Acknowledging a considerable literature on modeling daily temperature data, we propose a multi-level spatiotemporal model which introduces several innovations in order to explain the daily maximum temperature in the summer period over 60 years in a region containing Aragón, Spain. The model operates over continuous space but adopts two discrete temporal scales, year and day within year. It captures temporal dependence through autoregression on days within year and also on years. Spatial dependence is captured through spatial process modeling of intercepts, slope coefficients, variances, and autocorrelations. The model is expressed in a form which separates fixed effects from random effects and also separates space, years, and days for each type of effect. Motivated by exploratory data analysis, fixed effects to capture the influence of elevation, seasonality, and a linear trend are employed. Pure errors are introduced for years, for locations within years, and for locations at days within years. The performance of the model is checked using a leave-one-out cross-validation. Applications of the model are presented including prediction of the daily temperature series at unobserved or partially observed sites and inference to investigate climate change comparison.Supplementary materials accompanying this paper appear online.
The analysis of trends and other non-stationary behaviours at the extremes of a series is an important problem in global warming. This work proposes and compares several statistical tools to analyse that behaviour, using the properties of the occurrence of records in i.i.d. series. The main difficulty of this problem is the scarcity of information in the tails, so it is important to obtain all the possible evidence from the available data. First, different statistics based on upper records are proposed, and the most powerful is selected. Then, using that statistic, several approaches to join the information of four types of records, upper and lower records of forward and backward series, are suggested. It is found that these joint tests are clearly more powerful. The suggested tests are specifically useful in analysing the effect of global warming in the extremes, for example, of daily temperature. They have a high power to detect weak trends and can be widely applied since they are non-parametric. The proposed statistics join the information of M independent series, which is useful given the necessary split of the series to arrange the data. This arrangement solves the usual problems of climate series (seasonality and serial correlation) and provides more series to find evidence. These tools are used to analyse the effect of global warming on the extremes of daily temperature in Madrid.
Water flows in the hydrosphere through a tangled and tortuous labyrinth of ways that is the hydrological cycle. Flow separation models are an attempt to group such complexity of paths into a few components of flow and storage so as to reflect the overall behaviour of a basin. A new method of analysis and separation of flow components, based on equations of dynamic relations between Linear Reservoirs connected in Parallel (PLR models), is developed in this article. A synthesis of models based on mathematical filter equations is carried out in order to make comparisons with the proposed model. Reference is also made to the methodology of adjustment and calibration of the PLR models based on the recession curves of the real hydrographs. The models are tested with the continuous register of a basin located in the northeast of Spain. The simulations are carried out with two reservoir models (2R models), three reservoirs (3R models) and with a mathematical filter model to compare the results. With the results of the models, flow duration curves (FDCs) and storage duration curves (SDCs) were elaborated, thus allowing assessment of the origin of the water resources of the basin, a guarantee of their regulation and availability, the dynamic storage in the catchment, residence times and other features.
Evidence of global warming induced from the increasing concentration of greenhouse gases in the atmosphere suggests more frequent warm days and heat waves. The concept of an extreme heat event (EHE), defined locally based on exceedance of a suitable local threshold, enables us to capture the notion of a period of persistent extremely high temperatures. Modeling for extreme heat events is customarily implemented using time series of temperatures collected at a set of locations. Since spatial dependence is anticipated in the occurrence of EHE’s, a joint model for the time series, incorporating spatial dependence is needed. Recent work by Schliep et al. (J R Stat Soc Ser A Stat Soc 184(3):1070–1092, 2021) develops a space-time model based on a point-referenced collection of temperature time series that enables the prediction of both the incidence and characteristics of EHE’s occurring at any location in a study region. The contribution here is to introduce a formal definition of the notion of the spatial extent of an extreme heat event and then to employ output from the Schliep et al. (J R Stat Soc Ser A Stat Soc 184(3):1070–1092, 2021) modeling work to illustrate the notion. For a specified region and a given day, the definition takes the form of a block average of indicator functions over the region. Our risk assessment examines extents for the Comunidad Autónoma de Aragón in northeastern Spain. We calculate daily, seasonal and decadal averages of the extents for two subregions in this comunidad. We generalize our definition to capture extents of persistence of extreme heat and make comparisons across decades to reveal evidence of increasing extent over time.
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