest谩, and E. M. Furrer, 2012: Reduced overdispersion in stochastic weather generators using a generalized linear modeling approach. Climate Research, 53, 13- 24.d241e216-31ae-48ad-a0aa-f96fe1b30b25676fcbbc67305b658d169196c976e5cchttp%3A%2F%2Fams.confex.com%2Fams%2F87ANNUAL%2Fwebprogram%2FPaper119147.htmlrefpaperuri:(b0cfcaaabe1c0d265537f979b7be18fc)http://ams.confex.com/ams/87ANNUAL/webprogram/Paper119147.htmlWe demonstrate how an approach based on generalized linear models (GLMs) can provide a general modeling framework for incorporating climate states into parametric stochastic weather generators. One advantage of the GLM approach is that software is readily available for fitting such models (e.g., the function glm in the open source statistical programming software R, available at www.r-project.org). Long ago, GLMs were advocated by Stern and Coe (1984) for the stochastic modeling of daily precipitation, and more recently by Chandler (2005) for stochastic modeling of individual daily weather variables more generally. This past work has demonstrated how temporal dependence and annual cycles, as well as climate states, can be incorporated into a stochastic model for a single weather variable. Here we extend this approach to treat several daily weather variables simultaneously, as required to construct a stochastic weather generator.
    MacDonald I. L., W. Zucchini, 1997: Hidden Markov and Other Models for Discrete-Valued Time Series. Chapman and Hall.10.2307/1271194e30fdb0bc283e723bc256d2ead48f1b2http%3A%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D1692202http://www.ams.org/mathscinet-getitem?mr=1692202Publication &raquo; Hidden Markov and other Models for Discrete-Valued Time Series.
    Mannig B., Coauthors, 2013: Dynamical downscaling of climate change in Central Asia. Global and Planetary Change, 110, 26- 39.10.1016/j.gloplacha.2013.05.008625532a67fe498ac72b2d1c88951445dhttp%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0921818113001331http://www.sciencedirect.com/science/article/pii/S0921818113001331The high-resolution regional climate model (RCM) REMO has been implemented over the region of Central Asia, including western China. A model run forced by reanalysis data (1/2° resolution), and two runs forced by a GCM (one run with 1/2° and one run with 1/6° resolution) have been realized. The model has been evaluated regarding its ability to simulate the mean climate of the period 1971–2000. It has been found that the spatial pattern of mean temperature and precipitation is simulated well by REMO. The REMO simulations are often closer to observational data than reanalysis data are, and show considerably higher spatial detail. The GCM-forced simulations extend to the year 2100 under the A1B scenario. The climate change signal of temperature is largest in winter in the northern part of the study area and over mountainous terrain. A warming up to 702°C is projected until the end of the 21st century. In summer, warming is strongest over the southern part of Central Asia. Changes in precipitation are spatially more heterogeneous.
    McCullagh P., J. A. Nelder, 1989: Generalized Linear Models.2nd ed. Chapman and Hall, 206 pages.10.2307/2347392608f301c1d030aeb394f2b139e9f869chttp%3A%2F%2Fwww.researchgate.net%2Fpublication%2F236853442_Generalized_Linear_Models_2nd_Edhttp://www.researchgate.net/publication/236853442_Generalized_Linear_Models_2nd_EdAddresses a class of statistical models that generalizes classical linear models-extending them to include many other models useful in statistical analysis. Incorporates numerous exercises, both theoretical and data-analytic Discusses quasi-likelihood functions and estimating equations, models for dispersion effect, components of dispersion, and conditional likelihoods Holds particular interest for statisticians in medicine, biology, agriculture, social science, and engineering
    Rajagopalan B., V. Lall, 1999: A k-nearest neighbor simulator for daily precipitation and other weather variables. Water Resour. Res., 35, 3089- 3101.10.1029/1999WR900028443ab1cc-80c6-46f3-a9e2-34634c00986fcc47fad308d972116f82d1e9455a18f2http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F1999WR900028%2Ffullrefpaperuri:(ae3e2e60cf2f8d3d7d05e98da212826b)http://onlinelibrary.wiley.com/doi/10.1029/1999WR900028/fullAbstract. A multivariate, nonparametric time series simulation method is provided to generate random sequences of daily weather variables that “honor ” the statistical properties of the historical data of the same weather variables at the site. A vector of weather variables (solar radiation, maximum temperature, minimum temperature, average dew point temperature, average wind speed, and precipitation) on a day of interest is resampled from the historical data by conditioning on the vector of the same variables (feature vector) on the preceding day. The resampling is done from the k nearest neighbors in state space of the feature vector using a weight function. This approach is equivalent to a nonparametric approximation of a multivariate, lag 1 Markov process. It does not require prior assumptions as to the form of the joint probability density function of the variables. An application of the resampling scheme with 30 years of daily weather data at Salt Lake City, Utah, is provided. Results are compared with those from the application of a multivariate autoregressive model similar to that of Richardson [1981].
    Richardson C. W., 1981: Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour. Res., 17, 182- 190.10.1029/WR017i001p00182da8b7f70cab36aaea83f8cb062afebd5http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2FWR017i001p00182%2Fabstracthttp://onlinelibrary.wiley.com/doi/10.1029/WR017i001p00182/abstractLong samples of weather data are frequently needed to evaluate the long-term effects of proposed hydrologic changes. The evaluations are often undertaken using deterministic mathematical models that require daily weather data as input. Stochastic generation of the required weather data offers an attractive alternative to the use of observed weather records. This paper presents an approach that may be used to generate long samples of daily precipitation, maximum temperature, minimum temperature, and solar radiation. Precipitation is generated independently of the other variables by using a Markov chain-exponential model. The other three variables are generated by using a multivariate model with the means and standard deviations of the variables conditioned on the wet or dry status of the day as determined by the precipitation model. Daily weather samples that are generated with this approach preserve the seasonal and statistical characteristics of each variable and the interrelations among the four variables that exist in the observed data.
    Stern R. D., R. Coe, 1984: A model fitting analysis of daily rainfall data. Journal of the Royal Statistical Society: Series A, 147, 1- 34.10.2307/2981736a04558af2f593575ae4195d7178cce71http%3A%2F%2Fwww.jstor.org%2Fstable%2F2981736http://www.jstor.org/stable/2981736We have recently shown that bimorph piezoelectric PVDF films induce formation of periosteal bone in vivo and attributed this phenomenon to a piezoelectric effect. In the present study films were implanted in rabbits to encircle the femoral diaphysis. Specimens obtained after 6 and 12 days were subjected to routine processing for electron microscopy as well as fixation using the Ka-pyroantimonate technique. The electron micrographs revealed that initial osteoblastic differentiation and formation of collagenous matrix were followed by Ca accumulation in mitochondria. Calcification of the matrix progressed with deposition of mineralizing nodules and their fusion to form larger calcified masses. This was associated with disappearance of the pyroantimonate positive material from mitochondria. These ultrastructural observations confirm that bimorph films induce bone formation and disclose some features of the calcification process of the osseous callus.
    Verdin A., B. Rajagopalan, W. Kleiber, and R. W. Katz, 2015: Coupled stochastic weather generation using spatial and generalized linear models. Stochastic Environmental Research and Risk Assessment, 29, 347- 356.10.1007/s00477-014-0911-634ca5b591ace44557a7838b2bc54d4a7http%3A%2F%2Flink.springer.com%2F10.1007%2Fs00477-014-0911-6http://link.springer.com/10.1007/s00477-014-0911-6We introduce a stochastic weather generator for the variables of minimum temperature, maximum temperature and precipitation occurrence. Temperature variables are modeled in vector autoregressive framework, conditional on precipitation occurrence. Precipitation occurrence arises via a probit model, and both temperature and occurrence are spatially correlated using spatial Gaussian processes. Additionally, local climate is included by spatially varying model coefficients, allowing spatially evolving relationships between variables. The method is illustrated on a network of stations in the Pampas region of Argentina where nonstationary relationships and historical spatial correlation challenge existing approaches.
    Wilby R. L., T. M. L. Wigley, 1997: Downscaling general circulation model output: A review of methods and limitations. Progress in Physical Geography, 21, 530- 548.10.1177/03091333970210040377fd0191d053b25f7f12e08c08179b7bhttp%3A%2F%2Fci.nii.ac.jp%2Fnaid%2F30030794057http://ci.nii.ac.jp/naid/30030794057General circulation models (GCMs) suggest that rising concentrations of greenhouse gases may have significant consequences for the global climate. What is less clear is the extent to which local (subgrid) scale meteorological processes will be affected. So-called 'downscaling' techniques have subsequently emerged as a means of bridging the gap between what climate modellers are currently able to provide and what impact assessors require. This article reviews the present generation of downscaling tools under four main headings: regression methods; weather pattern (circulation)-based approaches; stochastic weather generators; and limited-area climate models. The penultimate section summarizes the results of an international experiment to intercompare several precipitation models used for downscaling. It shows that circulation-based downscaling methods perform well in simulating present observed and model-generated daily precipitation characteristics, but are able to capture only part of the daily precipitation variability changes associated with model-derived changes in climate. The final section examines a number of ongoing challenges to the future development of climate downscaling.
    Wilby R. L., T. M. L. Wigley, D. Conway, P. D. Jones, B. C. Hewitson, J. Main, and D. S. Wilks, 1998: Statistical downscaling of general circulation model output: A comparison of methods. Water Resour. Res., 34, 2995- 3008.10.1029/98WR025778759003a8d770613118171c428931d59http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F98WR02577%2Fabstracthttp://onlinelibrary.wiley.com/doi/10.1029/98WR02577/abstractA range of different statistical downscaling models was calibrated using both observed and general circulation model (GCM) generated daily precipitation time series and intercompared. The GCM used was the U.K. Meteorological Office, Hadley Centre's coupled ocean/atmosphere model (HadCM2) forced by combined CO 2 and sulfate aerosol changes. Climate model results for 1980&ndash;1999 (present) and 2080&ndash;2099 (future) were used, for six regions across the United States. The downscaling methods compared were different weather generator techniques (the standard &ldquo;WGEN&rdquo; method, and a method based on spell-length durations), two different methods using grid point vorticity data as an atmospheric predictor variable (B-Circ and C-Circ), and two variations of an artificial neural network (ANN) transfer function technique using circulation data and circulation plus temperature data as predictor variables. Comparisons of results were facilitated by using standard sets of observed and GCM-derived predictor variables and by using a standard suite of diagnostic statistics. Significant differences in the level of skill were found among the downscaling methods. The weather generation techniques, which are able to fit a number of daily precipitation statistics exactly, yielded the smallest differences between observed and simulated daily precipitation. The ANN methods performed poorly because of a failure to simulate wet-day occurrence statistics adequately. Changes in precipitation between the present and future scenarios produced by the statistical downscaling methods were generally smaller than those produced directly by the GCM. Changes in daily precipitation produced by the GCM between 1980&ndash;1999 and 2080&ndash;2099 were therefore judged not to be due primarily to changes in atmospheric circulation. In the light of these results and detailed model comparisons, suggestions for future research and model refinements are presented.
    Wilby R. L., S. P. Charles, E. Zorita, B. Timbal, P. Whetton, and L. O. Mearns, 2004: Guidelines for use of climate scenarios developed from statistical downscaling methods. Supporting material for Data Distribution Centre of Intergovernmental Panel on Climate Change. [Available online at http://www.ipcc-data.org/guidelines/dgmno2400v1092004.pdf].33efd45a38959695ba9e90a151e8a0fahttp%3A%2F%2Fwww.citeulike.org%2Fgroup%2F14742%2Farticle%2F8861447http://www.citeulike.org/group/14742/article/8861447Search all the public and authenticated articles in CiteULike. Include unauthenticated resultstoo (may include "spam") Enter a search phrase. You can also specify a CiteULike article id(123456),. a DOI (doi:10.1234/12345678). or a PubMed ID (pmid:12345678).
    Wilks D. S., 1989: Conditioning stochastic daily precipitation models on total monthly precipitation. Water Resour. Res., 25, 1429- 1439.10.1029/WR025i006p014295d5ddc77cb0bdd13d27e475bcbad7f27http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2FWR025i006p01429%2Fabstracthttp://onlinelibrary.wiley.com/doi/10.1029/WR025i006p01429/abstractABSTRACT Chain-dependent stochastic daily precipitation models are fit to dry, near-normal, and wet subsets of monthly total precipitation data, using category definitions consistent with the 30-day forecasts issued by the Climate Analysis Center of the National Oceanic and Atmospheric Administration. The resulting models are compared to those derived unconditionally from entire data records. It is found that for the 10 selected North American stations investigated, the unconditional models produce distributions of total monthly precipitation having too few dry and wet months as compared to the observations, while appropriate probability mixtures of the three conditional models can accurately reproduce the climatological distributions of total monthly precipitation. Application of the conditional precipitation models to generation of daily data consistent with certain longer-term aspects of the observations is also illustrated.
    Wilks D. S., R. L. Wilby, 1999: The weather generator game: A review of stochastic weather models. Progress in Physical Geography, 23, 329- 357.
    Xu Z. F., Z. L. Yang, 2012: An improved dynamical downscaling method with GCM bias corrections and its validation with 30 years of climate simulations. J.Climate, 25, 6271- 6286.10.1175/JCLI-D-12-00005.165e9224f-1c85-4251-9b9e-a6cda57917a3f252401a541820250a58a59c2e801f56http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F233409970_An_Improved_Dynamical_Downscaling_Method_with_GCM_Bias_Corrections_and_Its_Validation_with_30_Years_of_Climate_Simulationsrefpaperuri:(bca895dcf28a91598081e2808aa73821)http://www.researchgate.net/publication/233409970_An_Improved_Dynamical_Downscaling_Method_with_GCM_Bias_Corrections_and_Its_Validation_with_30_Years_of_Climate_SimulationsAbstract An improved dynamical downscaling method (IDD) with general circulation model (GCM) bias corrections is developed and assessed over North America. A set of regional climate simulations is performed with the Weather Research and Forecasting Model (WRF) version 3.3 embedded in the National Center for Atmospheric Research's (NCAR's) Community Atmosphere Model (CAM). The GCM climatological means and the amplitudes of interannual variations are adjusted based on the National Centers for Environmental Prediction (NCEP)鈥揘CAR global reanalysis products (NNRP) before using them to drive WRF. In this study, the WRF downscaling experiments are identical except the initial and lateral boundary conditions derived from the NNRP, original GCM output, and bias-corrected GCM output, respectively. The analysis finds that the IDD greatly improves the downscaled climate in both climatological means and extreme events relative to the traditional dynamical downscaling approach (TDD). The errors of downscaled climatological mean air temperature, geopotential height, wind vector, moisture, and precipitation are greatly reduced when the GCM bias corrections are applied. In the meantime, IDD also improves the downscaled extreme events characterized by the reduced errors in 2-yr return levels of surface air temperature and precipitation. In comparison with TDD, IDD is also able to produce a more realistic probability distribution in summer daily maximum temperature over the central U.S.鈥揅anada region as well as in summer and winter daily precipitation over the middle and eastern United States.
    Yates D., S. Gangopadhyay, B. Rajagopalan, and K. Strzepek, 2003: A technique for generating regional climate scenarios using a nearest neighbor algorithm. Water Resour. Res., 39,1199, doi: 10.1029/2002WR001769.
    Yoon J. H., L. Y. R. Leung, and J. Correia Jr., 2012: Comparison of dynamically and statistically downscaled seasonal climate forecasts for the cold season over the United States. J. Geophys. Res., 117,D21109, doi: 10.1029/2012JD017650.10.1029/2012JD017650f3bf845c94d1eced785842297b527453http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F2012JD017650%2Fcitedbyhttp://onlinelibrary.wiley.com/doi/10.1029/2012JD017650/citedby[1] This study compares two approaches, dynamical and statistical downscaling, for their potential to improve regional seasonal forecasts for the United States (U.S.) during the cold season. In the MultiRCM Ensemble Downscaling (MRED) project, seven regional climate models (RCMs) are used to dynamically downscale the Climate Forecast System (CFS) seasonal prediction over the conterminous U.S. out to 5 months for the period of 1982鈥2003. The simulations cover December to April of next year with 10 ensemble members from each RCM with different initial and boundary conditions from the corresponding ensemble members. These dynamically downscaled forecasts are compared with statistically downscaled forecasts produced by two bias correction methods applied to both the CFS and RCM forecasts. Results of the comparison suggest that the RCMs add value in seasonal prediction application, but the improvements largely depend on location, forecast lead time, variables, and skill metrics used for evaluation. Generally, more improvements are found over the Northwest and North Central U.S. for the shorter lead times. The comparison results also suggest a hybrid forecast system that combines both dynamical and statistical downscaling methods have the potential to maximize prediction skill.
  • [1] Wu Jindong, Wang Shili, 2001: Incorporating Stochastic Weather Generators into Studies on Climate Impacts: Methods and Uncertainties, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 937-949.
    [2] Kun-Hui YE, Chi-Yung TAM, Wen ZHOU, Soo-Jin SOHN, 2015: Seasonal Prediction of June Rainfall over South China: Model Assessment and Statistical Downscaling, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 680-689.  doi: 10.1007/s00376-014-4047-x
    [3] Jianfeng WANG, Ricardo M. FONSECA, Kendall RUTLEDGE, Javier MARTÍN-TORRES, Jun YU, 2020: A Hybrid Statistical-Dynamical Downscaling of Air Temperature over Scandinavia Using the WRF Model, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 57-74.  doi: 10.1007/s00376-019-9091-0
    [4] ZHU Congwen, Chung-Kyu PARK, Woo-Sung LEE, Won-Tae YUN, 2008: Statistical Downscaling for Multi-Model Ensemble Prediction of Summer Monsoon Rainfall in the Asia-Pacific Region Using Geopotential Height Field, ADVANCES IN ATMOSPHERIC SCIENCES, 25, 867-884.  doi: 10.1007/s00376-008-0867-x
    [5] FAN Lijun, Deliang CHEN, FU Congbin, YAN Zhongwei, 2013: Statistical downscaling of summer temperature extremes in northern China, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1085-1095.  doi: 10.1007/s00376-012-2057-0
    [6] Cecilia HELLSTR?M, Deliang CHEN, 2003: Statistical Downscaling Based on Dynamically Downscaled Predictors: Application to Monthly Precipitation in Sweden, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 951-958.  doi: 10.1007/BF02915518
    [7] Dangfu YANG, Shengjun LIU, Yamin HU, Xinru LIU, Jiehong XIE, Liang ZHAO, 2023: Predictor Selection for CNN-based Statistical Downscaling of Monthly Precipitation, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 1117-1131.  doi: 10.1007/s00376-022-2119-x
    [8] Zhizhen XU, Jing CHEN, Zheng JIN, Hongqi LI, Fajing CHEN, 2020: Representing Model Uncertainty by Multi-Stochastic Physics Approaches in the GRAPES Ensemble, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 328-346.  doi: 10.1007/s00376-020-9171-1
    [9] DAI Qiudan, SUN Shufen, 2006: A Generalized Layered Radiative Transfer Model in the Vegetation Canopy, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 243-257.  doi: 10.1007/s00376-006-0243-7
    [10] DAI Qiudan, SUN Shufen, 2007: A Simplified Scheme of the Generalized Layered Radiative Transfer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 213-226.  doi: 10.1007/s00376-007-0213-8
    [11] FENG Lei, ZHOU Tianjun, WU Bo, Tim LI, Jing-Jia LUO, 2011: Projection of Future Precipitation Change over China with a High-Resolution Global Atmospheric Model, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 464-476.  doi: 10.1007/s00376-010-0016-1
    [12] Deliang CHEN, Christine ACHBERGER, Jouni R¨AIS¨ANEN, Cecilia HELLSTR¨OM, 2006: Using Statistical Downscaling to Quantify the GCM-Related Uncertainty in Regional Climate Change Scenarios: A Case Study of Swedish Precipitation, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 54-60.  doi: 10.1007/s00376-006-0006-5
    [13] Temesgen Gebremariam ASFAW, Jing-Jia LUO, 2024: Downscaling Seasonal Precipitation Forecasts over East Africa with Deep Convolutional Neural Networks, ADVANCES IN ATMOSPHERIC SCIENCES, 41, 449-464.  doi: 10.1007/s00376-023-3029-2
    [14] DONG Lu, and ZHOU Tianjun, 2013: Steric Sea Level Change in Twentieth Century Historical Climate Simulation and IPCC-RCP8.5 Scenario Projection: A Comparison of Two Versions of FGOALS Model, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 841-854.  doi: 10.1007/s00376-012-2224-3
    [15] LI Hongmei, FENG Lei, ZHOU Tianjun, 2011: Multi-model Projection of July--August Climate Extreme Changes over China under CO$_{2}$ Doubling. Part I: Precipitation, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 433-447.  doi: 10.1007/s00376-010-0013-4
    [16] Vladimir A. Lobanov, 2001: Empirical-Statistical Methodology and Methods for Modeling and Forecasting of Climate Variability of Different Temporal Scales, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 844-863.
    [17] Chao LIU, Li FU, Dan YANG, David R. MILLER, Junming WANG, 2020: Non-Gaussian Lagrangian Stochastic Model for Wind Field Simulation in the Surface Layer, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 90-104.  doi: 10.1007/s00376-019-9052-7
    [18] Ding Yuguo, Tu Qipu, Wen Min, 1995: A Statistical Model for Investigating Climatic Trend Turning Points, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 47-56.  doi: 10.1007/BF02661286
    [19] Keon Tae SOHN, 2013: Statistical Guidance on Seasonal Forecast of Korean Dust Days over South Korea in the Springtime, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1343-1352.  doi: 10.1007/s00376-012-2112-x
    [20] Mu Mu, Guo Huan, Wang Jiafeng, LiYong, 2000: The Impact of Nonlinear Stability and Instability on the Validity of the Tangent Linear Model, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 375-390.  doi: 10.1007/s00376-000-0030-9

Get Citation+

Export:  

Share Article

Manuscript History

Manuscript received: 08 May 2015
Manuscript revised: 20 July 2015
Manuscript accepted: 17 August 2015
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Temporal Statistical Downscaling of Precipitation and Temperature Forecasts Using a Stochastic Weather Generator

  • 1. Department of Statistics, Kyungpook National University, Daegu, 41566, Korea
  • 2. Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, Colorado, 80203, USA
  • 3. Department of Astronomy and Atmospheric Sciences, Center for Atmospheric Remote Sensing, Kyungpook National University, Daegu, 41566, Korea

Abstract: Statistical downscaling is based on the fact that the large-scale climatic state and regional/local physiographic features control the regional climate. In the present paper, a stochastic weather generator is applied to seasonal precipitation and temperature forecasts produced by the International Research Institute for Climate and Society (IRI). In conjunction with the GLM (generalized linear modeling) weather generator, a resampling scheme is used to translate the uncertainty in the seasonal forecasts (the IRI format only specifies probabilities for three categories: below normal, near normal, and above normal) into the corresponding uncertainty for the daily weather statistics. The method is able to generate potentially useful shifts in the probability distributions of seasonally aggregated precipitation and minimum and maximum temperature, as well as more meaningful daily weather statistics for crop yields, such as the number of dry days and the amount of precipitation on wet days. The approach is extended to the case of climate change scenarios, treating a hypothetical return to a previously observed drier regime in the Pampas.

1. Introduction
  • Techniques to downscale climate information can be divided into two main categories: dynamical and statistical. Dynamical downscaling effectively increases the spatial resolution, through coupling a higher resolution numerical model (e.g., regional) to a lower resolution model (e.g., global) (Giorgi and Mearns, 1991; Hostetler et al., 2011; Xu and Yang, 2012; Mannig et al., 2013). The alternative technique of statistical downscaling involves empirical relationships between weather and climate variations at different temporal and/or spatial scales (Wilby and Wigley, 1997; Wilby et al., 1998; Wilby et al., 2004; Benestad et al., 2008). (Yoon et al., 2012) compared dynamically and statistically downscaled seasonal climate forecast for the cold season over the U.S. Recently, (Caldwell et al., 2014) used a K-nearest neighbor weather generator for downscaling of IRI (Research Institute for Climate and Society) seasonal forecasts and discussed the skill in the shifts. Although a dynamical approach is appealing in principle, a statistical approach has the advantage of being much simpler to develop and implement in practice. In the present paper, we adopt a statistical approach and focus only on temporal, not spatial, downscaling.

    Stochastic weather generators can be used to temporally downscale climate information, such as seasonal forecasts (Wilks and Wilby, 1999; Benestad et al., 2008). Approaches to stochastic weather generation can be divided into two main categories: parametric [starting with (Richardson, 1981)] and non-parametric [generally based on resampling, e.g., (Rajagopalan and Lall, 1999)]. We adopt the recently introduced generalized linear modeling (GLM) (McCullagh and Nelder, 1989) approach to parametric weather generators, which has the advantage of being readily able to incorporate covariates, accounting for seasonality and teleconnections (e.g., with the El Niño phenomenon) (Furrer and Katz, 2007). Yet, one important limitation of parametric stochastic weather generators is their underestimation of the observed interannual variance of seasonally aggregated variables, sometimes termed "overdispersion" (Buishand, 1978; Katz and Parlange, 1998). Such variance underestimation is a shortcoming of statistical downscaling techniques more generally (Benestad et al., 2008).

    To reduce the overdispersion phenomenon, (Kim et al., 2012) incorporated time series of seasonal total precipitation and seasonal mean minimum and maximum temperature in the GLM weather generator as covariates. These seasonal time series are smoothed using locally weighted scatterplot smoothing (LOESS) (Cleveland, 1979; Hastie and Tibshirani, 1990) to avoid introducing underdispersion (i.e., too much variance instead of not enough variance). Because the aggregate variables appear explicitly in the weather generator, downscaling to daily sequences can be readily implemented. It should be noted that (Wilks, 1989) conditioned a stochastic model for daily precipitation based on monthly total precipitation, and that (Hansen and Mavromatis, 2001) adjusted the parameters of a stochastic weather generator in an ad hoc fashion to correct for overdispersion.

    In section 2, first, the extended GLM approach to stochastic weather generators, involving the introduction of aggregated climate statistics as covariates, is briefly reviewed. Next, these models are fitted to time series of daily weather at Pergamino and Pilar in the Argentine Pampas, evaluating the model fit in terms of overdispersion. Section 3 demonstrates the feasibility of statistical downscaling. The IRI seasonal forecasts are used as prototypes, with a resampling scheme (Apipattanavis et al., 2007) adopted to translate the uncertainty in the seasonal forecasts into the corresponding uncertainty for the daily weather statistics. In section 4, the proposed approach is applied to downscaling shorter-term (e.g., decadal) projections under climate change scenarios. Finally, the study's findings are discussed in section 5.

2. Revisiting the GLM weather generator
  • The GLM approach to stochastic weather generators, introduced by (Furrer and Katz, 2007), focuses on the simplest form of a generator first proposed by (Richardson, 1981). Using the observed (i.e., unsmoothed) seasonal climate statistics as covariates may introduce excessive noise into the daily weather statistics and result in "underdispersion" for aggregated climate statistics. (Kim et al., 2012) considered smoothed seasonal climate statistics as covariates in the GLM weather generator, and adopted LOESS as a smoothing tool (Cleveland, 1979), which is a computationally intensive method. Except for smoothed seasonal covariates, the GLM stochastic weather generator of (Kim et al., 2012) is essentially the same as in (Stern and Coe, 1984) and (Furrer and Katz, 2007).

    Let Jt denote the precipitation occurrence state on day t of a given year (i.e., Jt=1 if precipitation occurs, Jt=0 otherwise), and let pt=P{Jt=1},t=1,2,…, denote the probability of a wet day. The logistic transformation of the probability of precipitation is modeled conditionally on the occurrence state on the previous day Jt-1: \begin{eqnarray} \ln\left(\dfrac{p_t}{1-p_t}\right)&=&\alpha_0+\alpha_1J_{t-1}+\beta_{11}C_t+\beta_{12}S_t+\gamma_1C_tJ_{t-1}+\nonumber\\ &&\gamma_2S_tJ_{t-1}+\beta_{1s}I_tP_{s,t}+\beta_{1w}(1-I_t)P_{w,t} , (1)\end{eqnarray} where Ct=cos(2π(t-181)/365) and \(S_t=\sin(2\pi(t-181)/\) 365). It is a seasonal indicator [i.e., It=1 in austral summer (October-March) and It=0 in austral winter (April-September)], while Ps,t and Pw,t are LOESS-smoothed summer and winter seasonal total precipitation, respectively. α011112121s and β1w are model coefficients.

    The daily precipitation intensity (i.e., the precipitation amount conditionally based on Jt=1) is modeled as a gamma distribution (e.g., Stern and Coe, 1984), with an annual cycle for mean intensity, denoted by μt: \begin{equation} \ln(\mu_t)=\alpha+\beta_{21}C_t+\beta_{22}S_t+\beta_{2s}I_tP_{s,t}+\beta_{2w}(1-I_t)P_{w,t} . (2)\end{equation} Here, α,β21222s and β2w are model coefficients. The coefficients β21 and β22 control the annual cycle in the mean intensity.

    Let (Xt,Yt) denote the minimum and maximum temperature on day t of a given year, jointly modeled as a bivariate first-order autoregressive process of the form (as in Richardson, 1981; Furrer and Katz, 2007) \begin{eqnarray} X_t&=&\mu_{X,0}+\mu_{X,1}J_t+\varphi_XX_{t-1}+\psi_XY_{t-1}+\beta_{X,1}C_t+\nonumber\\ &&\beta_{X,2}S_t+\beta_{X,s}I_tN_{s,t}+\beta_{X,w}(1-I_t)N_{w,t}+\varepsilon_{X,t} ,(3) \end{eqnarray} and \begin{eqnarray} Y_t&=&\mu_{Y,0}+\mu_{Y,1}J_t+\varphi_YY_{t-1}+\psi_Y X_t+\beta_{Y,1}C_t+\beta_{Y,2}S_t+\nonumber\\ &&\beta_{Y,s} I_tM_{s,t}+\beta_{Y,w}(1-I_t)M_{w,t}+\varepsilon_{Y,t} , (4)\end{eqnarray} where μ(X,0),μY,0X,1Y,1XYXYX,1X,2Y,1, βY,2X,sX,w, βY,s and βY,w are model coefficients. Ns,t and Nw,t (Ms,t and Mw,t) are the LOESS-smoothed summer and winter seasonal mean minimum (maximum) temperatures. Here, the two error terms, εX,t and εY,t, besides being normally distributed with zero means, have no autocorrelation or cross correlation.

    Note that the seasonal indicators in Eqs. (1-4) allow for different relationships with the aggregated covariates depending on the season. The degree of LOESS smoothing is determined by the criterion based on minimizing the overdispersion phenomenon, through trial and error ranging from the case of no smoothing to as smooth as possible. (Kim et al., 2012) considered the same degree of smoothness (i.e., 0.4) in all GLM models at the two locations.

    (Kim et al., 2012) illustrated that the proposed model virtually eliminates the overdispersion phenomenon in nearly all cases in reproducing variances of annual, as well as summer and winter, total precipitation (mm) and mean minimum and maximum temperatures (°C) at two locations in the Argentine Pampas, Pergamino and Pilar. Both locations have a marked wet season in the Southern Hemisphere summer. They also reported that the results (not shown) were not very sensitive to the precise value of the parameter governing the degree of smoothing in LOESS (e.g., the overdispersion in the summer total precipitation at Pergamino was still virtually eliminated if the degree of smoothing was 0.5 instead of 0.4). It was noted that the introduction of the temporal trend in the temperature models was insufficient to correct the overdispersion, and the original model came close to reproducing the precipitation variability in winter.

    In the application to downscaling seasonal forecasts (section 3), daily weather statistics, such as the total number of dry days and the median daily precipitation intensity within a season, are considered. It was verified that the GLM weather generator with aggregated covariates simulates the climatological distribution of these statistics reasonably well (results not shown). Furthermore, (Kim et al., 2012) already extensively validated the proposed GLM weather generator applied to Pergamino and Pilar.

3. Downscaling seasonal forecasts
  • The IRI seasonal forecast product has been issued since October 1997 (Barnston et al., 2010). At present, the forecasts of seasonal total precipitation and mean temperature have at least a 0.5-month lead time (e.g., the forecasts for the October through December season are released in mid-September). Seasonal forecasts with longer lead times of up to 3.5 months are also produced (e.g., forecasts for the January through March season are also issued in mid-September). These IRI forecasts are probabilistic in nature, in that they are provided as a percentage likelihood in an A:N:B format, where "A" denotes the percentage chance of above-normal seasonal total rainfall, "N" denotes the percentage chance of near-normal rainfall, and "B" denotes the percentage chance of below-normal rainfall——and the three categories are typically based on the terciles. For example, a forecast of A:N:B=40:35:25 for an area means that there is a 40% chance of seasonal total rainfall being above normal, a 35% chance of rainfall being near normal, and a 25% chance of below-normal precipitation. Forecasts of seasonal mean temperature are issued in the same format.

    (Barnston et al., 2010) thoroughly evaluated the skill of the IRI seasonal forecasts. Any such skill is necessarily limited, with the forecast probabilities frequently coinciding with climatology [i.e., (1/3,1/3,1/3)] and only rarely being higher than 2/3 for a given category. Seasonal precipitation probability forecasts are reliable (i.e., well-calibrated in the sense that they can be taken at face value), with the reliability of seasonal temperature forecasts suffering from a failure to correctly incorporate global warming trends. The forecast skill tends to match the strength of the ENSO signal, both in terms of geographic location and time of year. So, not surprisingly, there is some real, if small, skill for both precipitation and temperature during the Southern Hemisphere summer half of the year (October through March) in the Argentine Pampas [for more information about the ENSO signal in the Argentine Pampas, see (Furrer and Katz, 2007)]. This contribution of the ENSO phenomenon to the IRI forecasts is another reason for not including ENSO as a covariate in the GLM weather generator.

    The IRI forecasts apply to a particular grid box, rather than a single location. As already mentioned, our approach is designed to deal with temporal, not spatial, downscaling. So, the IRI forecasts will be treated as if they apply to individual points. Because Pergamino and Pilar are closely situated, relative to the size of the grid boxes or the typical size of the contiguous area for which a deviation from climatology is predicted, the same IRI forecast probabilities always apply to both locations. Nevertheless, the downscaled daily weather statistics will differ both because of different downscaling relationships and because of different climatology (i.e., as reflected in the coefficients in the GLM weather generators). Finally, the climate statistics used as covariates in the GLM were aggregated over six months, not three months as in the IRI seasonal forecasts. Rather than attempting to combine the IRI forecasts for two consecutive three-month periods (which are not always available for the second three months), we adopt the pragmatic approach of using the IRI forecasts for the first three months and only the climatology for the second three months. Stochastic weather generators based on the K-nearest neighbor resampling approach (Rajagopalan and Lall, 1999; Beersma and Adri Buishand, 2003; Apipattanavis et al., 2007) have been modified (Briggs and Wilks, 1996; Yates et al., 2003) to provide weather scenarios consistent with the seasonal probabilistic forecasts. We use this modification, first proposed by (Yates et al., 2003) and used in (Apipattanavis et al., 2007), in the current research. To the best of our knowledge, this is the first application of its kind to a GLM-based, or any other parametric, weather generator.

    Figure 1.  Downscaling of IRI forecasts for October to December 1997-2007, showing boxplots of the corresponding forecast distributions of summer (October to March) total precipitation (a), mean maximum temperature (b) and mean minimum temperature (c), along with the climatology (CLIM) and observed values (denoted by circles) for Pergamino. Boxplots are not shown for years in which the forecast coincides with the climatology.

    Figure 2.  Downscaling of IRI forecasts for October to December 1997-2007, showing boxplots of the corresponding forecast distribution of the summer (October to March) mean number of dry days (a) and median daily precipitation intensity (b), along with the climatology (CLIM) and observed values (denoted by circles) for Pergamino. Boxplots are not shown for years in which the forecast coincides with the climatology.

    The methodology proceeds as follows: (1) Historical years are classified into three categories——wet, normal and dry, based on the terciles of the smoothed historical summer (October-March) season precipitation (i.e., consistent with the covariates used in the GLM weather generator). (2) The historical years are resampled with replacement based on the seasonal probabilistic forecast as the weight metric. Following the previous example of a 40:35:25 forecast, we would select years from the wet category with a 0.40 probability, normal years with a 0.35 probability, and dry years with a 0.25 probability. (3) The smoothed seasonal (October-March and April-September) precipitation values of the resampled years are used in the GLM weather generator as covariates to generate a rich variety of daily weather sequences at the point scale. An analogous approach is employed for the simulation of minimum and maximum temperature based on the seasonal forecast of mean temperature. The seasonal forecasts are available only for the mean temperature and we assume that it reflects the minimum and maximum temperatures as well. The resampling, step (2), is performed on the probabilistic forecast of the three-month seasonal mean temperature——and the corresponding smoothed seasonal (October-March and April-September) maximum and minimum temperatures are used in their respective GLM models as covariates.

    Probability distributions of a suite of weather statistics (mentioned earlier) that are of importance in agricultural decision making will be computed, and compared with the corresponding climatological distribution to quantify the shift in the probabilities and consequently the risk estimates. This approach has been demonstrated successfully in a resampling-based weather generator (Apipattanavis et al., 2007) and has been applied to seasonal crop yield forecasts, quantifying delays in highway constructions, and in streamflow forecasts (Apipattanavis, 2008; Apipattanavis et al., 2010a, 2010b).

    To demonstrate statistical downscaling based on the GLM weather generator, we make use of the IRI seasonal forecasts issued in mid to late September for October through December in the years 1997 to 2007. For both total precipitation and mean temperature, the forecast probabilities deviated from the climatology for only six of the 11 years. Figure 1 shows boxplots of the downscaled forecast probability distributions of summer (i.e., October through March) total precipitation, maximum temperature, and minimum temperature at Pergamino. For comparative purposes, the corresponding boxplots for the climatological distributions are included as well, along with the observed seasonal statistics for each forecast year (indicated by circles on the boxplots).

    For total precipitation, the IRI seasonal forecasts with the greatest deviations from the climatology were for 1997, with a probability of 0.55 for the above-normal category, and for 1998, with a probability of 0.60 for the below-normal category. The consistent shift in the downscaled forecast boxplots toward wetter than normal conditions in 1997 (drier in 1998) is evident in the figures, with the observed total precipitation being below normal for both years at Pergamino, but near normal for both years at Pilar. For mean temperature, the IRI seasonal forecasts with the greatest deviations from the climatology were for 1998 and 2003, with a probability of 0.50 for the above-normal category. The consistent shift in the downscaled forecast boxplots toward warmer than normal conditions for both maximum and minimum temperature is evident in the figures. In 1998, the observed seasonal mean maximum temperature was above normal at Pergamino, but near normal at Pilar, with the observed seasonal mean minimum temperature being above normal at both Pergamino and Pilar. In 2003, the observed mean maximum temperature was below normal at Pergamino and near normal at Pilar, with the observed seasonal mean minimum temperature being above normal at Pilar, but near normal at Pergamino.

    In an attempt to further downscale the IRI seasonal precipitation forecasts into more meaningful daily statistics, Fig. 2 shows boxplots of downscaled forecast probability distributions for the number of dry days and the median precipitation intensity at Pergamino. Focusing again on 1997 and 1998, the years with the highest seasonal forecast probability of above- (or below-) normal total precipitation, the forecast boxplots of the number of dry days consistently shift toward less dry days in 1997 (more dry days in 1998) and the boxplots of the median intensity consistently shift toward higher values in 1997 (lower values in 1998). In 1997, the observed seasonal number of dry days was near normal at Pergamino and below normal at Pilar, with the median intensity being below normal at Pergamino but near normal at Pilar. In 1998, the observed seasonal number of dry days was near normal at Pergamino and below normal at Pilar, with the median intensity being below normal at both Pergamino and Pilar.

    Figure 3.  The PDF of summer precipitation (a), maximum temperature (b) and minimum temperature (c) from the simulation (dashed line), climatological PDF (solid line) and the observed value (vertical line) at Pergamino based on dry seasonal IRI forecasts (2004).

    The performance of the downscaled seasonal forecasts shown in Fig. 2 is evaluated using the ranked probability skill score (RPSS) (Wilks, 2006, Chapter 7). The RPSS is calculated based on three categories at the tercile boundaries. RPSS=0 corresponds to no skill over the climatology, whereas RPSS=1 for perfect forecasts. In order to calculate the RPSS, the forecast probabilities of below normal, near normal, and above normal are first derived from the forecast probability density function (PDF) for each climate variable. At least limited skill is indicated for seasonal total precipitation, with RPSS=0.042 for Pergamino and RPSS=0.143 for Pilar. Because these forecasts apply to 6-month seasons, their skill is necessarily less than that for the original IRI forecasts for the first half of the time period.

    Figure 4.  The PDF of summer precipitation (a), maximum temperature (b) and minimum temperature (c) from the simulation (dashed line), climatological PDF (solid line) and the observed value (vertical line) at Pergamino based on wet seasonal IRI forecasts (2000).

    Figure 5.  The PDF of the number of dry days (a) and hot days (b) from the simulation (dashed line) and climatological PDF (solid line) at Pergamino based on seasonal forecasts from IRI (2004).

    Figure 6.  The PDF of the number of dry days (a) and hot days (b) from the simulation (dashed line) and climatological PDF (solid line) at Pilar based on seasonal forecasts from IRI (2000).

    For seasonal mean minimum temperature the results are inconsistent, with RPSS=-0.015 for Pergamino but RPSS=0.073 for Pilar. Similarly, for seasonal mean maximum temperature, with RPSS=0.151 for Pergamino but RPSS=-0.118 for Pilar. Given that five out of 11 years had a climatological forecast, and in other years the climate forecast skill is modest at best, we do not expect a high overall RPSS value. This limited or lack of skill may be attributable in part to the original IRI forecasts being specified only in terms of mean temperature, not minimum and maximum temperature, as mentioned earlier.

    A clear shift of the forecast PDF of precipitation to the left of the climatology, consistent with a dry forecast, can be seen at Pilar, but is not quite as apparent at Pergamino (Fig. 3). However, the shift in the temperature PDFs to the right of the climatology, consistent with a warmer than normal temperature forecast probability, can be seen at both locations. The forecast PDFs of precipitation for the wet year of 2000 show similar consistent shifts relative to the climatology (Fig. 4), but are somewhat subtler compared to the dry forecast case in Fig. 1-and this can be attributed to the fact that the seasonal forecast for the dry year is closer to the climatology than that of the wet forecast. The shifts in the temperature PDFs are consistent with the IRI forecast representing near-normal conditions. These shifts have significant implications for the tail probabilities, i.e., the extremes and, consequently, crops yield impacts in agricultural applications.

    We computed the PDFs of summer dry days (i.e., total number of days with no rainfall) and hot days (i.e., total number of days with maximum temperature above 35°C) at the two locations for the dry year 2004 (Fig. 5). The shifts in the PDF of hot days at both locations relative to the climatology towards higher values, consistent with the shift in the PDF of mean maximum temperature (Fig. 1), can be seen quite clearly, while the summer dry days exhibit weaker shifts. The corresponding results for the wet-year forecasts of 2000 are shown in Fig. 6, with the most noticeable shift being toward a near normal number of hot days at Pilar.

4. Downscaling climate change scenarios
  • Climate change projections for the 21st century are available at a monthly time scale and for a spatial scale given by the climate model grid-size (typically, hundreds of square kilometers) based on an ensemble of global climate change models (e.g., the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, IPCC AR4). For a point location, the time series of monthly precipitation and of temperature, consisting of the ensemble of climate change projections at the grid box containing the location, are considered for simplicity. Ensembles of weather sequences based on these projections can be generated by using the procedure described in the previous section——especially step (3). In particular, the seasonal projected values of precipitation, suitably smoothed, can be used as a covariate in the GLM weather generator described earlier to generate an ensemble of daily weather sequences consistent with the projections. This approach can also be used for downscaling shorter-term (e.g., decadal) projections.

    Figure 7.  The simulated means (dashed line) and 95th projection band (dotted line) for summer seasonal total precipitation (a), mean maximum temperature (b) and mean minimum temperatures (c) during the 1931-55 epoch, along with the smoothed observed time series (solid line), for Pergamino.

    Figure 8.  The PDF of the simulated projections (dashed line) of the summer total precipitation (a), mean maximum temperature (b) and mean minimum temperature (c) for the 1931-55 epoch, along with the model climatology (solid line), for Pergamino.

    Figure 9.  The PDF of simulated projections (dashed line) of the number of dry days (a) and hot days (b) for the 1931-55 epoch, along with the model climatology (solid line), for Pergamino.

    To demonstrate this approach, we selected an earlier dry epoch (1931-55) in the Argentine Pampas. The LOESS-smoothed seasonal precipitation and temperature for each year of these epochs were used a covariates to the GLM weather generator to produce daily weather sequences consistent with the decadal variability of these epochs. As before, probability distributions of a suite of weather statistics were computed and compared with the corresponding climatological distributions to check for epochal shifts.

    The simulated summer seasonal precipitation, maximum and minimum temperature for the epoch, along with the projections at both locations, are shown in Fig. 7. The 2.5th and 97.5th percentiles of the ensembles, the median and the smoothed time series projection during this epoch are shown in the figure. It can be seen that the ensembles track the projection very well at both locations, indicating that the methodology is able to generate consistent weather sequences with a rich variety. The PDFs from the simulations of the summer precipitation (Fig. 8) both show clear shifts consistent with the drier epoch relative to the climatological PDF at both locations. Most noticeable shifts in temperature are towards lower minimum temperature at Pergamino. Shifts in the PDFs of summer dry days towards drier conditions are also clear at the two locations (Fig. 9).

5. Conclusions
  • Using the incorporation of smoothed seasonally aggregated climate statistics into the GLM model as covariates, it has been demonstrated how the incorporation of such seasonally aggregated climate statistics facilitates statistical downscaling of seasonal climate forecasts. These results are encouraging in that the methodology provides a robust tool to generate weather sequences consistent with any seasonal climate forecast of potential use in resources planning and management. In the case of seasonal forecasts, the GLM weather generator makes it straightforward to translate the uncertainty in the seasonal forecast product into that for the corresponding conditional daily weather statistics.

    From a climate diagnostics perspective, it is somewhat uninformative to remove overdispersion through explicit use of seasonal aggregated climate statistics as covariates in the GLM weather generator. A more appealing approach could involve replacing these covariates with a hidden variable to reflect unobserved shifts in climate "regimes" on an interannual or longer (e.g., decadal) time scale. Using a hidden Markov model (e.g., MacDonald and Zucchini, 1997) to represent this regime state would allow for long-term persistence, as well as having the advantage of being a fully probabilistic approach (i.e., explicitly modeling the uncertainty about which climate regime is presently occurring). In addition, our approach can be applied in the spatiotemporal versions of GLM weather generators by using seasonal spatial average precipitation as the covariate (Verdin et al., 2015).

Reference

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return