# Global RTOFS Sea Ice Validation

Global RTOFS is coupled to the Community Ice CodE (CICE) or Los Alamos Sea Ice Model. CICE is a computer code developed through years of community collaborations, which solve a collection of mathematical equations that represent the physical processes that occur during sea ice evolution: growth, melting, and movement of sea ice, along with the snow and melt water carried with it.

This page compares the polar sea ice concentrations computed in Global RTOFS and compares it to the NCEP Sea Ice analysis. Global RTOFS is coupled to the Community Seaice Model (CICE) version 3.1, and the sea ice data is incorporated in the daily RTOFS data sets, available from NOMADS. The NCEP Sea Ice analysis is available from the NCEP Sea Ice Home Page.

## Difference

Global RTOFS (1/12 deg tripolar grid) is interpolated to the NCEP Sea Ice 5-min modeler's grid. Both data sets are masked to exclude grid points whose ice concentration below 15%. The difference is computed for grid points that contain data in either set. The average weighted by the cell areas of the difference and standard deviation of the difference field are calculated as well as the following list of statistics:

• ### Bias

The area-weighted difference between the model and observations, measures the tendency of the model process to over- or under-estimate the value of a parameter. Smaller absolute bias values indicate better agreement between measured and calculated values. Positive bias means overprediction, negative means underprediction.

```        diff = model_data - buoy_data
bias = numpy.average(diff,weights=cell_areas)
```

• ### Root-Mean-Square Error (RMS Error)

Also called the root-mean-squared deviation, it's a measure of the differences between the observed and predicted values. Smaller RMSE values indicate better agreement between measured and calculated values.

```        rmse=(numpy.average(diff**2,weights=cell_areas))**0.5
```

• ### Correlation Coefficient

The cross-correlation coefficient is a measure of the similarity of two time-series of model and observed values. The standard Pearson product-moment correlation coefficient is computed from a pair-wise correlation of the two fields (model, observation), disregarding any NaN or missing values, except where the ice analysis or the model predicts ice and the other does not. In this case the missing data is set to zero.

```        cc=numpy.ma.corrcoef(obs.flatten(),model.flatten())[0,1]
```

• ### Scatter Index (SI)

Defined as the standard deviation of the difference between model and observations, normalised by the mean of the observations. Smaller values of SI indicate better agreement between the model and observations. Note that low ice concentrations during the summer months can result in highly variable SI values.

```        scatter_index=100.0*((numpy.average(diff**2,weights=cell_areas)**0.5-bias**2)/
numpy.average(obs,weights=cell_areas)
cell_areas = the grid cell surface areas, used as weights in the average
diff = model-obs
bias = numpy.average(diff,weights=cell_areas)
```

## Extent & Area

The Sea Ice Area and Sea Ice Extent are computed for both Global RTOFS and NCEP Sea Ice analysis on their respective native grids and saved. The Time Series plot tracks the metric over time from the selected date and back 6 months. The following definitions of Sea Ice Area and Sea Ice Extent are from the National Snow and Ice Data Center Frequently Asked Questions on Arctic Sea Ice

• ### Sea Ice Area

Area takes the percentages of sea ice within data cells and adds them up to report how much of the Arctic is covered by ice; area typically uses a threshold of 15%. So in the same example, with three 25 km x 25 km (16 miles x 16 miles) grid cells of 16% ice, 2% ice, and 90% ice, multiply the grid cell areas that are over the 15% threshold by the percent of sea ice in those grid cells, and add it up. You would have a total area of 662 square km (255.8 square miles).

• ### Sea Ice Extent

Extent defines a region as “ice-covered” or “not ice-covered.” For each satellite data cell, the cell is said to either have ice or to have no ice, based on a threshold. The most common threshold is 15 percent, meaning that if the data cell has greater than 15 percent ice concentration, the cell is considered ice covered; less than that and it is said to be ice free. Example: Let’s say you have three 25 kilometer (km) x 25 km (16 miles x 16 miles) grid cells covered by 16% ice, 2% ice, and 90% ice. Two of the three cells would be considered “ice covered,” or 100% ice. Multiply the grid cell area by 100% sea ice and you would get a total extent of 1,250 square km (482 square miles).

## Statistics

The accumulated difference statistics are plotted in a time series from the selected date with a 6-month look back.