GELE Adjustment Computations (Least Squares) — Adjustment of Level Nets and TraversesConcept Map

Concept

Level-Net Adjustment

Sub Concepts

• Misclosure (elevation error)
• Proportional Distribution by Distance
• Proportional Distribution by Setups
• Tolerance Checking (√K formula)
• Correction Application

Relationship To Central

Primary adjustment method for elevations in closed level loops

Concept

Traverse Adjustment

Sub Concepts

• Latitude Error (ΣLat)
• Departure Error (ΣDep)
• Error of Closure (EC)
• Relative Precision
• Bowditch Rule (Compass Rule)
• Transit Rule

Relationship To Central

Primary adjustment method for horizontal positions in closed traverses

Concept

Adjustment Principles

Sub Concepts

• Least Squares Concept
• Error Distribution Logic
• Correction Sign Convention
• Proportional Weighting
• Closure Criteria

Relationship To Central

Theoretical foundations underlying both level and traverse adjustments

Concept

Quality Control & Precision

Sub Concepts

• Allowable Misclosure (Level)
• Relative Precision Ratio
• Error of Closure Magnitude
• Precision Classification
• Tolerance Limits

Relationship To Central

Methods to verify adjustment acceptability and measurement quality

Concept

Computational Methods

Sub Concepts

• Proportional Factor Calculation
• Distance Ratios
• Latitude/Departure Corrections
• Cumulative Adjustment
• Verification Checks

Relationship To Central

Mathematical techniques for calculating adjustments

To

Misclosure

From

Level-Net Adjustment

Strength

strong

Relationship

Misclosure is the input quantity that drives the entire level adjustment process

To

Proportional Distribution by Distance

From

Misclosure

Strength

strong

Relationship

Misclosure magnitude is distributed among sections in proportion to their measured distances

To

Tolerance Checking (√K formula)

From

Level-Net Adjustment

Strength

strong

Relationship

Tolerance limits determine whether a level loop is acceptable before adjustment proceeds

To

Latitude Error (ΣLat)

From

Traverse Adjustment

Strength

strong

Relationship

Latitude error is one of two components that define traverse misclosure and drives adjustment

To

Departure Error (ΣDep)

From

Traverse Adjustment

Strength

strong

Relationship

Departure error is the second component of traverse misclosure, independent of latitude error

To

Error of Closure (EC)

From

Latitude Error

Strength

strong

Relationship

ΣLat is one component in the Pythagorean calculation of total error magnitude EC

To

Error of Closure (EC)

From

Departure Error

Strength

strong

Relationship

ΣDep is the second component in the Pythagorean calculation of total error magnitude EC

To

Relative Precision

From

Error of Closure (EC)

Strength

strong

Relationship

EC is the numerator in the precision ratio; smaller EC indicates better precision

To

Quality Control & Precision

From

Relative Precision

Strength

strong

Relationship

Relative precision is the primary metric for determining if a traverse is acceptably accurate

To

Computational Methods

From

Bowditch Rule (Compass Rule)

Strength

strong

Relationship

Bowditch Rule employs proportional distribution by length as its computational method

To

Computational Methods

From

Transit Rule

Strength

strong

Relationship

Transit Rule employs proportional distribution by latitude/departure magnitude as its method

To

Bowditch Rule (Compass Rule)

From

Proportional Weighting

Strength

strong

Relationship

Bowditch uses line length as the weighting factor for distribution

To

Transit Rule

From

Proportional Weighting

Strength

moderate

Relationship

Transit uses coordinate magnitude as the weighting factor for distribution

To

Adjustment Principles

From

Correction Sign Convention

Strength

strong

Relationship

Corrections must have opposite sign to the misclosure to properly cancel the error

To

Proportional Factor Calculation

From

Error Distribution Logic

Strength

strong

Relationship

Proportional factors determine how the total error is logically distributed among components

To

Adjustment Principles

From

Least Squares Concept

Strength

moderate

Relationship

Least squares principle underlies the theoretical justification for proportional error distribution

To

Tolerance Checking (√K formula)

From

Allowable Misclosure (Level)

Strength

strong

Relationship

The √K formula defines the allowable limit for level loop misclosure

To

Error of Closure Magnitude

From

Relative Precision Ratio

Strength

strong

Relationship

Precision ratio is calculated by dividing error of closure by perimeter

To

Tolerance Limits

From

Closure Criteria

Strength

strong

Relationship

Closure criteria define the mathematical limits that measurements must satisfy for acceptance

To

Level-Net Adjustment

From

Adjustment Principles

Strength

strong

Relationship

General principles of adjustment underlie the specific procedures used for level nets

To

Traverse Adjustment

From

Adjustment Principles

Strength

strong

Relationship

General principles of adjustment underlie the specific procedures used for traverses

To

Distance Ratios

From

Computational Methods

Strength

strong

Relationship

Distance ratios are the intermediate values computed before applying final corrections

To

Coordinate Update

From

Latitude/Departure Corrections

Strength

strong

Relationship

Corrections are added to original coordinates to produce adjusted positions

To

Quality Control & Precision

From

Verification Checks

Strength

strong

Relationship

Verification ensures that adjustments are mathematically sound and meet acceptance criteria

To

Correction Application

From

Cumulative Adjustment

Strength

moderate

Relationship

Cumulative adjustment tracks the running total of applied corrections through sections or lines

To

Correction Application

From

Sign Convention

Strength

strong

Relationship

Proper sign assignment ensures corrections properly counteract the original error

To

Level-Net Adjustment

From

Proportional Distribution by Setups

Strength

moderate

Relationship

Alternative method to distance-based distribution when setup counts are known more reliably

To

Error of Closure (EC)

From

Misclosure Concept

Strength

moderate

Relationship

Both represent survey closure error but misclosure is for levels while EC is for traverses

To

Precision Classification

From

Allowable Limits

Strength

moderate

Relationship

Precision classification categories are based on established allowable limit standards