# SEA ICE DRIFT GUIDANCE

## by R. W. Grumbine

### 1. INTRODUCTION

In the late 1970s, the National Centers for Environmental Prediction (NCEP) implemented the Skiles (1968) sea ice drift model at the request of the National Ice Center (NIC). This model provides sea ice drift direction and speed forecast guidance for the Arctic region at 207 fixed points from 24- through 144-h at 24-h intervals. The positions of the points are given in Table 1.

In April 1993, a newer model (Thorndike and Colony 1982) was implemented experimentally for the northern hemisphere. This model makes predictions at the Skiles points and also at a variable set of points along the northern hemisphere ice edge. The latter set of points is taken from the current northern hemisphere ice edge analysis. The number of points and their location varies weekly with the NIC analysis cycle. A sea ice model for the southern hemisphere (Martinson and Wamser 1990) was also added. Prediction points for this model come only from the NIC weekly southern hemisphere analysis.

A comparative evaluation of the operational and experimental forecasts at the Skiles points has been done and is explained in detail in section 5.

### 2. METHOD

The method used to derive all the sea ice drift models is statistical. The model differences lie in the variables used for the prediction equations and the associated coefficients and constants derived through regression techniques.

### 3. DEVELOPMENT AND DEFINITIONS

Sea ice drift models are based on the observation that sea ice tends to drift at an angle to the geostrophic wind direction and at a fraction of the geostrophic wind speed. In the Skiles model, the drift speed is a function of the "roughened" geostrophic wind speed. The roughened geostrophic wind speed is determined by adding to the original pressure field terms proportional to the second derivative of the pressure field. The drift direction is a function of both the geostrophic wind direction and the roughened geostrophic wind speed. In Thorndike and Colony and Martinson and Wamser, the drift speed is strictly a function of the geostrophic wind speed, and the drift direction is a function of the geostrophic wind direction only.

### 4. FORECAST CONTENT AND DISSEMINATION

Sea ice drift is computed for all 207 of the Skiles points and for points along the NIC analysis of the ice edge. The guidance is disseminated daily in alphanumeric format only, via ftp to various machines at NCEP. A special file is constructed daily for the Weather Service Forecast Office at Anchorage, Alaska which contains only those parts of the full forecast which are near Alaska.

### a. NCEP Computers and File Names

Table 2 gives the NCEP computer or workstation and data set name for the experimental global ice drift point forecasts and the Alaska subset of these data.

When the NAS - 9000 computer is decommissioned, the files currently on that machine will also disappear. The operational Skiles model will also cease producing its output. When the moratorium on implementing products is lifted, the experimental products will replace the Skiles products. For a time, the only way to receive these data will be from the Cray machines or by ftp (file transfer protocol) to the address given in Table 2 over the INTERNET.

### b. Formats for Operational and Experimental Data

The operational Skiles sea ice drift forecasts are sent daily to the weather forecast offices in Anchorage and Fairbanks on a dedicated circuit, the NIC, and a Fleet Weather and Oceanography Facility at Keflavik, Iceland. The bulletins to Alaska are sent out with a WMO header of FQGA40 KWBC on an X.25 dedicated communications line. They contain only the forecast points for Alaska. The bulletins sent to Keflavik contain only forecast points of interest to them.

The experimental guidance contains forecasts at the Skiles points and along the ice edges in the northern and southern hemispheres (see Fig. 1). The file contains a title for each forecast which gives the projection day (1 - 6) of the forecast and the date the forecast was made (day zero). This line is followed by the guidance at the Skiles points and the guidance at the ice edge points as indicated.

The guidance at the Skiles points contain the point number, the Thorndike and Colony drift direction in degrees and drift in nautical miles, and the Skiles drift direction and drift distance for comparative purposes. When the new guidance becomes operational the Skiles sea ice drift will no longer be computed. The drift direction follows the meteorological convention for wind direction, ie., "270" means drift from 270 degrees (west) to 090 degrees (east).

The ice edge point guidance consists of a point number, the initial longitude, the initial latitude, the drift direction in degrees, and the drift distance in nautical miles. The drift direction is in the same sense as at the Skiles points. The ice edge points change in position and number from week to week with the sea ice edge

analysis schedule at the NIC. A negative latitude means the latitude is south of the equator. The longitude is reckoned from 0 degrees to 360 degrees east of the prime meridian.

Both the experimental and operational guidance is generated once per day on the 0000 UTC cycle from the Medium Range Forecast of NCEP's Global Atmospheric Model.

### 5. EVALUATION

A comparative evaluation of the Thorndike and Colony and Skiles sea ice drift models was carried out from April 1993 through January 1995. No evaluation of the Martinson and Wamser sea ice drift model could be done due to a lack of observation data and lack of any other co-located model data to compare.

Forecasts of sea ice drift were verified by comparison with drift observed by drifting buoys which are set on ice floes. Buoys had to be within plus or minus 3 hours of the valid time of the forecast and within 0.5 degrees of the position of the point at the valid time of the forecast.

Forecast skill was measured by three different means: correlation of forecast drift distance with observed, index of agreement between forecast drift distance and observed, and vector correlation between forecast drift vector and observed. The index of agreement ranges from 0 to 1 and measures the forecast error relative to the observation. If the forecast is wrong by 2 n mi, and the observed drift is only 2 n mi, this is penalized more than a 2 n mi error on a 20 n mi observation. The vector correlation has the same character as a linear correlation, except for being in two dimensions, and that we use the squared correlations. The two-dimensional nature gives a range of 0 to 2, rather than 0 to 1 that ordinary correlation squared would have.

Figure 1 shows model skill as a function of the forecast length. We see that regardless of the skill measure, the model skill had essentially no dependance on forecast length. We also see that the Thorndike and Colony model appears to be superior to the Skiles model at all forecast lengths and by all measures except for the vector correlation at day 1, where it is slightly worse.

Figure 2 shows the model skill at day 6 from April 1993 through January 1995, excluding July 1994 which experienced an archive failure. The Thorndike and Colony model is consistently superior to the Skiles model. By index of agreement, it is better in 18 of the 21 months. The correlation is better 16 months and ties once. The vector correlation is better in 15 of the 21 months. Since the index of agreement is the measure which shows the greatest model to model differences, it is the preferred skill measure.

### 6. REFERENCES

Martinson, D. G. and C. Wamser, 1990: Ice drift and momentum exchange in winter Antarctic pack ice. J. Geophys. Res., 95, 1741-1755.

Skiles, F., 1968: Empirical wind drift of sea ice. Arctic Drifting Stations, Arctic Institute of North America, 239-252.

Thorndike, A. S. and R. Colony, 1982: Sea ice motion in response to geostrophic winds. J. Geophys. Res., 87, 5845-5852.