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Uncertainty propagation of the downscaling model results

GEOSTATISTICAL DOWNSCALING OF OFFSHORE WIND SPEED DATA DERIVED FROM NUMERICAL WEATHER PREDICTION MODELS USING HIGHER SPATIAL RESOLUTION

3. Methodology

3.2. Uncertainty propagation of the downscaling model results

The uncertainty in wind power density (WPD) is additionally examined within a Monte Carlo context via the use of geostatistical simulation. Consensus fusion (Deutsch and Zanon, 2004; Doyen et al., 1996) is adopted to estimate a local distribution at each 1km pixel. The mean of that local distribution is a weighted combination of UERRA a, b Weibull parameters downscaled using Area-to-Point Ordinary Kriging (ATPOK) and Sentinel a, b Weibull parameters. The variance of that local distribution is a combination of error-variances attached to each source of information (i.e., ATPOK variance for downscaled UERRA, bootstrap variance for Sentinel).

Standard Gaussian unconditional realizations are simulated (via Cholesky decomposition) for each Weibull parameter, using the corresponding Sentinel-derived correlogram/variogram model. Each pair of simulated Gaussian deviates at each 1km x 1km pixel is transformed into (cross)correlated realizations to account for the fact that Weibull a and b parameters exhibit significant (cross)correlation.

Figure 4. Two WPD realizations computed by the respectful simulated Weibull a and b parameters

Weibull a and b parameter values are simulated at each location by multiplying each simulated Gaussian deviate with the corresponding local standard deviation and adding the corresponding local mean; spatial correlation in simulated Gaussian deviates induces spatial correlation in simulated Weibull parameters.

Finally, the simulated WPD is computed at each 1km x 1km pixel using pairs of simulated Weibull a and b parameter values; Figure 4 depicts two realizations of WPD.

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4. Results

The inclusion of Sentinel-1 fine resolution information in the downscaling method employed in this work furnishes important local variability in the downscaling endeavor that is otherwise missing from downscaling UERRA data alone. The downscaled a, and b Weibull parameter predictions computed by ATPKED are depicted in Figure 5.

Figure 5. Downscaled a, and b-Weibull parameter estimation computed by ATPKED

Similarly, wind power density spatial patterns derived by the above described ATPKED downscaling method tend to be less smooth compared to downscaling methods only incorporating UERRA coarse wind data.

Moreover, the uncertainty analysis conducted via the simulation of Weibull a, and b parameters results in an ensemble of simulated wind power density realizations; Figure 6 depicts the ensemble WPD average and standard deviations of the simulated WPD values at each 1km grid node.

Figure 6. Ensemble average (left) and std deviation (right) of the WPD realizations

A measure of uncertainty is obtained via the downscaled estimates allowing to report the deviation around the wind power density values which does not seem to be particularly high in this case (ranges between 0-3.5 W⁄m^2 ). The proposed geostatistical uncertainty analysis may lead to risk conscious policy making for a potential future wind farm allocation scheme for the offshore area of Cyprus.

5. Discussion and Conclusions

The analysis and modeling based on satellite products depend heavily on spatial and temporal resolutions of such products. Using satellite products (Sentinel-1 wind data in this project) with appropriate spatial resolutions is crucial for both global/regional and local analyses. The revisiting time or temporal resolution is also important in the proper selection of satellite products for periodic monitoring. Periodic environmental monitoring and time-series analysis are possible using reanalysis products (UERRA wind data in this work) owing to their high temporal resolutions. However, the spatial resolution of reanalysis products is too coarse to perform analysis at a local scale.

138 Spatial downscaling is often applied to coarse scale satellite products with high temporal resolution for

environmental monitoring at a finer scale. This work describes the implementation of area-to-point Kriging with External Drift (ATPKED) algorithm for the downscaling of Weibull a, and b parameters derived by UERRA coarse scale data, also accounting for the Sentinel data available at a fine scale resolution. The ATPKED algorithm combines regression modeling and residual correction with area-to-point kriging. The employed geostatistical downscaling of coarse scale Weibull parameters demonstrates that ATPKED algorithm generates downscaling results in which overall variations/patterns in input coarse scale data are preserved and local details are also well captured. Although the applicability of ATPRK was tested on regular raster data such as satellite Sentinel products, the tool is flexible and can be applied to spatial data with irregular shapes because any objects with irregular shapes are discretized by internal points.

Additionally, downscaled UERRA and Sentinel a, b Weibull parameters are employed in a Monte Carlo framework for assessing the uncertainty in spatial distribution of Wind Power Density (WPD) derived from the downscaled Weibull distributions. In this approach, the integration two datasets is achieved via the use of consensus fusion; the local distribution is described by the weighted average of the two levels of information and the variance by the combination by the Kriging variance for downscaled UERRA, and the bootstrap variance for Sentinel. Such simulated realizations can be used to assess the uncertainty in WPD values linked to a potential future wind farm allocation scheme in the offshore areas of Cyprus.

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