The question explores the complexities surrounding the re-establishment of boundaries based on historical survey plans, particularly when inconsistencies arise between the plan’s depicted dimensions and physical evidence on the ground. The core principle guiding such re-establishments in Western Australia, and indeed generally in cadastral surveying, is to prioritize the *best available evidence* of the original surveyor’s intent. This doesn’t automatically mean slavishly adhering to the numerical dimensions recorded on the plan. Physical monuments, if reliably identified as original, hold significant weight. They represent the tangible expression of the surveyor’s work at the time of the original survey. However, the mere existence of a monument isn’t conclusive. Its integrity must be assessed. Is it undisturbed? Does it align with other evidence? Is there a chain of reliable connections back to the original survey? Occupation, such as fences or buildings, also provides evidence, especially if that occupation has been long-standing and unchallenged. The principle of *ad medium filum viae* (to the middle of the road) is a common law presumption that land ownership extends to the center of an adjoining road, unless explicitly excluded in the land title. However, this presumption can be rebutted by evidence to the contrary, such as a specific reservation or a clearly defined boundary on the plan. When discrepancies exist, a surveyor must weigh all available evidence, including the plan dimensions, monuments, occupation, historical records, and local knowledge. The goal is to determine the most probable location of the original boundary, minimizing disturbance to established occupation and respecting the intent of the original survey. This often involves applying principles of proportionate measurement to distribute discrepancies fairly. Section 139 of the *Transfer of Land Act 1893 (WA)* addresses situations where boundaries are uncertain or incorrectly defined, empowering the Registrar of Titles to take action to resolve the uncertainty. The surveyor’s role is to provide the Registrar with the best possible evidence and reasoned opinion to facilitate that resolution.

The scenario describes a complex situation involving the subdivision of land in Western Australia, highlighting the interplay between cadastral surveying principles, the *Planning and Development Act 2005*, and the potential for boundary disputes. The key is to understand the hierarchy of evidence in boundary determination. Original survey marks, when undisturbed and accurately connected to, hold the highest weight. However, when discrepancies arise, particularly in older subdivisions, surveyors must consider a range of factors. These include historical plans, adjoiner evidence, occupation (fences, buildings), and local knowledge. The *Planning and Development Act 2005* governs subdivision approvals and requires compliance with relevant regulations. The act itself doesn’t dictate surveying methodology but provides the legal framework within which subdivisions must occur. The surveyor’s duty is to re-establish the original boundaries as accurately as possible, considering all available evidence. When occupation clearly deviates from the original surveyed boundary, but has been unchallenged for a significant period (potentially leading to adverse possession), the surveyor must carefully assess the legal implications and advise their client accordingly. The surveyor must also consider the principles of *pro rata* apportionment if the original dimensions are found to be in error, distributing the error proportionally among the lots. The Licensing Board expects surveyors to act ethically and competently, prioritizing the accurate re-establishment of boundaries while considering the legal rights of all parties involved. The surveyor must meticulously document all findings and the rationale behind their decisions, as this may be subject to scrutiny in the event of a dispute. The surveyor must balance the legal requirements with the practical realities of the site, potentially requiring negotiation with adjoining owners to reach an amicable solution.

The problem involves calculating the adjusted coordinates of a survey traverse using the Bowditch method (also known as the compass rule). This method distributes the total error in latitude and departure proportionally to the length of each course in the traverse. First, calculate the total error in latitude (\(\Delta Lat\)) and departure (\(\Delta Dep\)): \[\Delta Lat = \sum Lat_{measured} = (N_2 – N_1) + (N_3 – N_2) + (N_4 – N_3) + (N_1 – N_4) = (100.000 – 100.020) + (200.000 – 99.980) + (199.980 – 200.020) + (100.020 – 199.980) = -0.020 + 100.020 – 0.040 – 99.960 = -0.020 – 0.040 -99.960 + 100.020 = -0.06\] \[\Delta Dep = \sum Dep_{measured} = (E_2 – E_1) + (E_3 – E_2) + (E_4 – E_3) + (E_1 – E_4) = (200.000 – 199.980) + (300.020 – 200.020) + (299.980 – 300.000) + (199.980 – 299.960) = 0.020 + 99.980 – 0.020 – 99.980 = 0\] The total perimeter \(P\) of the traverse is: \[P = 100 + 100 + 100 + 100 = 400 \ m\] The correction for latitude (\(C_{Lat}\)) and departure (\(C_{Dep}\)) for each course is calculated as: \[C_{Lat,i} = -\Delta Lat \cdot \frac{Length_i}{P}\] \[C_{Dep,i} = -\Delta Dep \cdot \frac{Length_i}{P}\] For course 1-2: \[C_{Lat,1-2} = -(-0.06) \cdot \frac{100}{400} = 0.06 \cdot 0.25 = 0.015\] \[C_{Dep,1-2} = -(0) \cdot \frac{100}{400} = 0\] The adjusted coordinates for point 2 are: \[N_{2,adjusted} = N_2 + C_{Lat,1-2} = 100.020 + 0.015 = 100.035\] \[E_{2,adjusted} = E_2 + C_{Dep,1-2} = 200.000 + 0 = 200.000\] Therefore, the adjusted coordinates of point 2 are (100.035, 200.000). This calculation uses the principles of traverse adjustment, specifically the Bowditch rule, which is fundamental in surveying to minimize errors and ensure the accuracy of land measurements. Understanding error propagation and adjustment techniques is crucial for a land surveyor to comply with the Surveying and Spatial Information Act and relevant Australian standards.

The correct approach involves understanding the interplay between the Surveying and Spatial Information Act (SSI Act), the Land Administration Act 1997 (LAA), and the specific regulations pertaining to re-establishment surveys in Western Australia. Re-establishment surveys are governed by the SSI Act, which provides the legislative framework for surveying practices. The LAA is also relevant as it deals with land tenure and administration. The Land Surveyors Licensing Board of Western Australia (LSLBWA) provides guidelines and standards that surveyors must adhere to. When a discrepancy is found during a re-establishment survey, particularly concerning a previously placed boundary mark, the surveyor has a professional and legal obligation to investigate and resolve the discrepancy. This involves reviewing original survey plans, considering the principles of adjoinment, and potentially consulting with neighboring landowners. Section 22 of the SSI Act outlines the requirements for licensed surveyors, including the need to act with reasonable skill and care. If the discrepancy cannot be resolved through investigation and consultation, the surveyor may need to refer the matter to the LSLBWA or seek legal advice. The key is to ensure that the re-establishment accurately reflects the original intent of the boundaries, while also adhering to current legislation and best practices. Ignoring the discrepancy or simply adopting the existing mark without due diligence would be a breach of professional standards and potentially violate the SSI Act. This requires the surveyor to demonstrate competency and a thorough understanding of boundary law principles. The surveyor must also document all findings and actions taken in a comprehensive survey report.

The correct approach involves understanding the interplay between the Surveying and Spatial Information Act, professional ethics, and the potential for legal ramifications when a surveyor acts negligently. Negligence in surveying can manifest in various forms, such as inaccurate boundary determinations, errors in construction staking, or flawed topographic mapping. These errors can lead to property disputes, construction delays, or environmental damage, resulting in financial losses for clients and third parties. The Land Surveyors Licensing Board of Western Australia (LSLBWA) holds surveyors accountable for their actions through disciplinary proceedings, which can include fines, suspension, or revocation of their license. Furthermore, surveyors can be sued for professional negligence, potentially leading to significant financial liabilities. The Surveying and Spatial Information Act provides the legal framework for surveying practices in Western Australia, and surveyors are expected to adhere to its provisions. A breach of the Act, coupled with negligence, can significantly increase the severity of the consequences. Professional indemnity insurance is crucial for surveyors as it provides financial protection against claims of negligence. However, insurance coverage may be limited or denied if the surveyor’s actions are deemed to be grossly negligent or intentional. The surveyor’s ethical obligations, as outlined in the code of conduct, also play a critical role. A surveyor who prioritizes speed and cost-cutting over accuracy and due diligence is likely to be found negligent if their work results in damages. In this scenario, given the surveyor’s awareness of the potential for errors and their deliberate decision to proceed without proper verification, their actions constitute a significant breach of professional standards and the Surveying and Spatial Information Act, making them highly vulnerable to legal and disciplinary action.

The problem involves calculating the horizontal distance between two points, given their slope distance and vertical angle, and then determining the reduced level of the second point using the calculated horizontal distance, vertical angle, slope distance, and the reduced level of the first point. First, we calculate the horizontal distance (\(HD\)) using the formula: \[HD = SD \cdot \cos(\theta)\] Where \(SD\) is the slope distance and \(\theta\) is the vertical angle. Given \(SD = 156.235\) m and \(\theta = 4^\circ 36′ 12”\), we convert the angle to decimal degrees: \[\theta = 4 + \frac{36}{60} + \frac{12}{3600} = 4 + 0.6 + 0.00333 = 4.60333^\circ\] Then, we calculate the horizontal distance: \[HD = 156.235 \cdot \cos(4.60333^\circ) = 156.235 \cdot 0.9967 = 155.728 \text{ m}\] Next, we calculate the vertical difference (\(VD\)) between the two points using the formula: \[VD = SD \cdot \sin(\theta)\] \[VD = 156.235 \cdot \sin(4.60333^\circ) = 156.235 \cdot 0.0802 = 12.536 \text{ m}\] Finally, we calculate the reduced level of point B (\(RL_B\)) using the reduced level of point A (\(RL_A\)), the vertical difference (\(VD\)), the height of the instrument (\(HI\)), and the staff reading at point B (\(SR_B\)): \[RL_B = RL_A + HI + VD – SR_B\] Given \(RL_A = 45.678\) m, \(HI = 1.562\) m, and \(SR_B = 2.345\) m: \[RL_B = 45.678 + 1.562 + 12.536 – 2.345 = 57.431 \text{ m}\] Therefore, the horizontal distance is 155.728 m and the reduced level of point B is 57.431 m. This question assesses the candidate’s ability to apply trigonometric principles to surveying calculations, convert angles, and compute reduced levels, all essential skills for a land surveyor in Western Australia.

The question delves into the complexities surrounding the legal standing of survey marks, particularly within the context of boundary disputes in Western Australia. The key lies in understanding the hierarchy of evidence and the surveyor’s role in interpreting that evidence. While survey marks are valuable, they are not absolute determinants of a boundary. Their significance is contingent on their reliability and consistency with other evidence, such as historical records, occupation, and adjoining titles. The *Land Administration Act 1997* (WA) and common law principles dictate that a surveyor must consider all available evidence to determine the original intent of the boundary creation. If a survey mark is demonstrably disturbed or inconsistent with other reliable evidence, it cannot be solely relied upon. The surveyor’s professional judgement is paramount in weighing the evidence and forming an opinion on the correct boundary location. The surveyor’s duty is to re-establish the *original* boundary, not simply perpetuate the position of a potentially erroneous mark. The *Licensed Surveyors (General Surveying Practice) Regulations 1961* also provide guidance on the proper procedures for boundary re-establishment, emphasizing the importance of thorough investigation and documentation. The surveyor must consider the principle of *ad medium filum aquae* (to the middle of the watercourse) if the boundary is adjacent to a non-tidal stream, unless explicitly excluded in the title. Ultimately, the surveyor’s opinion, if challenged, is subject to review by the State Administrative Tribunal (SAT) or the courts, which will consider the surveyor’s reasoning and the evidence presented.

Land tenure systems in Western Australia are complex, reflecting both historical practices and contemporary legislation. Freehold tenure grants the greatest degree of ownership, allowing the owner to use and dispose of the land as they see fit, subject to planning regulations and other statutory limitations. Leasehold tenure involves a right to occupy and use land for a specified period under the terms of a lease agreement with the Crown or another landowner. Crown land, which comprises a significant portion of Western Australia, is managed by the state government and may be subject to various forms of tenure, including leasehold, reserves, and unallocated Crown land. The Surveyor General’s Office plays a crucial role in maintaining accurate land records and ensuring that land transactions comply with relevant legislation. Native Title rights, recognised under the Native Title Act 1993 (Cth), can coexist with other forms of tenure, adding another layer of complexity to land management. Understanding the interplay between these different tenure systems is essential for land surveyors operating in Western Australia. The Surveyor General’s Office has specific guidelines and requirements for cadastral surveys involving Crown land, including procedures for dealing with pastoral leases and reserves. In boundary disputes, the legal principles governing land ownership and the interpretation of survey plans are paramount. The accuracy of survey data and the surveyor’s adherence to professional standards are critical in resolving such disputes. Surveyors must be familiar with the relevant legislation, including the Land Administration Act 1997 (WA) and the Strata Titles Act 1985 (WA), to ensure that their work is legally sound.

To determine the adjusted bearing and distance of the line PQ after applying a Bowditch adjustment, we need to distribute the errors in latitude and departure proportionally to the length of each line in the traverse. First, calculate the total perimeter of the traverse: \( Perimeter = 150.00 + 200.00 + 250.00 + 300.00 = 900.00 \, m \) Next, calculate the error in latitude (\(\Delta Lat\)) and departure (\(\Delta Dep\)): \( \Delta Lat = \sum (Distance \times cos(Bearing)) = (150 \times cos(60^\circ)) + (200 \times cos(150^\circ)) + (250 \times cos(240^\circ)) + (300 \times cos(330^\circ)) \) \( \Delta Lat = (150 \times 0.5) + (200 \times -0.866) + (250 \times -0.5) + (300 \times 0.866) = 75 – 173.2 + (-125) + 259.8 = 36.6 \, m \) \( \Delta Dep = \sum (Distance \times sin(Bearing)) = (150 \times sin(60^\circ)) + (200 \times sin(150^\circ)) + (250 \times sin(240^\circ)) + (300 \times sin(330^\circ)) \) \( \Delta Dep = (150 \times 0.866) + (200 \times 0.5) + (250 \times -0.866) + (300 \times -0.5) = 129.9 + 100 + (-216.5) + (-150) = -136.6 \, m \) Now, apply the Bowditch adjustment to the latitude and departure of line PQ: Adjustment to Latitude: \( \delta Lat_{PQ} = -\frac{Length_{PQ}}{Perimeter} \times \Delta Lat = -\frac{150}{900} \times 36.6 = -6.1 \, m \) Adjustment to Departure: \( \delta Dep_{PQ} = -\frac{Length_{PQ}}{Perimeter} \times \Delta Dep = -\frac{150}{900} \times -136.6 = 22.77 \, m \) Adjusted Latitude and Departure for line PQ: \( Adjusted \, Lat_{PQ} = 150 \times cos(60^\circ) + \delta Lat_{PQ} = 75 – 6.1 = 68.9 \, m \) \( Adjusted \, Dep_{PQ} = 150 \times sin(60^\circ) + \delta Dep_{PQ} = 129.9 + 22.77 = 152.67 \, m \) Calculate the adjusted bearing: \( Adjusted \, Bearing = arctan(\frac{Adjusted \, Dep_{PQ}}{Adjusted \, Lat_{PQ}}) = arctan(\frac{152.67}{68.9}) = arctan(2.2158) \approx 65.7^\circ \) Calculate the adjusted distance: \( Adjusted \, Distance = \sqrt{(Adjusted \, Lat_{PQ})^2 + (Adjusted \, Dep_{PQ})^2} = \sqrt{(68.9)^2 + (152.67)^2} = \sqrt{4747.21 + 23308.1889} = \sqrt{28055.3989} \approx 167.5 \, m \) Therefore, the adjusted bearing is approximately \(65.7^\circ\) and the adjusted distance is approximately \(167.5 \, m\). This question assesses the understanding of Bowditch adjustment, a fundamental concept in surveying used to correct errors in traverse surveys. The Bowditch method assumes that errors in latitude and departure are proportional to the length of the traverse legs. This method is crucial for ensuring the accuracy and reliability of survey data, particularly in cadastral and engineering surveys. A thorough understanding of this adjustment method is essential for land surveyors in Western Australia, as it directly impacts compliance with surveying standards and legislation. Additionally, the question requires proficiency in coordinate geometry and trigonometric calculations, which are vital skills for solving practical surveying problems.

The question explores the complexities of boundary determination in Western Australia, particularly when historical survey records are ambiguous or conflicting. The *Land Administration Act 1997* (WA) provides the legal framework for land administration, including boundary definition. Section 137 of the Act is crucial, outlining the Surveyor-General’s powers in resolving boundary disputes and determining boundaries where survey marks are missing or unreliable. Common law principles, such as *ad medium filum aquae* (ownership to the centre of a watercourse), may also apply if the boundary is a non-tidal watercourse, but this principle can be rebutted by evidence to the contrary. The *Transfer of Land Act 1893* (WA) governs land registration and the indefeasibility of title, but this indefeasibility is subject to certain exceptions, including prior registered interests and errors in the original survey. When historical surveys conflict, surveyors must apply the principle of *original monumentation* – giving priority to the original survey marks placed on the ground. However, if these are lost or unreliable, the best available evidence of their original position must be sought. This evidence may include historical plans, field notes, occupation evidence (fences, buildings), and the testimony of long-term residents. The surveyor’s role is to gather all available evidence, analyze it critically, and form an opinion on the most likely location of the original boundary. This opinion must be defensible based on sound surveying principles and legal precedent. The surveyor must also consider the potential impact of their determination on adjoining landowners and strive to achieve a solution that is equitable and minimizes disputes. In cases of significant uncertainty, the surveyor may recommend a resurvey under the direction of the Surveyor-General or suggest that the landowners seek a determination from the State Administrative Tribunal (SAT).

The correct approach involves understanding the hierarchy of surveying legislation and standards in Western Australia. The *Surveying and Spatial Information Act 2021* (or its successor legislation) forms the primary legal framework. This Act delegates authority for specific regulations and standards to the Land Surveyors Licensing Board (LSLB) and other relevant bodies. While Australian Standards provide valuable technical guidance, they do not automatically have the force of law unless explicitly referenced and mandated within the Act or associated regulations. The LSLB’s specific policies and guidelines, published notices, and directives, which are designed to provide clarification and direction on specific issues, are also crucial for surveyors to comply with. The hierarchy ensures that legal requirements are met first, followed by adherence to professional standards and best practices, which are often reflected in Australian Standards. Therefore, the Act takes precedence, followed by regulations made under the Act, and then LSLB policies and guidelines, with Australian Standards providing additional guidance where relevant and mandated.

To determine the adjusted bearing of the line PQ, we need to apply the Bowditch rule (also known as the compass rule) for traverse adjustment. This rule distributes the errors in latitude and departure proportionally to the length of each line in the traverse. First, calculate the total error in latitude and departure: Total error in latitude = Sum of latitudes = -0.06 m Total error in departure = Sum of departures = +0.08 m Next, calculate the correction to be applied to the latitude and departure of line PQ: Correction to latitude of PQ = -(Length of PQ / Total length of traverse) * Total error in latitude Correction to latitude of PQ = -(250 m / 1000 m) * (-0.06 m) = 0.015 m Correction to departure of PQ = -(Length of PQ / Total length of traverse) * Total error in departure Correction to departure of PQ = -(250 m / 1000 m) * (0.08 m) = -0.02 m Now, apply these corrections to the unadjusted latitude and departure of line PQ: Adjusted latitude of PQ = Unadjusted latitude + Correction to latitude Adjusted latitude of PQ = 125.00 m + 0.015 m = 125.015 m Adjusted departure of PQ = Unadjusted departure + Correction to departure Adjusted departure of PQ = 216.51 m – 0.02 m = 216.49 m Calculate the adjusted bearing using the adjusted latitude and departure: Adjusted bearing = \(arctan(\frac{Adjusted \ Departure}{Adjusted \ Latitude})\) Adjusted bearing = \(arctan(\frac{216.49}{125.015})\) Adjusted bearing = \(arctan(1.7317)\) = \(59.997\) degrees Since both the adjusted latitude and departure are positive, the line is in the first quadrant (North-East). Thus, the adjusted bearing is N \(59.997\)° E. Converting the decimal degrees to degrees, minutes, and seconds (DMS): \(0.997\) degrees * 60 minutes/degree = \(59.82\) minutes \(0.82\) minutes * 60 seconds/minute = \(49.2\) seconds Adjusted bearing = N \(59\)° \(59’\) \(49”\) E The Bowditch rule is a fundamental concept in surveying, particularly relevant under the Surveying and Spatial Information Act and related regulations in Western Australia. It’s crucial for ensuring the accuracy and reliability of survey data, especially in cadastral surveys where boundary definitions must adhere to strict legal standards. Understanding error propagation and adjustment methods like the Bowditch rule is essential for land surveyors to meet professional responsibilities and maintain the integrity of land tenure systems. The adjustment ensures compliance with surveying standards and minimizes discrepancies in land parcel identification, directly impacting land registration and administration.

The correct approach involves understanding the principles of land tenure in Australia, particularly the differences between freehold, leasehold, and Crown land, and how these interact with native title rights as recognised under the *Native Title Act 1993* (Cth). Freehold land grants the owner the greatest bundle of rights, subject to existing encumbrances. Leasehold grants a right to possession for a defined period. Crown land is land owned by the government. Native title rights are communal, group or individual rights and interests of Aboriginal peoples or Torres Strait Islanders in relation to land or waters, where those rights and interests are possessed under traditional laws acknowledged and traditional customs observed by the Aboriginal peoples or Torres Strait Islanders. When Crown land is converted to freehold, native title is not automatically extinguished. The *Native Title Act 1993* (Cth) provides a framework for determining when and how native title is affected by government actions, including the grant of freehold title. Future acts that affect native title must comply with the Act. The “past act” regime in the *Native Title Act 1993* (Cth) validates certain acts that may have been invalid because of the existence of native title. The conversion of Crown land to freehold may be a “past act”. The *Native Title Act 1993* (Cth) provides for compensation where native title is extinguished or impaired. Therefore, while the conversion may impact native title, it does not necessarily extinguish it. The specific circumstances, including the nature of the native title rights and interests, and the provisions of the *Native Title Act 1993* (Cth), will determine the outcome.

Land tenure systems in Australia, particularly in Western Australia, are complex and involve various types of ownership, including freehold, leasehold, and Crown land. Easements, encroachments, and rights-of-way significantly impact land use and ownership rights. Easements grant specific rights to another party over a portion of land, such as access or utility lines. Encroachments occur when a structure or object extends onto another’s property. Rights-of-way provide passage across land. The Surveying and Spatial Information Act of Western Australia governs surveying practices and land boundary determinations. Surveyors play a crucial role in accurately defining and documenting these aspects of land tenure. When a surveyor identifies a potential encroachment during a boundary survey, their ethical and legal obligations require them to inform all affected parties. This includes the property owners involved and any relevant authorities. This ensures transparency and allows for resolution of the encroachment, which may involve legal action, negotiation, or adjustments to property boundaries. Ignoring an encroachment would violate professional standards and potentially lead to legal liabilities for the surveyor. The surveyor must document the encroachment, its extent, and its potential impact on the affected properties.

To determine the adjusted bearing of line CD, we must first calculate the angular misclosure of the traverse. The sum of the interior angles of a five-sided traverse should be \((n-2) \times 180^\circ\), where \(n\) is the number of sides. In this case, \(n = 5\), so the sum should be \((5-2) \times 180^\circ = 540^\circ\). The measured sum is \(105^\circ 15′ 30″ + 110^\circ 20′ 15″ + 115^\circ 30′ 45″ + 108^\circ 45′ 00″ + 100^\circ 08′ 30″ = 539^\circ 59′ 00″\). The angular misclosure is therefore \(540^\circ – 539^\circ 59′ 00″ = 0^\circ 01′ 00″\), or 60 seconds. This misclosure must be distributed among the five angles. Assuming equal distribution, the correction per angle is \(60″ / 5 = 12″\). Since the measured sum is less than the theoretical sum, we add the correction to each angle. The corrected angle at C is \(115^\circ 30′ 45″ + 12″ = 115^\circ 30′ 57″\). Now, we can calculate the bearing of line CD. Given the bearing of BC is \(S 45^\circ 00′ 00″ E\), we use the corrected angle at C to calculate the bearing of CD. To do this, we first convert the bearing of BC to an azimuth from South, which is \(180^\circ – 45^\circ 00′ 00″ = 135^\circ 00′ 00″\). Next, we add the corrected angle at C to this azimuth: \(135^\circ 00′ 00″ + 115^\circ 30′ 57″ = 250^\circ 30′ 57″\). Since this azimuth is greater than \(180^\circ\), we subtract \(180^\circ\) to express it as a bearing from South: \(250^\circ 30′ 57″ – 180^\circ = 70^\circ 30′ 57″\). Thus, the bearing of CD is \(S 70^\circ 30′ 57″ W\).

The scenario presents a complex situation involving a long-term leasehold property near Kalgoorlie, Western Australia, where significant infrastructure investments have been made by the lessee, a mining company. The critical aspect is determining the appropriate compensation mechanism when the lease expires, considering the improvements made. This requires a deep understanding of land tenure systems in Australia, specifically leasehold arrangements under Western Australian law, and the principles of valuing improvements on leased land. Several factors influence the compensation: 1. **Nature of the Lease Agreement:** The specific terms of the lease agreement are paramount. It dictates whether the lessee is entitled to compensation for improvements, the method of valuation, and any limitations on the type or value of compensable improvements. The agreement might specify that improvements become the property of the lessor upon lease expiry without compensation, or it might outline a detailed valuation process. 2. **Relevant Legislation:** The *Land Administration Act 1997* (WA) and associated regulations govern leasehold land in Western Australia. This legislation provides a framework for dealing with improvements on leasehold land, including provisions for compensation. The Act may specify default rules that apply if the lease agreement is silent on certain matters. The *Mining Act 1978* (WA) may also be relevant, given the mining company’s involvement. 3. **Valuation Principles:** If compensation is payable, the valuation of improvements needs to be determined. This typically involves assessing the “fair market value” of the improvements at the time of lease expiry. Different valuation methods may be applicable, such as: * **Cost Approach:** Estimating the current replacement cost of the improvements, less depreciation. * **Income Approach:** Determining the present value of the income stream generated by the improvements. * **Market Approach:** Comparing the value of similar improvements in the market. The choice of valuation method depends on the nature of the improvements and the availability of data. 4. **Dispute Resolution:** If the lessor and lessee cannot agree on the compensation amount, a dispute resolution mechanism needs to be invoked. This might involve mediation, arbitration, or litigation. The Land Surveyors Licensing Board of Western Australia does not directly resolve such disputes, but land surveyors may be called upon as expert witnesses to provide valuation evidence. The most appropriate compensation mechanism is one that is fair to both parties, consistent with the terms of the lease agreement, and compliant with relevant legislation. A mechanism that involves independent valuation by a qualified valuer, with recourse to dispute resolution if necessary, is generally considered to be the most robust.

The key to understanding this scenario lies in the interplay between the *Surveying and Spatial Information Act* of Western Australia, the concept of adverse possession, and the duties of a licensed surveyor. Adverse possession, though possible under certain circumstances, requires continuous, open, and exclusive possession of the land for a statutory period (typically 12 years in Western Australia), coupled with the intent to possess. Crucially, simply maintaining a fence line, even for an extended period, does not automatically grant ownership via adverse possession. The Act mandates that a surveyor must act impartially and in accordance with the law. Surveyors cannot unilaterally decide boundary disputes; their role is to accurately represent the facts on the ground and provide expert opinion. A surveyor has a duty to inform all parties of potential discrepancies and recommend legal counsel if necessary. In this case, if the surveyor believes there is a legitimate claim of adverse possession, they must advise both parties to seek legal advice and cannot simply adjust the boundary to favor one party. The surveyor’s primary responsibility is to accurately reflect the existing situation and advise on the legal implications, not to adjudicate the dispute. The surveyor’s actions must align with the Act’s emphasis on accuracy, integrity, and the protection of land ownership rights. Therefore, the surveyor must advise both parties to seek legal counsel and accurately depict the existing fence line and its relationship to the title boundaries on the survey plan.

To solve this problem, we need to apply the principles of traverse surveying and error adjustment. The key is to understand how misclosure in latitude and departure affects the positions of subsequent points and how to proportionally adjust these errors using the Bowditch method (also known as the compass rule). First, calculate the total misclosure in latitude (\(\Delta Lat\)) and departure (\(\Delta Dep\)): \[\Delta Lat = \sum Lat = (N_1 – N_0) + (N_2 – N_1) + (N_3 – N_2) = N_3 – N_0\] \[\Delta Dep = \sum Dep = (E_1 – E_0) + (E_2 – E_1) + (E_3 – E_2) = E_3 – E_0\] Given \(N_0 = 1000.00\) m, \(E_0 = 2000.00\) m, \(N_3 = 1999.96\) m, and \(E_3 = 2999.92\) m, we have: \[\Delta Lat = 1999.96 – 1000.00 = 999.96 \text{ m}\] \[\Delta Dep = 2999.92 – 2000.00 = 999.92 \text{ m}\] The misclosure errors are: \[e_{Lat} = \text{Expected } \Delta Lat – \text{Observed } \Delta Lat = 1000 – 999.96 = 0.04 \text{ m}\] \[e_{Dep} = \text{Expected } \Delta Dep – \text{Observed } \Delta Dep = 1000 – 999.92 = 0.08 \text{ m}\] The total perimeter (P) of the traverse is the sum of the lengths of each leg: \[P = L_{0-1} + L_{1-2} + L_{2-3} = 300 + 400 + 300 = 1000 \text{ m}\] Now, we apply the Bowditch adjustment to correct the coordinates of point 2. The correction for latitude (\(C_{Lat,1-2}\)) and departure (\(C_{Dep,1-2}\)) for the leg from point 1 to point 2 is calculated as: \[C_{Lat,1-2} = -e_{Lat} \cdot \frac{L_{1-2}}{P} = -0.04 \cdot \frac{400}{1000} = -0.016 \text{ m}\] \[C_{Dep,1-2} = -e_{Dep} \cdot \frac{L_{1-2}}{P} = -0.08 \cdot \frac{400}{1000} = -0.032 \text{ m}\] To find the unadjusted coordinates of point 2, we need the latitude and departure of the leg from 1 to 2: \(Lat_{1-2} = N_2 – N_1\) \(Dep_{1-2} = E_2 – E_1\) We can rearrange the equations from above to get \(N_2\) and \(E_2\): The Latitude and Departure from station 0 to 1: \(Lat_{0-1} = N_1 – N_0\) \(Dep_{0-1} = E_1 – E_0\) \(N_1 = Lat_{0-1} + N_0 = 300 + 1000 = 1300\) m \(E_1 = Dep_{0-1} + E_0 = 400 + 2000 = 2400\) m \(Lat_{1-2} = N_2 – N_1 = 300\) m \(Dep_{1-2} = E_2 – E_1 = 399.98\) m \(N_2 = Lat_{1-2} + N_1 = 300 + 1300 = 1600\) m \(E_2 = Dep_{1-2} + E_1 = 399.98 + 2400 = 2799.98\) m Now, apply the corrections to the unadjusted coordinates of point 2: \[N_{2, adjusted} = N_2 + C_{Lat,1-2} = 1600 – 0.016 = 1599.984 \text{ m}\] \[E_{2, adjusted} = E_2 + C_{Dep,1-2} = 2799.98 – 0.032 = 2799.948 \text{ m}\] Therefore, the adjusted coordinates of point 2 are approximately (1599.984 m, 2799.948 m).

Land tenure systems in Australia, particularly in Western Australia, are governed by a complex interplay of historical common law principles, statutory regulations, and administrative practices. The concept of ‘radical title’ is central to understanding land ownership. Radical title is the ultimate ownership vested in the Crown (the State government in Western Australia), stemming from the assertion of sovereignty. This doesn’t mean the Crown owns all land absolutely, but rather holds the underlying title from which all other land interests derive. Freehold, leasehold, and Crown land represent distinct forms of tenure. Freehold is the closest to absolute ownership, granting the holder significant rights subject to statutory limitations and common law principles (like nuisance). Leasehold grants rights to occupy and use land for a specified period under specific conditions, with the Crown retaining radical title. Crown land is land directly managed by the government for various public purposes. Native Title, recognised by the High Court in *Mabo v Queensland (No 2)* (1992), exists where Indigenous Australians have maintained a continuous connection with the land and their traditional laws and customs recognise that connection. Native Title can coexist with other forms of tenure, potentially impacting development and land management. The *Land Administration Act 1997* (WA) provides the legislative framework for land management and dealings with Crown land in Western Australia. Easements, covenants, and other encumbrances can further complicate land ownership, creating rights and obligations that affect land use. Understanding these nuances is crucial for surveyors when determining boundaries, advising clients, and ensuring compliance with legal requirements.

The scenario describes a complex situation where a surveyor, Bronte, is tasked with re-establishing a boundary line defined by a historical survey using the “metes and bounds” system. The key issue is the discrepancy between the historical magnetic bearing and the current magnetic declination. The Land Surveyors Licensing Board of Western Australia emphasizes the importance of following the principles of *ad medium filum aquae* (to the middle thread of the watercourse) when boundaries are defined by non-tidal watercourses, and this principle needs to be carefully considered in conjunction with the historical survey data. The original survey used a magnetic bearing, which is subject to magnetic declination. Magnetic declination is the angle between true north and magnetic north, and it varies over time and location. Therefore, simply using the historical magnetic bearing with today’s magnetic declination will result in an incorrect boundary line. To accurately re-establish the boundary, Bronte needs to: 1. **Determine the historical magnetic declination:** Research historical records (e.g., surveyor’s field notes, historical maps, geological survey data) to find the magnetic declination at the time of the original survey. 2. **Calculate the true bearing:** Convert the historical magnetic bearing to a true bearing using the historical magnetic declination. This involves adding or subtracting the declination from the magnetic bearing, depending on whether the declination was east or west. 3. **Apply the *ad medium filum aquae* principle:** Understand that the boundary follows the centerline of the creek as it existed at the time of the original survey. Changes to the creek’s course over time might necessitate adjustments based on legal precedents and surveying best practices. Bronte must also determine if the creek is considered a “substantial” watercourse as defined by relevant legislation, as this may affect how the *ad medium filum aquae* principle is applied. 4. **Re-establish the boundary:** Use the calculated true bearing and the principle of *ad medium filum aquae*, along with any other available evidence (e.g., original survey monuments, witness trees), to re-establish the boundary line on the ground. The most accurate approach involves determining the original true bearing, applying the *ad medium filum aquae* principle correctly, and considering the legal implications of changes to the watercourse. This requires a thorough understanding of historical surveying practices, boundary law, and the relevant regulations in Western Australia.

The problem requires us to calculate the horizontal distance between two points, A and B, given their grid coordinates and a combined scale factor. The combined scale factor accounts for both the map projection scale and the elevation factor. First, we calculate the difference in eastings (\(\Delta E\)) and northings (\(\Delta N\)): \[\Delta E = E_B – E_A = 456789.123 \, \text{m} – 456123.456 \, \text{m} = 665.667 \, \text{m}\] \[\Delta N = N_B – N_A = 6789012.345 \, \text{m} – 6789567.890 \, \text{m} = -555.545 \, \text{m}\] Next, we calculate the grid distance (\(d_{grid}\)) using the Pythagorean theorem: \[d_{grid} = \sqrt{(\Delta E)^2 + (\Delta N)^2} = \sqrt{(665.667)^2 + (-555.545)^2} = \sqrt{443107.555 + 308629.803} = \sqrt{751737.358} = 867.028 \, \text{m}\] Finally, we calculate the horizontal distance (\(d_{horizontal}\)) by dividing the grid distance by the combined scale factor (CSF): \[d_{horizontal} = \frac{d_{grid}}{CSF} = \frac{867.028 \, \text{m}}{1.0000567} = 866.979 \, \text{m}\] Therefore, the horizontal distance between points A and B is approximately 866.979 meters. This calculation incorporates fundamental surveying principles, including coordinate geometry and scale factor correction, which are crucial for accurate land surveying practices in Western Australia. Understanding these concepts is essential for land surveyors to ensure compliance with surveying standards and legislation, particularly when dealing with cadastral surveys and infrastructure development projects. The correct application of these principles ensures accurate land parcel identification and adherence to relevant regulations.

This question tests the understanding of LiDAR (Light Detection and Ranging) technology and its applications in surveying. LiDAR is a remote sensing technique that uses laser light to measure distances to the Earth’s surface. It is commonly used to create high-resolution digital elevation models (DEMs) and digital terrain models (DTMs). There are two main types of LiDAR: airborne LiDAR, which is mounted on aircraft, and terrestrial LiDAR, which is ground-based. Airborne LiDAR is suitable for large-area mapping and topographic surveys, while terrestrial LiDAR is used for detailed surveys of smaller areas, such as building facades or infrastructure. LiDAR data can be used to generate contour maps, calculate volumes, and detect changes in land elevation. The accuracy of LiDAR data depends on factors such as the quality of the LiDAR sensor, the flying height (for airborne LiDAR), and the processing techniques used. However, LiDAR generally provides higher accuracy and resolution than traditional photogrammetry, especially in vegetated areas. In surveying, LiDAR is used for a wide range of applications, including topographic mapping, construction monitoring, and environmental surveys.

Land tenure in Western Australia is governed by a complex interplay of historical precedent, legislation, and common law principles. Freehold tenure, offering the greatest degree of ownership, is subject to limitations imposed by planning regulations, environmental laws, and native title rights. Leasehold tenure, commonly associated with Crown land, grants rights to use and occupy land for a specified period, subject to conditions outlined in the lease agreement. Crown land, managed by the state government, encompasses vast areas used for conservation, resource extraction, and public purposes. Easements, rights-of-way, and restrictive covenants further complicate land ownership by granting specific rights to third parties or imposing limitations on land use. The interaction of these factors necessitates a thorough understanding of the Surveying and Spatial Information Act, the Land Administration Act, and relevant case law to accurately determine land boundaries and ownership rights. A surveyor must consider all relevant factors, including historical records, survey plans, and legal instruments, to provide accurate and reliable advice to clients. The surveyor’s role is to interpret and apply these complex legal and technical principles to resolve boundary disputes, facilitate land development, and ensure compliance with regulatory requirements.

The problem involves calculating the combined scale factor for a survey project in Western Australia, considering both the project’s elevation and its location relative to the Geocentric Datum of Australia 2020 (GDA2020) grid. The combined scale factor \( K \) is the product of the grid scale factor \( k_0 \) and the height (elevation) scale factor \( k_h \). First, calculate the height scale factor \( k_h \). This factor accounts for the reduction in distance due to the Earth’s curvature and is calculated using the formula: \[k_h = \frac{R}{R + H}\] where \( R \) is the Earth’s radius (approximately 6371000 meters) and \( H \) is the average project elevation. Given \( H = 350 \) meters, we have: \[k_h = \frac{6371000}{6371000 + 350} = \frac{6371000}{6371350} \approx 0.99994506\] Next, the grid scale factor \( k_0 \) is given as 0.99984. The combined scale factor \( K \) is then: \[K = k_0 \times k_h = 0.99984 \times 0.99994506 \approx 0.99978507\] Therefore, the combined scale factor for the project is approximately 0.99978507. This factor is crucial for reducing grid distances to ground distances, ensuring accurate measurements in surveying projects. It reflects the distortions introduced by projecting the curved Earth onto a flat plane (grid scale factor) and the effect of elevation on distances (height scale factor). Understanding and applying the combined scale factor is essential for surveyors to comply with surveying standards and regulations in Western Australia. The Land Surveyors Licensing Board of Western Australia emphasizes the importance of accurate scale factor application in cadastral and engineering surveys.

The question explores the complexities surrounding the legal status of Crown land in Western Australia, particularly when it borders a pre-existing freehold property and is subject to ambiguous historical documentation. The key to understanding the correct answer lies in recognizing the paramount importance of the *Land Administration Act 1997* (WA) and the principle of indefeasibility of title under the *Transfer of Land Act 1893* (WA). Even if historical documentation suggests a potential historical claim or informal agreement regarding the Crown land’s use, the current legal framework takes precedence. The Land Administration Act vests control and management of Crown land in the State. The Registrar of Titles is bound by the legislation and the registered title. While historical context is important, it cannot override the explicit provisions of current legislation and the principle of indefeasibility. Furthermore, any potential claim would need to be rigorously substantiated and pursued through the appropriate legal channels, such as the State Administrative Tribunal (SAT) or the Supreme Court, with the burden of proof resting heavily on the claimant. The mere existence of old documents is insufficient to automatically extinguish Crown land status. The surveyor’s professional responsibility is to advise the client on the legal complexities and the need for formal legal advice.

The Surveying and Spatial Information Act of Western Australia provides the legal framework for surveying practices within the state. A key aspect of this act, particularly relevant to boundary disputes and land tenure, is the requirement for surveyors to act impartially and adhere to strict guidelines when re-establishing boundaries. Section 24 outlines the surveyor’s duty to thoroughly investigate historical records, including original survey plans and any subsequent dealings that may affect the boundary’s position. Furthermore, the act emphasizes the hierarchy of evidence in boundary re-establishment, prioritizing original monuments and marks where their positions can be reliably determined. Where original marks are missing, the surveyor must consider other evidence such as occupation, fencing, and historical usage, but only in the context of their consistency with the original survey. The surveyor must also consider the principles of *ad medium filum viae* (ownership to the centre of the road) and the implications of any historical subdivisions or amalgamations of land parcels. The Act requires surveyors to lodge a ‘Re-establishment Survey Report’ with Landgate, detailing the methodology, evidence considered, and the surveyor’s professional opinion on the boundary’s location. This report provides transparency and allows for scrutiny by other surveyors or affected landowners. The surveyor must demonstrate a clear understanding of the relevant case law, such as *Easton v Bowman*, which clarifies the weight to be given to various forms of evidence in boundary disputes. The Act also covers the process for resolving disputes, including referral to the State Administrative Tribunal (SAT) if necessary.

The problem involves calculating the horizontal distance and reduced level of point C given observations from point A and point B. We must account for the curvature and refraction corrections. First, calculate the curvature and refraction correction \(C\) using the formula: \[C = 0.0675K^2\] where \(K\) is the distance in kilometers. For the distance AC (2000m or 2km), the curvature and refraction correction \(C_{AC}\) is: \[C_{AC} = 0.0675 \times (2)^2 = 0.27 \, \text{m}\] For the distance BC (1500m or 1.5km), the curvature and refraction correction \(C_{BC}\) is: \[C_{BC} = 0.0675 \times (1.5)^2 = 0.151875 \, \text{m}\] Next, calculate the height difference between A and C using the observed vertical angle and horizontal distance. The observed vertical angle from A to C is \(1^\circ 30′ 00”\), which is \(1.5^\circ\). The height difference \(h_{AC}\) is: \[h_{AC} = D_{AC} \tan(\theta) + C_{AC}\] \[h_{AC} = 2000 \times \tan(1.5^\circ) + 0.27\] \[h_{AC} = 2000 \times 0.026176 + 0.27 = 52.352 + 0.27 = 52.622 \, \text{m}\] The reduced level of point A is 100.000 m. Therefore, the reduced level of point C based on observations from A is: \[RL_C = RL_A + h_{AC} = 100.000 + 52.622 = 152.622 \, \text{m}\] Now, calculate the height difference between B and C using the observed vertical angle and horizontal distance. The observed vertical angle from B to C is \(-0^\circ 45′ 00”\), which is \(-0.75^\circ\). The height difference \(h_{BC}\) is: \[h_{BC} = D_{BC} \tan(\theta) + C_{BC}\] \[h_{BC} = 1500 \times \tan(-0.75^\circ) + 0.151875\] \[h_{BC} = 1500 \times -0.01309 + 0.151875 = -19.635 + 0.151875 = -19.483 \, \text{m}\] The reduced level of point B is 172.105 m. Therefore, the reduced level of point C based on observations from B is: \[RL_C = RL_B + h_{BC} = 172.105 – 19.483 = 152.622 \, \text{m}\] Since both calculations give the same reduced level for point C, the reduced level of point C is 152.622 m. To calculate the horizontal distance between A and B (D_{AB}), we can use the law of cosines: \[D_{AB}^2 = D_{AC}^2 + D_{BC}^2 – 2 \times D_{AC} \times D_{BC} \times \cos(\angle ACB)\] \[D_{AB}^2 = 2000^2 + 1500^2 – 2 \times 2000 \times 1500 \times \cos(120^\circ)\] \[D_{AB}^2 = 4000000 + 2250000 – 6000000 \times (-0.5)\] \[D_{AB}^2 = 6250000 + 3000000 = 9250000\] \[D_{AB} = \sqrt{9250000} = 3041.38 \, \text{m}\] Therefore, the horizontal distance between A and B is 3041.38 m and the reduced level of C is 152.622 m.

The scenario involves a complex subdivision approval process under Western Australian planning regulations. The key is understanding the hierarchy of planning instruments and the surveyor’s role in navigating them. The surveyor must first identify the relevant zoning under the local planning scheme. This scheme dictates permissible land uses, density controls, and other development standards. The proposed subdivision must comply with these standards. The surveyor then assesses the proposed subdivision against the State Planning Policy 7.3 (SPP7.3) – Urban Growth. SPP7.3 promotes well-planned urban growth and outlines principles for coordinating land use and infrastructure. The surveyor must demonstrate that the subdivision aligns with these principles, particularly regarding efficient use of land, access to services, and integration with existing development. Furthermore, the surveyor must consider any relevant structure plans or activity centre plans that apply to the area. These plans provide more detailed guidance on the desired form and character of development. The surveyor must ensure that the subdivision is consistent with the objectives and provisions of these plans. If there are any conflicts between the various planning instruments, the surveyor must advise the client on the appropriate course of action, which may involve seeking variations or amendments to the plans. The surveyor’s role is to provide expert advice on the planning implications of the proposed subdivision and to ensure that it complies with all relevant planning regulations. This requires a thorough understanding of the planning framework and the ability to interpret and apply planning policies and guidelines. The surveyor also plays a crucial role in communicating with the local government and other stakeholders to address any concerns and to facilitate the approval process.

Land tenure in Western Australia is a complex system comprising freehold, leasehold, and Crown land, each governed by distinct legal frameworks. Freehold tenure grants the holder the greatest bundle of rights, including the right to possess, use, and dispose of the land, subject to certain statutory restrictions. Leasehold tenure, on the other hand, confers a right to occupy and use land for a specified period, subject to the terms and conditions of the lease agreement, with the reversionary interest remaining with the Crown or another landowner. Crown land encompasses all land owned by the State of Western Australia, managed under the Land Administration Act 1997, and can be used for various public purposes or leased to private individuals or entities. The concept of ‘native title’ further complicates land tenure. The Native Title Act 1993 (Cth) recognises and protects the rights and interests of Aboriginal and Torres Strait Islander people in land and waters, where those rights and interests are based on traditional laws and customs. A ‘pastoral lease’ is a specific type of leasehold tenure granted by the Crown for grazing purposes, often covering vast areas of land. The interaction between native title and pastoral leases has been a subject of significant legal and political debate in Australia. In Western Australia, the coexistence of native title rights with pastoral leases requires careful consideration. The exercise of native title rights on pastoral lease land is generally subject to the rights of the pastoralist to conduct their grazing operations. However, native title holders may still be able to exercise their rights for traditional purposes, such as hunting, gathering, and cultural activities, provided that these activities do not unduly interfere with the pastoralist’s operations. Therefore, understanding the hierarchy of land rights and the specific provisions of relevant legislation is crucial for land surveyors in Western Australia, particularly when undertaking cadastral surveys or providing advice on land development proposals. The High Court’s decisions in cases such as *Mabo v Queensland (No 2)* and *Wik Peoples v Queensland* have significantly shaped the legal landscape surrounding native title and its interaction with other forms of tenure.

To solve this problem, we need to understand how errors propagate in traverse surveying and how to calculate the linear misclosure and relative precision. First, we calculate the total error in northing (\(\Delta N\)) and easting (\(\Delta E\)). Then, we calculate the linear misclosure (\(LM\)) using the Pythagorean theorem. Finally, we calculate the relative precision by dividing the linear misclosure by the total traverse length. Given: Total traverse length, \(P = 1500\) m Error in northing, \(\Delta N = 0.15\) m Error in easting, \(\Delta E = 0.20\) m The linear misclosure \(LM\) is calculated as: \[LM = \sqrt{(\Delta N)^2 + (\Delta E)^2}\] \[LM = \sqrt{(0.15)^2 + (0.20)^2}\] \[LM = \sqrt{0.0225 + 0.04}\] \[LM = \sqrt{0.0625}\] \[LM = 0.25 \text{ m}\] The relative precision (\(RP\)) is calculated as the ratio of the linear misclosure to the total traverse length: \[RP = \frac{LM}{P}\] \[RP = \frac{0.25}{1500}\] \[RP = 0.00016667\] To express this as a ratio where the numerator is 1, we take the reciprocal of \(RP\): \[\frac{1}{RP} = \frac{1}{0.00016667} \approx 6000\] Therefore, the relative precision is approximately 1:6000. Understanding error propagation and adjustment is crucial in surveying. This involves recognizing that errors accumulate during measurements and computations. The linear misclosure provides a measure of the overall error in a closed traverse, while the relative precision indicates the quality of the survey. In practical surveying, surveyors must minimize errors through careful measurement techniques, instrument calibration, and appropriate adjustment procedures, such as least squares adjustment, to ensure the accuracy and reliability of survey results. This question assesses not only the ability to perform the calculations but also the understanding of the significance of these parameters in evaluating survey accuracy.