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Поредната сбирка на Националния семинар по стохастика ще се проведе на 27 ноември 2019 г. (сряда) от 14:00 часа в зала 403 на ИМИ – БАН. Доклад на тема:

Statistical calibration of numerical models

ще изнесе Marek Brabec (Institute of Computer Science, Czech Academy of Sciences).

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Резюме. We will present a general semiparametric approach to calibration of numerical model against measurements and illustrate it on large-scale data from ongoing projects.

The measurement of the air pollution is typically sparsely located in space. Physically formulated mesoscale weather prediction models (WRF) coupled with chemical transport models (CAMx) can provide valuable source of additional information. Physical/chemical/transport models can be viewed as a formalized post-processing of emission and weather data adhering to basic physical/chemical laws via massive computations based essentially on PDE solvers. Due to errors in inputs or numerical model (NM) formulation, the raw output of the NM is not overwhelmingly precise on small spatio-temporal scales of interest. We approach this problem as a semiparametric, time-varying calibration of the raw NM against available pollutant concentration measurements. Effectively, we take the NM output as one of the inputs of a structured, semiparametric generalized additive model (GAM) with penalized spline components to account for possible nonlinearities and time-varying nature of some key relationships. The performance of calibrated model is far better than that of the raw NM output or of interpolated measurements alone. Moreover, GAM allows for exploration of the complicated raw NM output bias structure. With suitably defined GAM model components, we can provide a valuable feedback – pointing to where the NM can be improved. One of the most problematic spots in the NM air pollution modeling is the quality of emission inventories. Additionally, raw NM is under-smooth and can be improved by appropriate smoothing. The smoothing has to respect underlying system dynamics and cannot be done simply along the time trajectories. We will show a suitable GAM model structure leading to realistic smoothing strategy. The approach will be illustrated on large scale data from a City of Prague air pollution monitoring project and from the Strategy AV21 collaborative initiative of the Czech Academy of Sciences.

If time will permit, we will also present general approach to statistical calibration of the NWP (numerical weather prediction) forecasts. In fact, we formulate a flexible statistical model framework which takes NWP output(s) as one of its inputs and produces estimates or predictions of quantities of interest (e.g. solar irradiance, wind energy and/or electric power generated). This is much less straightforward than it might seem. First, the NWP outputs inevitably have systematic biases with complicated spatio-temporal structure. Next, as we will show, they can be viewed as substantially undersmooth predictors of the true meteorological or energy production variables. This presents several obstacles to subsequent statistical modeling and calibration. We will illustrate the approach on examples from photovoltaic and/or wind energy applications.