Ensemble based groundwater level prediction using neural network pattern fitting

44-50Prediction of groundwater level is implemented using Time-series prediction model and combined prediction model for learning the pattern and trend in groundwater level fluctuation, result show that the combined prediction model using, groundwater level time series and precipitation time series as input predictors is a better predictor. Study also shows that prediction is dependent on the pattern and trends at a particular location as every dataset depends on the dynamics of the location namely the geomorphology of the aquifer, the drainage inside the aquifer and pumping from the aquifer. Ensemble based forecasting is studied to fix the upper and lower limit of the prediction. Ensembles helped in fixing a range for the forecast instead of relying on a single unique value

Variational data assimilation using targetted random walks

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces

Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems

It has been widely realized that Monte Carlo methods (approximation via a sample ensemble) may fail in large scale systems. This work offers some theoretical insight into this phenomenon in the context of the particle filter. We demonstrate that the maximum of the weights associated with the sample ensemble converges to one as both the sample size and the system dimension tends to infinity. Specifically, under fairly weak assumptions, if the ensemble size grows sub-exponentially in the cube root of the system dimension, the convergence holds for a single update step in state-space models with independent and identically distributed kernels. Further, in an important special case, more refined arguments show (and our simulations suggest) that the convergence to unity occurs unless the ensemble grows super-exponentially in the system dimension. The weight singularity is also established in models with more general multivariate likelihoods, e.g. Gaussian and Cauchy. Although presented in the context of atmospheric data assimilation for numerical weather prediction, our results are generally valid for high-dimensional particle filters.Comment: Published in at http://dx.doi.org/10.1214/193940307000000518 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Ensemble based groundwater level prediction using neural network pattern fitting

Prediction of groundwater level is implemented using Time-series prediction model and combined prediction model for learning the pattern and trend in groundwater level fluctuation, result show that the combined prediction model using, groundwater level time series and precipitation time series as input predictors is a better predictor. Study also shows that prediction is dependent on the pattern and trends at a particular location as every dataset depends on the dynamics of the location namely the geomorphology of the aquifer, the drainage inside the aquifer and pumping from the aquifer. Ensemble based forecasting is studied to fix the upper and lower limit of the prediction. Ensembles helped in fixing a range for the forecast instead of relying on a single unique value

Monte Carlo Based Ensemble Forecasting

Ensemble forecasting involves the use of several integrations of a numerical model. Even if this model is assumed to be known, ensembles are needed due to uncertainty in initial conditions. The ideas discussed in this paper incorporate aspects of both analytic model approximations and Monte Carlo arguments to gain some efficiency in the generation and use of ensembles. Efficiency is gained through the use of importance sampling Monte Carlo. Once ensemble members are generated, suggestions for their use, involving both approximation and statistical notions such as kernel density estimation and mixture modeling are discussed. Fully deterministic procedures derived from the Monte Carlo analysis are also described. Examples using the three-dimensional Lorenz system are described. Address: Mark Berliner Department of Statistics Ohio State University 1958 Neil Ave. Columbus, OH 43210-1247 USA e-mail: [email protected] Keywords and Phrases: Chaos, Importance sampling, Kernel density es..