A dynamic nonstationary spatio-temporal model for short term prediction of precipitation

Sigrist, Fabio; Künsch, Hans R.; Stahel, Werner A.

doi:10.1214/12-aoas564

Cited by 75 publications

(74 citation statements)

References 84 publications

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“…The space-time interaction function g(·) can be modelled as a parameterized Gaussian dispersal kernel which captures the underlying physical processes behind the spatio-temporal evolution of rainfall, i.e., diffusion, advection, and convection [20,21]. In this case, the spacetime interaction function is given as g(x,…”

Section: State Model 231 a Kernel-based State Modelmentioning

confidence: 99%

“…The quantity w t is the advective displacement during the temporal sampling interval δ t , which can be represented more precisely as w t = v t δ t , where v t is the advection velocity. Note that the aforementioned model is non-stationary when the advection vector w t changes with time, which happens in many real scenarios [20]. If there is no advection, i.e., w t = 0 and D = I, the model is stationary and isotropic.…”

Section: State Model 231 a Kernel-based State Modelmentioning

confidence: 99%

“…We assume that the dynamic model, i.e., the state transition matrix H t is perfectly known through the parameters w t , D, and α which are considered to be deterministic and known. Without loss of generality, we follow the assumptions of [20] and [30] that the distribution of q t is given by…”

Section: State Model 231 a Kernel-based State Modelmentioning

confidence: 99%

“…This is a modelling approximation. One notable advantage of the model in [20] is the linear relation of the rainfall intensities in one snapshot with the ones in the previous snapshot.…”

Section: State Model 231 a Kernel-based State Modelmentioning

confidence: 99%

“…In the first case, we assume that the dynamics of the rainfall field are perfectly known. In this case, we use a linear but non-stationary dynamical model for the space-time evolution of the rainfall event, which incorporates physical phenomena like advection, diffusion, and convection [20,21]. In the second case, we assume that the information regarding the dynamics is not perfectly known.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic rainfall monitoring using microwave links

Roy

Gishkori

Leus

2016

EURASIP J. Adv. Signal Process.

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In this work, we propose a sparsity-exploiting dynamic rainfall monitoring methodology using rain-induced attenuation measurements from microwave links. To estimate rainfall field intensity dynamically from a limited number of non-linear measurements, we exploit physical properties of the rainfall such as spatial sparsity and non-negativity along with the dynamics of rainfall intensity. We develop a dynamic state estimation algorithm, where the aforementioned spatial properties are utilized as prior information. To exploit spatial sparsity, we use a basis function to tailor the sparse representation of the rainfall intensity. The basis is selected based on some criteria for sparse reconstruction such as orthonormality and mutual coherence. The tuning parameter that controls the sparsity in the spatial rainfall distribution is dynamically updated at every correction step. The developed methodology is applied to dynamically monitor the rainfall field intensity in an area with a specified spatial resolution using less number of simulated non-linear measurements than pixels. The proposed methodology can be generalized for any dynamic field reconstruction, where the limited number of non-linear measurements are field intensities integrated over a linear path.

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Section: State Model 231 a Kernel-based State Modelmentioning

confidence: 99%

Section: State Model 231 a Kernel-based State Modelmentioning

confidence: 99%

Section: State Model 231 a Kernel-based State Modelmentioning

confidence: 99%

“…This is a modelling approximation. One notable advantage of the model in [20] is the linear relation of the rainfall intensities in one snapshot with the ones in the previous snapshot.…”

Section: State Model 231 a Kernel-based State Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dynamic rainfall monitoring using microwave links

Roy

Gishkori

Leus

2016

EURASIP J. Adv. Signal Process.

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A spatiotemporal precipitation generator based on a censored latentGaussian field

Baxevani

Lennartsson

2015

Water Resources Research

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A daily stochastic spatiotemporal precipitation generator that yields precipitation realizations that are quantitatively consistent is described. The methodology relies on a latent Gaussian field that drives both the occurrence and intensity of the precipitation process. For the precipitation intensity, the marginal distributions, which are space and time dependent, are described by a composite model of a gamma distribution for observations below some threshold with a generalized Pareto distribution modeling the excesses above the threshold. Model parameters are estimated from data and extrapolated to locations and times with no direct observations using linear regression of position covariates. One advantage of such a model is that stochastic generator parameters are readily available at any location and time of the year inside the stationarity regions. The methodology is illustrated for a network of 12 locations in Sweden. Performance of the model is judged through its ability to accurately reproduce a series of spatial dependence measures and weather indices.

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Describing the catchment‐averaged precipitation as a stochastic process improves parameter and input estimation

Giudice

Albert

Rieckermann

et al. 2016

Water Resources Research

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Rainfall input uncertainty is one of the major concerns in hydrological modeling. Unfortunately, during inference, input errors are usually neglected, which can lead to biased parameters and implausible predictions. Rainfall multipliers can reduce this problem but still fail when the observed input (precipitation) has a different temporal pattern from the true one or if the true nonzero input is not detected. In this study, we propose an improved input error model which is able to overcome these challenges and to assess and reduce input uncertainty. We formulate the average precipitation over the watershed as a stochastic input process (SIP) and, together with a model of the hydrosystem, include it in the likelihood function. During statistical inference, we use ''noisy'' input (rainfall) and output (runoff) data to learn about the ''true'' rainfall, model parameters, and runoff. We test the methodology with the rainfall-discharge dynamics of a small urban catchment. To assess its advantages, we compare SIP with simpler methods of describing uncertainty within statistical inference: (i) standard least squares (LS), (ii) bias description (BD), and (iii) rainfall multipliers (RM). We also compare two scenarios: accurate versus inaccurate forcing data. Results show that when inferring the input with SIP and using inaccurate forcing data, the whole-catchment precipitation can still be realistically estimated and thus physical parameters can be ''protected'' from the corrupting impact of input errors. While correcting the output rather than the input, BD inferred similarly unbiased parameters. This is not the case with LS and RM. During validation, SIP also delivers realistic uncertainty intervals for both rainfall and runoff. Thus, the technique presented is a significant step toward better quantifying input uncertainty in hydrological inference. As a next step, SIP will have to be combined with a technique addressing model structure uncertainty.

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A dynamic nonstationary spatio-temporal model for short term prediction of precipitation

Cited by 75 publications

References 84 publications

Dynamic rainfall monitoring using microwave links

Dynamic rainfall monitoring using microwave links

A spatiotemporal precipitation generator based on a censored latentGaussian field

Describing the catchment‐averaged precipitation as a stochastic process improves parameter and input estimation

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