Javier Amezcua

Validation of three new measure-correlate-predict models for the long-term prospection of the wind resource

The estimation of the long-term wind resource at a prospective site based on a relatively short on-site measurement campaign is an indispensable task in the development of a commercial wind farm. The typical industry approach is based on the measure-correlate-predict (MCP) method where a relational model between the site wind velocity data and the data obtained from a suitable reference site is built from concurrent records. In a subsequent step, a long-term prediction for the prospective site is obtained from a combination of the relational model and the historic reference data. In the present paper, a systematic study is presented where three new MCP models, together with two published reference models (a simple linear regression and the variance ratio method), have been evaluated based on concurrent synthetic wind speed time series for two sites, simulating the prospective and the reference site. The synthetic method has the advantage of generating time series with the desired statistical properties, i...

The Effects of the RAW Filter on the Climatology and Forecast Skill of the SPEEDY Model

In a recent study, Williams introduced a simple modification to the widely used Robert‐Asselin (RA) filter for numerical integration. The main purpose of the Robert‐Asselin‐Williams (RAW) filter is to avoid the undesirednumericaldampingofthe RAfilterandto increasetheaccuracy.Inthe presentpaper,the effectsof the modification are comprehensively evaluated in the Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY) atmospheric generalcirculation model. First, the authors search for significant changes in the monthly climatology due to the introduction of the new filter. After testing both at the local level and at the field level, no significant changes are found, which is advantageous in the sense that the new scheme does not require a retuning of the parameterized model physics. Second, the authors examine whether the new filter improves the skill of short- and medium-term forecasts. January 1982 data from the NCEP‐NCAR reanalysis are used to evaluate the forecast skill. Improvements are found in all the model variables (except the relative humidity, which is hardly changed). The improvements increase with lead time and are especially evident in medium-range forecasts (96‐144 h). For example, in tropical surface pressure predictions, 5-day forecasts made using the RAW filter have approximately the same skill as 4-day forecasts made using the RA filter. The results of this work are encouraging for the implementation of the RAW filter in other models currently using the RA filter.

Gaussian anamorphosis in the analysis step of the EnKF:a joint state-variable/observation approach

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state-variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)–(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

A weak-constraint 4DEnsembleVar. Part II: experiments with larger models

ABSTRACT In recent years, hybrid data-assimilation methods which avoid computation of tangent linear and adjoint models by using ensemble 4-dimensional cross-time covariances have become a popular topic in Numerical Weather Prediction. 4DEnsembleVar is one such method. In spite of its capabilities, its application can sometimes become problematic due to the not-trivial task of localising cross-time covariances. In this work we propose a formulation that helps to alleviate such issues by exploiting the presence of model error, i.e. a weak-constraint 4DEnsembleVar. We compare the weak-constraint 4DEnsembleVar to that of other data-assimilation methods. This is part II of a two-part paper. In part I, we describe the 4DEnsembleVar framework and problems with localised temporal cross-covariances associated with this method are discussed and illustrated on the Korteweg de Vries model. We also introduce our weak-constraint 4DEnsemble-Var formulation and show how it can alleviate—at least partially—the problem of having low-quality time cross-covariances. The second part of this paper deals with experiments on larger and more complicated models, namely the Lorenz 1996 model and a modified shallow-water model with simulated convection, both of them under the presence of model error. We investigate the performance of weak-constraint 4DEnsembleVar against strong-constraint 4DEnsembleVar (both with and without localisation) and other traditional methods (4DVar and the Local Ensemble Transform Kalman Smoother). Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering observation density (in time and space), observation period, ensemble sizes and assimilation window length. In this part we also explain how to perform outer loops in the EnVar methods. We show that their use can be counter-productive if the presence of model error is ignored by the assimilation method. We show that the addition of a weak-constraint generally improves the RMSE of 4DEnVar in cases where model error has time to develop, especially in cases with long assimilation windows and infrequent observations. We have assumed good knowledge of the statistics of this model error.

A weak-constraint 4DEnsembleVar. Part I: formulation and simple model experiments

ABSTRACT 4DEnsembleVar is a hybrid data assimilation method which purpose is not only to use ensemble flow-dependent covariance information in a variational setting, but to altogether avoid the computation of tangent linear and adjoint models. This formulation has been explored in the context of perfect models. In this setting, all information from observations has to be brought back to the start of the assimilation window using the space-time covariances of the ensemble. In large models, localisation of these covariances is essential, but the standard time-independent localisation leads to serious problems when advection is strong. This is because observation information is advected out of the localisation area, having no influence on the update. This is part I of a two-part paper in which we develop a weak-constraint formulation in which updates are allowed at observational times. This partially alleviates the time-localisation problem. Furthermore, we provide—for the first time—a detailed description of strong- and weak-constraint 4DEnVar, including implementation details for the incremental form. The merits of our new weak-constraint formulation are illustrated using the Korteweg-de-Vries equation (propagation of a soliton). The second part of this paper deals with experiments in larger and more complicated models, namely the Lorenz (1996) model and a shallow water equations model with simulated convection.

Ensemble clustering in deterministic ensemble Kalman filters

ABSTRACT Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M–1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

Time‐correlated model error in the (ensemble) Kalman smoother

Data assimilation is often performed in a perfect‐model scenario, where only errors in initial conditions and observations are considered. Errors in model equations are increasingly being included, but typically using rather adhoc approximations with limited understanding of how these approximations affect the solution and how these approximations interfere with approximations inherent in finite‐size ensembles. We provide the first systematic evaluation of the influence of approximations to model errors within a time window of weak‐constraint ensemble smoothers. In particular, we study the effects of prescribing temporal correlations in the model errors incorrectly in a Kalman smoother, and in interaction with finite‐ensemble‐size effects in an ensemble Kalman smoother. For the Kalman smoother we find that an incorrect correlation time‐scale for additive model errors can have substantial negative effects on the solutions, and we find that overestimating of the correlation time‐scale leads to worse results than underestimating. In the ensemble Kalman smoother case, the resulting ensemble‐based space–time gain can be written as the true gain multiplied by two factors, a linear factor containing the errors due to both time‐correlation errors and finite ensemble effects, and a nonlinear factor related to the inverse part of the gain. Assuming that both errors are relatively small, we are able to disentangle the contributions from the different approximations. The analysis mean is affected by the time‐correlation errors, but also substantially by finite‐ensemble effects, which was unexpected. The analysis covariance is affected by both time‐correlation errors and an in‐breeding term. This first thorough analysis of the influence of time‐correlation errors and finite‐ensemble‐size errors on weak‐constraint ensemble smoothers will aid further development of these methods and help to make them robust for e.g. numerical weather prediction.

Statistical evaluation of the early-stage development of Jatropha energy plantations in Northeastern Mexico

A systematic evaluation of agricultural factors affecting the adaptation of the tropical oil plant Jatropha curcas L. to the semi-arid subtropical climate in Northeastern Mexico has been conducted. The factors studied include plant density and topology, as well as fungi and virus abundances. A multiple regression analysis shows that total fruit production can be well predicted by the area per plant and the total presence of fungi. Four common herbicides and a mechanical weed control measure were established at a dedicated test array and their impact on plant productivity was assessed.