1. Practical Salinity (PSS-78):
S = a₀ + a₁R₁/² + a₂R + a₃R³/² + a₄R² + a₅R⁵/² Where: R = C(S,T,P)/C(35,15,0), C = conductivity Explanation: UNESCO standard for calculating salinity from conductivity, temperature, and pressure
2. Potential Temperature:
θ = T - ∫₀ᴾ (∂T/∂P)ₛ dP ≈ T - 0.0375×P Where: T = in-situ temperature, P = pressure Explanation: Temperature a water parcel would have if moved adiabatically to surface
3. Density (UNESCO EOS-80):
ρ = ρ(S,T,P) = ρ₀ + ρ₁S + ρ₂T + ρ₃P + ... Where: ρ₀ = 999.842594 kg/m³ at (S=0, T=0, P=0) Explanation: Seawater density as function of salinity, temperature, and pressure
4. Brunt-Väisälä Frequency:
N² = -(g/ρ)(∂ρ/∂z) = 2.5e-4 s⁻² Where: g = gravitational acceleration, z = depth Explanation: Measure of water column stability and stratification strength
5. Mixed Layer Depth:
MLD = depth where Δρ = ρ(z) - ρ(10m) > 0.03 kg/m³
MLD = 15 m Explanation: Depth of surface mixed layer based on density criterion
📊 Analysis Options
🔍 Layer Detection
Profile Analysis Results
Process CTD data and analyze profile characteristics.
💧 Water Mass Analysis
Water Mass Identification
Surface Water
0-20m
Thermocline
20-80m
Deep Water
>80m
0.75
Mixing Index
Water Mass Analysis Equations:
1. T-S Diagram Analysis:
Water masses plotted in Temperature-Salinity space
Mixing lines: T_mix = f₁T₁ + f₂T₂, S_mix = f₁S₁ + f₂S₂ Where: f₁ + f₂ = 1 (mixing fractions) Explanation: Conservative mixing between water masses follows straight lines in T-S space
3. Water Mass Fraction:
f = (S - S₂)/(S₁ - S₂) for conservative mixing Where: S₁, S₂ are end-member salinities Explanation: Fraction of water mass 1 in binary mixture
4. Isopycnal Analysis:
σₜ = ρ(S,T,0) - 1000 kg/m³
σθ = ρ(S,θ,0) - 1000 kg/m³ Where: σₜ = in-situ density, σθ = potential density Explanation: Density referenced to surface pressure for water mass tracking
🌡️ Stratification Analysis
2.8
Stratification Index
1.2e-3
Max N² (s⁻²)
0.85
Richardson Number
35
Pycnocline Depth (m)
Stratification Analysis Equations:
1. Brunt-Väisälä Frequency:
N² = -(g/ρ₀)(∂ρ/∂z) = 1.2e-3 s⁻²
N = √N² = 0.035 s⁻¹ Where: g = 9.81 m/s², ρ₀ = reference density Explanation: Natural frequency of internal gravity waves, stability measure
2. Stratification Index:
SI = ∫₀ᴴ N²(z) dz = 2.8 s⁻²·m Where: H = total depth Explanation: Integrated measure of water column stability
3. Potential Energy Anomaly:
φ = (1/H) ∫₀ᴴ g(ρ̄ - ρ(z))z dz Where: ρ̄ = depth-averaged density Explanation: Energy required to mix water column completely
4. Richardson Number:
Ri = N²/(∂u/∂z)² = 0.85 Where: ∂u/∂z = vertical shear (assumed) Explanation: Ratio of buoyancy to shear forces (Ri > 0.25 = stable)
Analyze water column stability and stratification patterns.
🧮 Derived Oceanographic Parameters
1520
Sound Speed (m/s)
2.1e-4
Thermal Expansion (K⁻¹)
7.8e-4
Haline Contraction (PSU⁻¹)
1.1e-4
Adiabatic Gradient (°C/dbar)
9.7e-4
Specific Volume (m³/kg)
0.85
Dynamic Height (m)
Derived Parameter Equations:
1. Sound Speed (Mackenzie, 1981):
c = 1448.96 + 4.591T - 5.304×10⁻²T² + 2.374×10⁻⁴T³
+ 1.340(S-35) + 1.630×10⁻²D + 1.675×10⁻⁷D²
c = 1520 m/s Where: T = temperature (°C), S = salinity (PSU), D = depth (m) Explanation: Speed of sound in seawater for acoustic applications
2. Thermal Expansion Coefficient:
α = -(1/ρ)(∂ρ/∂T)ₛ,ₚ = 2.1e-4 K⁻¹ Explanation: Fractional density change per unit temperature change
3. Haline Contraction Coefficient:
β = (1/ρ)(∂ρ/∂S)ₜ,ₚ = 7.8e-4 PSU⁻¹ Explanation: Fractional density change per unit salinity change
4. Adiabatic Temperature Gradient:
Γ = (∂T/∂P)ₛ = 1.1e-4 °C/dbar Explanation: Temperature change for adiabatic compression/expansion
6. Specific Volume Anomaly:
δ = α(S,T,P) - α(35,0,P) Where: α = specific volume (1/ρ) Explanation: Deviation from standard seawater specific volume
Export Derived Parameters
🔍 Quality Control Analysis
95.2
Data Quality (%)
3
Spikes Detected
7
Outlier Points
0.92
Stability Index
Quality Control Equations:
1. Spike Detection (Median Filter):
Spike if |X(i) - median(X(i-n:i+n))| > k × MAD Where: MAD = median absolute deviation, k = threshold factor Explanation: Identifies sudden jumps in sensor readings
2. Density Inversion Check:
Flag if ∂ρ/∂z < -threshold for stable water column Where: threshold = density gradient limit Explanation: Detects physically unrealistic density inversions
3. Range Check:
Flag if T < T_min or T > T_max (regional limits)
Flag if S < S_min or S > S_max (regional limits) Explanation: Identifies values outside expected regional ranges
4. Gradient Check:
Flag if |∂T/∂z| > gradient_limit
Flag if |∂S/∂z| > gradient_limit Explanation: Detects unrealistic vertical gradients
5. Stability Ratio:
R_ρ = (α∂T/∂z)/(β∂S/∂z) Where: α = thermal expansion, β = haline contraction Explanation: Ratio for double-diffusive instability assessment
🔧 QC Parameters
📊 Range Limits
Quality Control Results
Run quality control analysis to identify data issues.