Prediction of air pollutants PM 10 by ARBX(1) processes Abstract This work adopts a Banach-valued time series framework for component-wise estimation and prediction, from temporal correlated functional data, in presence of exogenous variables. The strong-consistency of the proposed functional estimator and associated plug-in predictor is formulated. The simulation study undertaken illustrates their large-sample size properties. Air pollutants PM10 curve forecasting, in the Haute-Normandie region (France), is addressed by implementation of the functional time series approach presented.

Effects of agricultural activities on the temporal variations of streamflow: trends and long memory Abstract Effects of agricultural activities on temporal variations in streamflow were investigated based on an integrated hydrological model in the Heihe River Basin (HRB). De-trended fluctuation analysis was conducted using the simulated time series of the daily streamflow at 13 observation points along the Heihe River. Both the original and deseasonalized streamflow were obtained and analyzed. We found that temporal variations of the natural watershed streamflow without the interference of agricultural activities are nonstationary, but become relatively stationary when agricultural activities occur. This indicates a weakened damping effect of the hydrological system on hydrological signals. Agricultural activities mainly affect the trends in streamflow, as the trends may have been gradually removed with increasing agricultural activities. Therefore, long-term correlation of the streamflow decreases and eventually converges to the long memory, which remains invariant under the disturbance of agricultural activities. A practical significance of the results from this study for the water resources management in the agricultural regions is that more attention should be given to the trend identification, especially when predicting extreme hydrological events, such as drought or flood.

Parametric variogram matrices incorporating both bounded and unbounded functions Abstract We construct a flexible class of parametric models for both traditional and pseudo variogram matrix (valued functions), where the off-diagonal elements are the traditional cross variograms and pseudo cross variograms, respectively, and the diagonal elements are the direct variograms, based on the method of latent dimensions and the linear model of coregionalization. The entries in the parametric variogram matrix allow for a smooth transition between boundedness and unboundedness by changing the values of parameters, and thus between joint second-order and intrinsically stationary vector random fields, or between multivariate geometric Gaussian processes and multivariate Brown–Resnick processes in spatial extreme analysis.

Filling missing data and smoothing altered data in satellite imagery with a spatial functional procedure Abstract Outliers and missing data are commonly found in satellite imagery. These are usually caused by atmospheric or electronic failures, hampering the correct monitoring of remote-sensing data. To avoid distorted data, we propose a procedure called “spatial functional prediction” (SFP). The SFP procedure consists of the following: (1) aggregating remote-sensing data for reducing the number of missing data and/or outliers; (2) additively decomposing the time series of images into a trend, a seasonal, and an error component; (3) defining the spatial functional data and predicting the trend component using an ordinary kriging; and (4) adding back the seasonal and error components to the predicted trend. The benefits of the SFP procedure are illustrated in the following scenarios: introducing random outliers, random missing data, mixtures of both, and artificial clouds in an extensive simulation study of composite images, and using daily images with real clouds. The following two derived variables are considered: land surface temperature (LST day) and normalized vegetation index (NDVI), which are obtained as remote-sensing data in a region in northern Spain during 2003–2016. The performance of SFP was checked using the root mean squared error (RMSE). A comparison with a procedure based on predicting with thin-plate splines (TpsP) is also made. We conclude that SFP is simpler and faster than TpsP, and provides smaller values of RMSE.

Gaussian process for estimating parameters of partial differential equations and its application to the Richards equation Abstract This paper proposes a new collocation method for estimating parameters of a partial differential equation (PDE), which uses Gaussian process (GP) as a basis function and is termed as Gaussian process for partial differential equation (GPPDE). The conventional method of estimating parameters of a differential equation is to minimize the error between observations and their estimates. The estimates are produced from the forward solution (numerical or analytical) of the differential equation. The conventional approach requires initial and boundary conditions, and discretization of differential equations if the forward solution is obtained numerically. The proposed method requires fitting a GP regression model to the observations of the state variable, then obtaining derivatives of the state variable using the property that derivative of a GP is also a GP, and finally adjusting the PDE parameters so that the GP derived partial derivatives satisfy the PDE. The method does not require initial and boundary conditions, however if these conditions are available (exactly or with measurement errors), they can be easily incorporated. The GPPDE method is evaluated by applying it on the diffusion and the Richards equations. The results suggest that GPPDE can correctly estimate parameters of the two equations. For the Richards equation, GPPDE performs well in the presence of noise. A comparison of GPPDE with HYDRUS-1D software showed that their performances are comparable, though GPPDE has significant advantages in terms of computational time. GPPDE could be an effective alternative to conventional approaches for finding parameters of high-dimensional PDEs where large datasets are available.

Birnbaum–Saunders functional regression models for spatial data Abstract With the advancement of technology, data are often recorded continuously and instantaneously. Since the early nineties, this kind of observations have been described by models for functional data. Usually a large set of records for each individual in the sample become in a curve (by using some smoothing method) which is considered as a realization of a random function. In functional regression models these curves are used to establish whether there is a relation with an scalar response (functional regression model with scalar response). If two or more sets of curves are obtained for each individual, more complex functional regression models can be established. In particular, in geosciences, where spatial statistics is a primary tool, functional regression is becoming more frequent. Therefore, it is of interest to develop methodologies for spatially correlated functional data. Also in geosciences, as well as in other areas, it is common that the response variables follow positive skew distributions (for example, those obtained in studies about the level of chemical elements in soil or air). Hence, the standard geostatistical assumption of Gaussian errors, or at least of symmetry, is inappropriate. This type of variables, in non-spatial contexts, have been successfully described by the Birnbaum–Saunders distribution, becoming its modeling a very active research field. However, the use of this distribution in the treatment of geostatistical data has only been applied under stationarity. This paper develops a Birnbaum–Saunders model for geostatistical data considering a non-stationary process using functional covariates. The corresponding parameters are estimated by maximum likelihood and their performance is evaluated through Monte Carlo simulations. We illustrate the proposed model with two geo-referenced data sets, which shows its potential applications and a better performance in relation to the Gaussian model.

Exploring the urban water-energy-food nexus under environmental hazards within the Nile Abstract The integrative approach of water, energy, and food nexus (WEF nexus) is now widely accepted to offer better planning, development, and operation of these resources. This study presents a first attempt towards understanding the WEF nexus of urban environments in the Nile River Basin under conditions of hydrological droughts and fluvial floods. A case study was conducted for the capital of Sudan, Khartoum, at the confluence of the White Nile and the Blue Nile for illustration. The results were based on analyses of river flow and water turbidity data, field observations, a printed questionnaire and an interview of farmers practicing irrigated agriculture, and hydropower modeling. The study analyzes indicators for the association of the river water resources environment (intra-annual regime, quantity, and quality), the status of urban irrigated agriculture, water treatment for domestic use, and hydropower generation under hydrological extremes, i.e. droughts and fluvial floods. It additionally examines the consequent interactions between the impacts on three sectors. The present study shows how floods and droughts impose impacts on seasonal river water quality and quantity, water treatment for domestic use, irrigated agriculture, and hydro-energy supply in an urban environment. The results demonstrate how the two hydrological phenomena determine the state of hydropower generation from dams, i.e. high energy production during floods and vice versa during droughts. Hydropower dams, in turn, could induce cons in the form of low fertile soils in the downstream due to sediment retention by the reservoir. Finally, present and potential options to minimize the above risks are discussed. This study is hoped to offer good support for integrated decision making to increase the resource use efficiency over the urban environment within the Nile Basin.

Covariance functions for multivariate Gaussian fields evolving temporally over planet earth Abstract The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space–time data arising from, e.g., climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance structure allows to capture both the space–time dependencies between the observations and the development of accurate predictions. For data observed over large portions of planet earth it is necessary to take into account the curvature of the planet. Hence the need for random field models defined over spheres across time. In particular, the associated covariance function should depend on the geodesic distance, which is the most natural metric over the spherical surface. In this work, we propose a flexible parametric family of matrix-valued covariance functions, with both marginal and cross structure being of the Gneiting type. We also introduce a different multivariate Gneiting model based on the adaptation of the latent dimension approach to the spherical context. Finally, we assess the performance of our models through the study of a bivariate space–time data set of surface air temperatures and precipitable water content.

Prediction of spatial functional random processes: comparing functional and spatio-temporal kriging approaches Abstract We present and compare functional and spatio-temporal (Sp.T.) kriging approaches to predict spatial functional random processes (which can also be viewed as Sp.T. random processes). Comparisons with respect to computational time and prediction performance via functional cross-validation is evaluated, mainly through a simulation study but also on a real data set. We restrict comparisons to Sp.T. kriging versus ordinary kriging for functional data (OKFD), since the more flexible functional kriging approaches pointwise functional kriging (PWFK) and the functional kriging total model coincide with OKFD in several situations. Here we formulate conditions under which we show that OKFD and PWFK coincide. From the simulation study, it is concluded that the prediction performance of the two kriging approaches in general is rather equal for stationary Sp.T. processes. However, functional kriging tends to perform better for small sample sizes, while Sp.T. kriging works better for large sizes. For non-stationary Sp.T. processes, with a common deterministic time trend and/or time varying variances and dependence structure, OKFD performs better than Sp.T. kriging irrespective of the sample size. For all simulated cases, the computational time for OKFD was considerably lower compared to those for the Sp.T. kriging methods.

Experimental evidence of the stochastic behavior of the conductivity in radial flow configurations Abstract We deal with the spatial distribution of the hydraulic conductivity K within heterogeneous porous formations where a radial flow (typical of pumping and slug tests) is taking place. In particular, the study provides a wide data-set which is instrumental to corroborate theoretical findings about the stochastic behavior of K in the above flow configuration. Here, K-data pertain to a series of slug tests conducted within a large caisson which was densely instrumented in order to capture the transitional behavior of the conductivity from the near field (close to the pumping well) to the far field (away from the pumping well). For the experiments at stake, it is shown that the apparent conductivity  \(K_{\mathrm{app}}\) is a very robust property. In fact, with the exception of a very tiny annulus surrounding the pumping well, \(K_{\mathrm{app}}\) can be used to solve flow (and transport) problems in close analogy to the effective theory approach adopted for a groundwater-type flow. It is hoped that the data-set exploited in the present study will be useful for other researchers who are engaged with similar studies.