Barotropic models
are two-dimensional models that are not dependent on temperature, wind direction, wind speed, and pressure. A forecast is made of the height of the 500mb pressure surface. Lines of temperature and wind speed are assumed to be parallel to the lines of the 500mb height field.Baroclinic models
are three-dimensional models that are dependent on temperature, wind direction, wind speed, and pressure. You can make a forecast at any level even above 500 mb of pressure. When you add in temperature measurements, the wind blows in several directions.