Thanks for clarification.
For a problem with no external forcing and homogenous profile, the density produced at 4 degree was 16. The variability with depth (500m) is linear and clear as shown, but the value is not tuned.
HEIGHT: (11000, 6) float32
Attributes:
_FillValue: -9.909999662373274e+16
MinValue: -0.0009765625
MaxValue: 0.00091552734375
long_name: Height
units: m
BOTTOM: (11000, 6) float32
Attributes:
_FillValue: -9.909999662373274e+16
MinValue: -500.0
MaxValue: -500.0
long_name: BOTTOM
units: Unknown
DENSITY: (11000, 6, 30) float32
Attributes:
_FillValue: -9.909999662373274e+16
MinValue: 15.87646484375
MaxValue: 18.24627685546875
long_name: sigma(T)
units: kg m^-3
TEMPERATURE: (11000, 6, 30) float32
Attributes:
_FillValue: -9.909999662373274e+16
MinValue: 4.0
MaxValue: 4.0
long_name: Temperature
units: deg Celcius