Mixed Layer Depth Calculator

Find the ocean mixed layer depth from a temperature profile using the 0.2 C threshold criterion and see it plotted against depth.

🌊 Mixed Layer Depth Calculator
Temperature profiledepth (m) and temperature (°C), up to 8 rows
Depth (m)
Temperature (°C)
Temperature threshold (ΔT)0.2 °C
°C
0.10.5
Reference depth (zref)10 m
m
050
Mixed layer depth
—
Reference temperature
—
Temperature at MLD
—
Stratification (next 50 m)
—

🌊 What is Mixed Layer Depth?

Mixed layer depth (MLD) is the thickness of the well-mixed surface layer of the ocean, the layer in which wind stress, breaking waves and convective cooling keep temperature, salinity and density almost uniform with depth. Below it lies the thermocline, where temperature drops quickly. Because the mixed layer is the part of the ocean in direct contact with the atmosphere, its thickness controls how much water must be heated or cooled to change sea surface temperature, how heat and carbon dioxide are carried downward, and how much light and nutrients reach phytoplankton.

Oceanographers, climate modellers and marine biologists use MLD constantly. Climate models need it to simulate sea surface temperature and air-sea heat exchange. Biologists compare it with the depth that sunlight reaches to predict spring plankton blooms. Fisheries scientists and naval acousticians use it to locate surface ducts that trap sound. Float programmes such as Argo, along with ship CTD casts, measure temperature profiles that can be turned into an MLD with a simple objective rule.

This calculator applies the widely used threshold criterion of de Boyer Montegut et al. (2004). It first finds the temperature at a reference depth, normally 10 m, then looks downward for the shallowest depth where the temperature differs from that reference by a chosen threshold, normally 0.2 °C. Linear interpolation between the two bracketing profile points gives a smooth depth rather than snapping to a measured level. A density-based criterion (a sigma-theta increase of 0.03 kg/m³) is the common alternative. With a thermal expansion coefficient near 2×10−4 per °C it is roughly equivalent to a 0.15 °C temperature threshold where salinity is uniform, which is why the 0.1 to 0.5 °C threshold range here covers both approaches.

A common misconception is that the MLD is a physical boundary with a single true value. It is not. It depends on the criterion, the threshold, the reference depth and the profile resolution, so always quote them. Another is that the mixed layer is always shallow: in winter in the subpolar North Atlantic and the Southern Ocean it can exceed 500 m, while in summer it can shrink to under 15 m. Enter your own profile above and the chart will show the profile, the reference and threshold temperatures, the MLD line and the shaded mixed layer.

📐 Formula

|T(zMLD) − T(zref)|  =  ΔT
T(zref) = temperature at the reference depth (°C), interpolated from the profile. Standard zref = 10 m (de Boyer Montegut et al., 2004).
ΔT = temperature threshold (°C). Standard value 0.2 °C.
zMLD = shallowest depth below zref where the criterion is met, located by linear interpolation: z = z1 + (ΔT − |T1 − Tref|) / (|T2 − Tref| − |T1 − Tref|) × (z2 − z1)
Stratification = T(zMLD) − T(zMLD + 50 m), the temperature drop across the next 50 m.
Example: Tref = 18.2 °C, ΔT = 0.2 °C. The profile reads 18.1 °C at 25 m and 17.9 °C at 40 m, so z = 25 + (0.2 − 0.1) / (0.3 − 0.1) × 15 = 32.5 m.

📖 How to Use This Calculator

Steps

1
Enter the temperature profile. Type up to 8 depths in metres (increasing downward) and the matching temperatures in °C. Leave unused rows blank.
2
Set threshold and reference depth. Choose the temperature threshold (0.2 °C is the standard) and the reference depth (10 m is the standard).
3
Read the MLD and chart. The calculator reports the mixed layer depth, reference temperature, temperature at the MLD and the 50 m stratification, and plots the profile with the mixed layer shaded.

💡 Example Calculations

Example 1 — Winter Deep Mixing (North Atlantic, February)

Profile 0 to 300 m, 9.8°C in the upper 100 m, threshold 0.2°C, reference depth 10 m

1
Reference temperature at 10 m is 9.80°C, so the target is 9.80 − 0.20 = 9.60°C.
2
At 100 m the profile reads 9.70°C (0.10°C below reference). At 150 m it reads 9.10°C (0.70°C below).
3
Interpolate: fraction = (0.20 − 0.10) / (0.70 − 0.10) = 0.1667, so depth = 100 + 0.1667 × 50 = 108.3 m.
4
Temperature at 158.3 m is 8.95°C, so the drop across the next 50 m is 9.60 − 8.95 = 0.65°C.
MLD = 108.3 m, Tref = 9.80°C, T at MLD = 9.60°C, stratification = 0.65°C
Try this example →

Example 2 — Summer Shallow Layer (Mid-Latitude, August)

Profile 0 to 100 m, warm surface water over a sharp seasonal thermocline, threshold 0.2°C

1
Reference temperature at 10 m is 22.40°C, so the target is 22.20°C.
2
At 15 m the profile reads 21.90°C (0.50°C below reference), so the crossing lies between 10 m and 15 m.
3
Interpolate: fraction = 0.20 / 0.50 = 0.40, so depth = 10 + 0.40 × 5 = 12.0 m.
4
Temperature at 62 m is 12.87°C, so the drop across the next 50 m is 22.20 − 12.87 = 9.33°C.
MLD = 12.0 m, Tref = 22.40°C, T at MLD = 22.20°C, stratification = 9.33°C
Try this example →

Example 3 — Tropical Warm Pool (Western Pacific)

Profile 0 to 200 m, SST near 28.9°C with a deeper isothermal layer, threshold 0.2°C

1
Reference temperature at 10 m is 28.90°C, so the target is 28.70°C.
2
At 50 m the profile reads 28.85°C (0.05°C below). At 70 m it reads 28.68°C (0.22°C below).
3
Interpolate: fraction = (0.20 − 0.05) / (0.22 − 0.05) = 0.882, so depth = 50 + 0.882 × 20 = 67.6 m.
4
Temperature at 117.6 m is 24.24°C, so the drop across the next 50 m is 28.70 − 24.24 = 4.46°C.
MLD = 67.6 m, Tref = 28.90°C, T at MLD = 28.70°C, stratification = 4.46°C
Try this example →

Example 4 — Polar Ocean (Southern Ocean, Near Freezing)

Profile 0 to 250 m, surface near −1.7°C over warmer deep water, threshold 0.1°C

1
Reference temperature at 10 m is −1.70°C. The threshold is 0.10°C, and in polar water the temperature rises with depth, so the target is −1.60°C.
2
At 20 m the profile reads −1.69°C (0.01°C above). At 40 m it reads −1.58°C (0.12°C above).
3
Interpolate: fraction = (0.10 − 0.01) / (0.12 − 0.01) = 0.818, so depth = 20 + 0.818 × 20 = 36.4 m.
4
Temperature at 86.4 m is −0.61°C, so the change across the next 50 m is −1.60 − (−0.61) = −0.99°C (negative means warming with depth).
MLD = 36.4 m, Tref = −1.70°C, T at MLD = −1.60°C, stratification = −0.99°C
Try this example →

❓ Frequently Asked Questions

What is mixed layer depth in the ocean?+
Mixed layer depth (MLD) is the thickness of the surface ocean layer where wind, waves and convection keep temperature (and usually salinity and density) nearly uniform. It typically ranges from about 10 to 30 m in summer to several hundred metres in winter at mid and high latitudes.
How do you calculate mixed layer depth from a temperature profile?+
Take the temperature at a reference depth (10 m), then find the shallowest depth where the temperature differs from it by a threshold (0.2 C). Linear interpolation between the two profile points that bracket the threshold gives the MLD, as in de Boyer Montegut et al. (2004).
Why does the criterion use a 10 m reference depth?+
A 10 m reference avoids the diurnal warming skin layer and wind-driven noise right at the surface, while still being inside the mixed layer in nearly all conditions. de Boyer Montegut et al. (2004) found 10 m a robust choice for global climatologies.
What threshold should I use, 0.2 C or something else?+
0.2 C is the standard global value and the default here. Smaller values such as 0.1 C suit sharply stratified or polar regions, while 0.5 C is more tolerant of noisy profiles. A smaller threshold always gives an equal or shallower MLD, so state the value you used.
How is a temperature threshold different from a density threshold?+
Density criteria use a sigma-theta increase (commonly 0.03 kg/m3) and account for salinity. Using a thermal expansion coefficient near 2e-4 per C, 0.03 kg/m3 corresponds to roughly 0.15 C, so the two methods agree closely where salinity is uniform but differ in salt-stratified waters.
What does the stratification result mean?+
It is the temperature at the MLD minus the temperature 50 m deeper, found by interpolation. A large positive value means a sharp thermocline just below the mixed layer. A value near zero means weak stratification, and a negative value means the water warms with depth, as in polar halocline regions.
What happens if the temperature never changes by the threshold?+
If no point in the profile differs from the reference temperature by the threshold, the mixed layer extends at least to the deepest measurement. The calculator then reports the MLD as greater than the deepest depth rather than inventing a value, and you should add deeper measurements.
What is the difference between mixed layer depth and thermocline depth?+
The mixed layer is the near-uniform layer at the top, while the thermocline is the layer beneath it where temperature falls fastest with depth. The MLD marks the top of the thermocline in many profiles, but the depth of maximum gradient lies deeper than the MLD.
Why is the mixed layer deeper in winter?+
Winter cooling and strong winds drive convective overturning and turbulent mixing that erode the seasonal thermocline, deepening the layer to hundreds of metres in places like the North Atlantic and Southern Ocean. In summer, surface heating and weak winds restrict it to tens of metres.
How many depth points do I need for a reliable MLD?+
At least 3 points are required here, but resolution matters. Linear interpolation between widely spaced points can bias the MLD, so include dense measurements near the expected base of the layer. Argo floats and CTD casts typically report data every 1 to 5 m in the upper ocean.
Does the mixed layer depth matter for climate and biology?+
Yes. The MLD sets the heat capacity that responds to surface forcing, controls how deeply carbon dioxide and heat are mixed, and determines the light and nutrient supply to phytoplankton. Deeper winter mixed layers bring nutrients up, and shallow summer ones trap plankton in bright water.
Tags: Mixed Layer Depth Calculator Ocean Mixed Layer Depth MLD Temperature Threshold De Boyer Montegut Criterion Ocean Temperature Profile Oceanography Calculator Calculator Formula Free Online

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What is mixed layer depth in the ocean?

Mixed layer depth (MLD) is the thickness of the surface ocean layer where wind, waves and convection keep temperature (and usually salinity and density) nearly uniform. It typically ranges from about 10 to 30 m in summer to several hundred metres in winter at mid and high latitudes.

How do you calculate mixed layer depth from a temperature profile?

Take the temperature at a reference depth (10 m), then find the shallowest depth where the temperature differs from it by a threshold (0.2 C). Linear interpolation between the two profile points that bracket the threshold gives the MLD, as in de Boyer Montegut et al. (2004).

Why does the criterion use a 10 m reference depth?

A 10 m reference avoids the diurnal warming skin layer and wind-driven noise right at the surface, while still being inside the mixed layer in nearly all conditions. de Boyer Montegut et al. (2004) found 10 m a robust choice for global climatologies.

What threshold should I use, 0.2 C or something else?

0.2 C is the standard global value and the default here. Smaller values such as 0.1 C suit sharply stratified or polar regions, while 0.5 C is more tolerant of noisy profiles. A smaller threshold always gives an equal or shallower MLD, so state the value you used.

How is a temperature threshold different from a density threshold?

Density criteria use a sigma-theta increase (commonly 0.03 kg/m3) and account for salinity. Using a thermal expansion coefficient near 2e-4 per C, 0.03 kg/m3 corresponds to roughly 0.15 C, so the two methods agree closely where salinity is uniform but differ in salt-stratified waters.

What does the stratification result mean?

It is the temperature at the MLD minus the temperature 50 m deeper, found by interpolation. A large positive value means a sharp thermocline just below the mixed layer. A value near zero means weak stratification, and a negative value means the water warms with depth, as in polar halocline regions.

What happens if the temperature never changes by the threshold?

If no point in the profile differs from the reference temperature by the threshold, the mixed layer extends at least to the deepest measurement. The calculator then reports the MLD as greater than the deepest depth rather than inventing a value, and you should add deeper measurements.

What is the difference between mixed layer depth and thermocline depth?

The mixed layer is the near-uniform layer at the top, while the thermocline is the layer beneath it where temperature falls fastest with depth. The MLD marks the top of the thermocline in many profiles, but the depth of maximum gradient lies deeper than the MLD.

Why is the mixed layer deeper in winter?

Winter cooling and strong winds drive convective overturning and turbulent mixing that erode the seasonal thermocline, deepening the layer to hundreds of metres in places like the North Atlantic and Southern Ocean. In summer, surface heating and weak winds restrict it to tens of metres.

How many depth points do I need for a reliable MLD?

At least 3 points are required here, but resolution matters. Linear interpolation between widely spaced points can bias the MLD, so include dense measurements near the expected base of the layer. Argo floats and CTD casts typically report data every 1 to 5 m in the upper ocean.

📌 Quick Tips

💡Always report the threshold and reference depth with your MLD. A 0.1 C threshold can give an MLD many metres shallower than a 0.5 C one, so values are only comparable when the criterion is the same.
💡Add profile points near the expected base of the mixed layer. Linear interpolation between points 50 m apart can misplace the MLD by tens of metres in a sharp thermocline.
💡Leave unused rows blank (both depth and temperature) if your cast has fewer than 8 points. At least 3 valid points are required.
💡In polar regions, temperature can increase with depth below the surface layer. The criterion here uses the absolute difference from the reference, so it still works, and the stratification result turns negative.
💡If the result says the MLD is greater than the deepest depth, no change of the threshold size was found. Add deeper measurements or lower the threshold.