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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.
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.
This paper presents a multimodel regression-sampling algorithm (MRS) for monthly streamflow simulation. MRS is motivated from the acknowledgment that typical nonparametric models tend to simulate sequences exhibiting too close a resemblance to historical records and parametric models have limitations in capturing complex distributional and dependence characteristics, such as multimodality and nonlinear autocorrelation. The aim of MRS is to generate streamflow sequences with rich scenarios while properly capturing complex distributional and dependence characteristics. The basic assumptions of MRS include: (1) streamflow of a given month depends on a feature vector consisting of streamflow of the previous month and the dynamic aggregated flow of the past 12 months and (2) streamflow can be multiplicatively decomposed into a deterministic expectation term and a random residual term. Given a current feature vector, MRS first relates the conditional expectation to the feature vector through an ensemble average of multiple regression models. To infer the conditional distribution of the residual, MRS adopts the k-nearest neighbor concept. More precisely, the conditional distribution is estimated by a gamma kernel smoothed density of historical residuals inside the k-neighborhood of the given feature vector. Rather than obtaining the residuals from the averaged model only, MRS retains all residuals from all the original regression models. In other words, MRS perceives that the original residuals put together would better represent the covariance structure between streamflow and the feature vector. By doing so, the benefit is that a kernel smoothed density of the residual with reliable accuracy can be estimated, which is hardly possible in a single-model framework. It is the smoothed density that ensures the generation of sequences with rich scenarios unseen in historical record. We evaluated MRS at selected stream gauges and compared with several existing models. Results show that (1) compared with typical nonparametric models, MRS is more apt at generating sequences with richer scenarios and (2) in contrast to parametric models, MRS can reproduce complex distributional and dependence characteristics. Since MRS is flexible at incorporating different covariates, it can be tailored for other potential applications, such as hydrologic forecasting, downscaling, as well as postprocessing deterministic forecasts into probabilistic ones.
Precipitation data of finer timescale and higher spatial density are crucial for continuous hydrological modelling and flood risk assessment. Disaggregation methods are often used to transform the coarser‐timescale precipitation data into finer resolutions. The nonparametric approach based on method of fragments (MOF) has received broad attention in precipitation disaggregation literature, given its superiority in reproducing the at‐site statistical attributes. However, a detailed literature review has shown that the MOF‐based resampling approaches are mainly focused in the single‐site precipitation disaggregation context, which may subject to limitations such as the unavailability of at‐site precipitation records and the incapability to preserve the inter‐site correlation structure. To address these issues, we propose three resampling approaches based on MOF. The first approach is a single‐site interval‐based resampling approach which only draws subdaily fragment vectors from at‐site record. The second one extends the first one to a regionalized version where subdaily fragment vectors are drawn from both the at‐site and neighbouring stations. The third one is a multi‐site approach developed to preserve the observed inter‐site correlation. The performances of the three methods are evaluated with applications to daily‐to‐hourly precipitation disaggregation at six rain gauges in Singapore and eight precipitation stations in Wangkuai reservoir catchment in northern China. An elaborate list of performance measures, including standard validation statistics, spatial correlation, inter‐day connectivity, annual extreme analysis, and intra‐day dry and wet spell characteristics are used to assess the performance. The proposed three methods are shown to be effective in reproducing the at‐site attributes, and no significant deterioration of performance is observed when moving from the single‐site method to the regionalized and multi‐site versions. As expected, the multi‐site approach is the only one method that is able to reconstruct the spatial correlation in the disaggregated precipitation field. The approaches can be applied for daily‐to‐subdaily precipitation disaggregation in different regions.
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