Section one
A risk assessment is only as good as its occupancy figure
Quantified Tree Risk Assessment works by combining three things: how long people occupy the space under and around a tree, how large the part most likely to fail is, and how likely that part of a tree is to fail. While, the latter two are matters for the arboriculturist standing under the tree but the first is a question about people and how they move through the site, and on an estate with beach, parkland, woodland, a hall, a village, farmland and an events programme, the honest answer at the outset was that nobody could be certain enough to provide an accurate estimate.
As per industry guidance (e.g., National Tree Safety Group, 2024), most large estates split their property into usage zones based on local on-site knowledge. However, this approach can be difficult to defend if an explanation is not provided for each zone: the boundaries are wherever somebody drew them, based on their subjective judgement at the time and if the zoning is ever queried the reasoning typically exists only in the assessor's head.
Also, it can be easy for an on-site team to identify high-traffic areas, the effect of their peak periods or to otherwise form an estimate of visitor flow based on outliers (conflating possible traffic with probable traffic; recalling seeing people use a path is not the same as understanding how many people use it). However, placing this usage in the context of a full year and accounting for night-time, closed periods, poor weather or seasonal visitor patterns, is less intuitive. In terms of target assessment it is just as useful to know when people aren't present as when they are.
A regular zoning review showed that Holkham Estate needed a defensible, reproducible, and updatable model that could be applied to the whole estate, rather than a set of zones drawn by hand. The Estate already had the data needed to do this, but it was not in a form that could be used directly: car park ticket sales were recorded, but not where those visitors went once they were on site; the Estate's LiDAR survey provided slope data, but not how easy it was to walk through each field or woodland block; and the Estate's own knowledge of what draws people off the obvious routes was not codified in any way.
A note on the numbers. Holkham Estate's visitor figures are commercially confidential and are not published here. Everything on this page that governs how the model behaves, the formulae, the decay constant, the friction values, the calibration logic, is given in full; the visitor counts that those formulae are applied to, and some variable values, are not. This page has been prepared with, and is published with, the Estate's agreement.
What this model is not. It is not a footfall count and it does not estimate how many people stand at any particular spot. It produces a relative index of use across the estate: values are proportional to intensity of visiting and are meaningful in comparison with one another, not as headcounts. It does not assess any tree, and it does not categorise trees. It sets the occupancy input that a QTRA assessment then uses, and nothing beyond that. Note also the direction of the QTRA scales: in all three inputs a lower number is the more serious one.
Section two
The model in five stages
The sequence below is the non-technical account that accompanies the policy itself. Each stage is then opened up in the sections that follow, with the arithmetic shown.
What is known about visitors
Car park ticket sales over a five year period, converted to visitor numbers using the Estate's own vehicle occupancy figure (based on in-house visitor counts per vehicle). Every path, track, field and woodland block mapped and scored for how hard it is to walk through, with slope taken from a LiDAR survey.
How far everyday visitors travel
From each car park, the easiest walking route to every point on the estate is calculated. Half of each car park's visitors wander, and the harder and longer the walk, the fewer of them are estimated to get there. The four car parks are modelled separately and combined, so places reachable from several show higher pressure.
Where visitors with a destination go
The other half head for a feature, such as the beach, the Hall or the walled garden, chosen by its appeal and how far away it is, and walk the easiest route to it. Close to each feature, where people linger, pressure is raised, up to double.
Adding event visitors
Races and organised walks follow known routes, so their numbers are mapped straight onto those routes. Temporary event car parks are handled differently again, by modelling the walking corridor between the car park and the event field.
The usage overview
Everything is combined into a single surface, classified into six inspection zones, and applied to the areas that trees can actually affect, so the number of trees in each zone can be counted and inspection planned against it.
Section three
Cost surface and terrain
The model's foundation is the observation that people are governed by effort rather than by distance. A surfaced drive invites a long walk; two hundred metres of bramble does not. The estate is therefore represented as a friction surface: a grid at five metre resolution in which every cell carries a value for how costly it is to cross.
Those values were assigned manually across the whole estate, informed by walk-over reassessments carried out in autumn and winter 2025 in which the physical signatures of use, undergrowth density, path wear and compaction, clearance around gateways, were recorded directly, and the mapped path network was supplemented with major desire lines plotted by GPS. Open water and dense woodland carry obstacle values; unclassified open ground carries a background cost several times that of a made path.
Show the working: how a path's cost is set, and how slope modifies it
Within the path network, cost is set by surface type and then adjusted for width, on the basis that a narrow path is slower and less inviting than a broad one of the same construction:
Slope is then applied as a multiplier, derived from a LiDAR digital terrain model:
The completed polygon layer is rasterised to the same five metre grid used throughout, on the British National Grid.
Show the working: accumulated cost, and what a cost unit means
From each car park's pedestrian exit, accumulated walking cost to every cell is calculated by a least-cost path algorithm, which finds the cheapest route through the friction surface rather than measuring straight-line distance. The output is a surface of accumulated cost, not metres, and the relationship between the two depends on what has been crossed to get there.
Cost accumulates per cell traversed, not per metre. A diagonal step carries the same friction scaled by the square root of two, and covers the square root of two times the ground distance, so the cost per metre is unchanged either way. For a walk of length L:
That relationship was checked against the model rather than assumed. In October 2026 the accumulated cost at about 2,500 m along the coastal path read about 1,400, against 1,330 predicted: an overhead of around five per cent, because a raster least-cost path is restricted to eight directions of travel. That sits comfortably inside the calibration assumption and does not change the constant derived from it.
What the friction values do
The panel below applies the two formulae above to a single stretch of ground. It shows how far a visitor gets for a given amount of walking effort, and, using the decay function set out in the next section, what proportion of a car park's wandering visitors are modelled as getting there.
Why the width term matters more than it looks. Narrowing a path does not halve the number of people who use it, but it does raise its friction as users slow down (especially where the remainder of the path cannot be seen), and friction compounds along a route. A pinch point early in a walk suppresses everything beyond it, which is the mechanism by which one narrow crossing can leave a large area modelled as lightly used. Where the model disagrees with what the Estate observes on the ground, a pinch point is usually the first place to look.
Section four
The decay function, and the one number everything rests on
With accumulated cost calculated, the model applies a gravity decay framework: the proportion of a car park's visitors reaching any point falls off exponentially with the walking effort required to get there. This is the standard form used in recreational visit modelling, and it matches the consistent finding that visit frequency declines approximately exponentially with distance from an access point.
The decay applies to the half of each car park's visitors who wander with no particular destination; the other half are routed to the features they head for, as set out in the next section. Lambda is a judgement, and it is the number most worth interrogating, so it is set explicitly rather than tuned until the map looked right. It is calibrated so that roughly one per cent of a car park's wanderers are modelled as reaching the far end of a typical long walk, taken as 2,500 m along paths.
Lambda was recalibrated in October 2026. It had been set at 0.004605 on an assumed mean on-path friction of 2.0; with the current cost surface, and slope applied correctly, the mean is 2.66, so the old value had come to mean one per cent at about 1.9 km rather than 2.5 km. The calibration rule is unchanged; only the measured friction it rests on was corrected.
What different values of lambda would mean
Move the control below to see how the choice of decay constant changes the proportion of wanderers modelled as reaching a given distance. The value adopted for the Estate is marked, and the value used before recalibration is kept for comparison.
Show the working: why this is a relative index and not a headcount
Each car park's decay surface is multiplied by the wanderer share of that car park's annual visitor total and the four are summed, together with the destination routes described next. It is tempting to read the resulting cell values as numbers of people, and that would be wrong. A single visitor's propensity is spread across many cells along their possible routes, so the totals are not conserved: the surface is proportional to intensity of use, but it does not add up to the number of visitors who came.
That is sufficient for the purpose. Zoning is a comparative exercise, and what the policy needs is a reliable ordering of places from busiest to quietest, together with a defensible basis for drawing thresholds between them. Where the surface is used to set those thresholds, the calibration is deliberately cautious, so the model is more likely to place an area in a busier zone than a quieter one.
Section five
Where visitors with a destination go
Walking cost alone assumes people wander outwards from a car park with no particular destination in mind. Many do. Many others head for something: the beach, the Hall, the lake, the walled garden. The model therefore splits each car park's visitors in two. Half wander, spreading out with the decay set out in section four. The other half are destination visitors: each heads for one named feature and walks the easiest route to it. Ten such features are mapped across the estate.
The half is a stated assumption, chosen to start the conversation rather than measured, and a short survey at the car parks asking people where they are heading would test it. The feature ratings and effect radii are professional judgement informed by site knowledge. With the share, they are the places in the model, after lambda, where a reviewer should focus attention.
Which feature they head for
Destination visitors are shared between the features by a gravity split, the standard Huff form: a feature's draw rises with its rating and falls with the walking cost of getting there from the car park.
Each car park's destination visitors then walk to their feature along a corridor, using the same bidirectional cost deviation device as the event car parks in section six: the full flow on the easiest route, falling away to either side as the cost of a detour rises.
How destination visitors are shared
One car park and three features at different walking distances. Move the share, the distance penalty and the distances to see how the car park's visitors are divided between wandering and each feature.
Dwell: where people linger
Reaching a feature is only part of it: people stay there, and occupancy is about time present as well as people passing. Close to each feature, all car park pressure is raised by a dwell boost. The effect radius now describes where people linger, between 50 and 250 m, not how far a feature draws visitors from.
| Rating | Typical stay | Dwell boost at the feature |
|---|---|---|
| 5 | A glance, under two minutes | × 1.25 |
| 10 | A short stop, five to ten minutes | × 1.5 |
| 15 | An extended stay, twenty to forty-five minutes | × 1.75 |
| 20 | A main destination, an hour or more | × 2.0 |
How dwell behaves
Move the interest rating and the effect radius to see the dwell multiplier at increasing walking distance from a feature. Adding a second feature nearby shows the soft union: the boost where the two overlap is higher than either alone, but never above × 2.
Show the working: why the attractor multiplier was replaced
Until October 2026 attractors were handled by multiplying car park pressure near each feature: first by the summed influence with a floor of 1.0, then, once the floor was found to discard most of each feature's reach, by one plus the summed influence. Both forms added visitors near features without routing anyone to them, so busy places could appear with no busier route leading to them.
After the features were rescored, the first full run still showed the weighting far too high. Car parks sat inside effect radii of up to a kilometre and were multiplied between 1.7 and 2.8 times, and a path 2.5 km from the nearest car park read about 25 times what the decay alone predicts where it crossed several attractor zones.
Routing a stated share of visitors to the features, and adding a capped dwell boost where they linger, moves visitors to the features rather than creating them there. At Holkham the area in the second-highest occupancy range fell to under a third of its previous extent.
Section six
Events, and why they needed a different model
The gravity decay framework describes people who arrived with a vague intention to walk somewhere pleasant. It does not describe somebody who has paid to run a ten kilometre race on a set course, or who has parked in a field and is walking to a marquee. Those people have a destination they will reach with near-certainty, and modelling them probabilistically would put most of them in the wrong place.
Fixed-route events
Races, organised walks and similar structured activities follow known courses, so their anticipated annual numbers are assigned directly to the route. The lines are cleaned, buffered to a corridor width appropriate to the event type, and burnt onto the same five metre grid, with overlapping routes accumulating rather than overwriting one another. These are added after the dwell boost, so a race is not amplified for passing a viewpoint.
Temporary event car parks: the corridor model
Thirteen events each year bring visitors to temporary car parks in fields, from which they walk to an event area. Neither end can be modelled by decay from a car park: essentially everybody who parks will reach the event, and the pressure between the two is concentrated along whichever route is easiest, not spread evenly in all directions.
The approach taken is a bidirectional cost deviation model, which is structurally the same device used for functional corridors in landscape connectivity analysis, where the question is how far an animal moving between two habitat patches is likely to stray from the optimal route. Visitors may park anywhere in the car park and head for anywhere in the event area, so about twenty-five sample points are spread across each polygon and an accumulated cost surface is calculated from every one. For each pairing of a car park point with an event point, the two surfaces added together give, for every cell on the estate, the total cost of a journey between them that passes through that cell. Subtract the cost of that pair's best route and what remains is the extra effort of detouring through the cell. Along the ideal route the extra effort is zero; a hundred metres off to one side it is small; over the far side of a wood it is large.
Show the working: why the corridor sampling changed
Until October 2026 each polygon was treated as a single source at zero cost, and the cost of the best route was read at the centre of the event area. That overstated the trip cost by the walk from the event's near edge to its centre, and the slack became a full-count band either side of the route whose width depended on how deep the event polygon was, rather than on μ.
Spreading sample points across both polygons removes it. Across the thirteen events, total corridor pressure fell to about a third, while the area reaching the lowest band was almost unchanged. Because every part of a polygon now carries weight, each one should be drawn round the area actually used, not the whole field it sits in.
Darker means more of the event's visitors are modelled as passing through. Cells are five metres, as in the model, so the view covers about 480 m by 280 m.
This panel runs the real calculation on a small demonstration grid: nine sample points in each area, a least-cost surface from every one, and for each of the 81 pairs the detour cost decayed, then averaged. Because it is built from walking cost rather than geometry, the corridor bends around obstacles and pinches where the ground funnels people together, which is exactly where trees along the route matter most.
Moving the dispersal control also shows how finely graded these choices are. There is no value that is obviously right and none that is obviously wrong; each one is a defensible statement about how tightly people keep to a route, and the shape of the answer changes steadily rather than snapping between options. The test that matters is not which number looks best on the map, but whether the result matches what estate staff see on the ground on the day of an event.
The practical benefit of doing it this way is that an event is now an input rather than an assumption. A new event can be added, moved or removed and the model re-run, and the output shows which parts of the estate change zone as a result, and how many trees fall into an area needing earlier inspection. That converts a difficult conversation about whether an event is acceptable into an arithmetic one about what it would cost to make it so.
Section seven
From a pressure surface to an inspection programme
The combined surface is classified into six zones corresponding to the pedestrian occupancy ranges used in the QTRA framework. Those ranges are part of the licensed QTRA system and are not reproduced here; what matters for this account is that the thresholds are external to the model, published, and peer reviewed, so the classification step introduces no further judgement of ours. This is the join between the modelling and the policy: everything before it is spatial analysis, and everything after it is tree management.
The scale runs from TR1, the busiest places, to TR6, the least used. A tree in a higher-use zone is inspected more often and managed more conservatively, because the consequence of a failure is more likely to involve somebody being present.
Six ranges, three management bands
The six occupancy ranges are therefore grouped into three management bands, High, Medium and Low use, and it is at that level that the Tree Risk Management Policy sets inspection frequency and risk tolerance (the six-way classification is retained underneath, because it is what allows a band boundary to be justified). This is the point at which the model stops being a piece of spatial analysis and becomes integrated with an operational document. The policy then sets out, for each band, how often trees are inspected.
Applying zones to the areas trees can actually reach
A zone boundary drawn across open parkland is of no operational use on its own. The final step intersects the zoned surface with the areas within which a tree could strike somebody, derived by offsetting mapped canopy extents by an allowance based on LiDAR vegetation heights. Each resulting fragment carries its zone, which means the Estate can count the trees or the woodland area falling into each inspection band and cost a survey programme directly from it.
Show the working: the classification and intersection steps
Classification is a single nested conditional evaluated across the raster, assigning each cell to one of the six zones by comparing its pressure value against the QTRA occupancy thresholds, with cells below the lowest threshold left unzoned. Inspection area polygons are then intersected with the zone boundaries, with a geometry repair step applied first, because invalid geometry at zone edges will otherwise stall the intersection.
What it delivers
The same rule everywhere
Every part of the estate is zoned by the same process from the same data, so two similar places get the same answer regardless of who is assessing them or when.
A stated basis for every boundary
If a zone boundary is questioned, the answer is a chain of inputs and formulae rather than a recollection. That matters most in the situation nobody wants, after an incident.
Scenarios instead of arguments
Adding an event, opening a new path or closing a car park can be modelled before it happens, and the change in survey liability quantified in advance.
Section eight
The whole model, run on an illustrative estate
Each panel above isolates one part of the model. This one runs all of them together, in the same order and with the same formulae, on a small invented estate: a beach to the north behind dunes and pinewoods, grazing marsh, a village on the coast road, and a walled park with a hall, a lake, a monument, an obelisk on rising ground, a walled garden and a block of dense woodland. Three permanent car parks feed it. The events programme adds a temporary car park and an event field on the east side of the park, and a race that follows the park tracks.
Every input represents a whole year, as it does in the model: car park figures are annual totals and the event controls stand for the full event calendar, so there is no setting for a busy weekend or a quiet month. Step through the six views to watch the surface build up, then change an input and see which ground, and which trees, change band. Select any point on the map, or move around it with the arrow keys, to see the arithmetic for that spot.
What this panel is not. It is not Holkham Estate - although it shares some similarities. The layout is invented, and the visitor numbers are illustrative units, not the Estate's figures. The band thresholds are illustrative too: they stand in for the QTRA occupancy ranges, which are licensed and not reproduced here, so the six ranges TR1 to TR6 are named but not drawn and the map shows only the three management bands. The trees are placed for demonstration. Nothing here assesses a tree.
Car parks
Ground and terrain
Destinations and dwell
Events
Decay constant
Selected point shown by the red square; click or tap the map, or use the arrow keys, to move it
Show the arithmetic for the selected point
Show the working: how the full model is scaled down for this panel
The grid is 20 metres rather than 5, covering about 3.2 km by 2 km in 16,000 cells, so that the calculation can run in a browser. Each step's cost is multiplied by four, so that walking cost per metre is the same as on the five metre grid. That keeps the published constants as they are: λ = 0.00346 at a mean on-path friction of 2.66, a destination share of 0.5 with β equal to λ, a route spread and event dispersal of 0.05, and a dwell maximum of 1.0, with each feature's boost falling to five per cent at its effect radius. Event corridors use nine sample points in each area rather than the model's twenty-five.
A path narrower than a cell cannot be drawn at its true width, so width enters through the cost formula only. Pinch points are therefore shown by their effect rather than their shape.
Everything else is the full method: a least-cost surface from each car park, exponential decay for the wanderers, the gravity split and routed corridors for destination visitors, the soft-union dwell boost applied to all car park pressure, the race burnt onto its route, and the sampled corridor for the event car park, combined as final_pressure = Σ ( wanderers + routes to features ) × dwell + event_routes + event_corridors.
The band thresholds are fixed at illustrative values on the demonstration index and are not controls, for the same reason the real thresholds are not: they sit outside the model. For counting, each tree here takes the busiest band within its own height of the stem, a cautious reading of the ground it could reach; in the model, the reachable area around each mapped canopy is split by zone instead.
Three things are worth trying. First, set the event car park to zero and back. The point already selected, on the woodland edge track at the south-west corner of East Wood, moves between Low and Medium use, and a band of ground along the west edge of the wood follows it. Then select the obelisk and move the race: it adds exactly its own number there, although the obelisk carries a dwell boost, because event pressure is added after dwell.
Second, close the boardwalk. It is the only made route from the beach car park to the beach, so closing it sends everyone through the pinewood: pressure along the whole beach falls, and about half of the trees on the seaward edge of the pines drop a band. That is the pinch point described in section three, made visible.
Third, lower the woodland friction. At 7 or below the event corridor starts to cut straight through East Wood as well as round it, and by 5 it has left the west edge altogether. Nothing else about the event has changed; only the judgement about how hard the wood is to walk through.
Section nine
Limits and caveats
Reproduced from the policy appendix.
- Only car park arrivals are modelled at baseline
Visitors arriving on foot from the surrounding villages, by bicycle or by public transport are not captured in the base surface.
- Event numbers are anticipated, not counted
They are drawn from historic averages and need updating annually as the events programme changes.
- No seasonal or weather variation
The friction surface reflects a judgement about relative traversability in general. It does not change between a dry August afternoon and a wet February morning, and neither does the output.
- The feature ratings and effect radii are indicative
Interest ratings and effect radii come from site knowledge and professional assessment rather than from measurement of where people actually went or how long they stayed.
- The destination share and distance penalty are stated assumptions
Half of each car park's visitors are taken to head for a feature, and the distance penalty that shares them between features is set equal to lambda, so a nearer feature can out-draw a higher-rated one further away. Both have a large effect on the result, and both are assumptions chosen to start the conversation, not measurements. Only data can refine them: a short survey at the car parks asking where people are heading would test both.
- One destination per visitor
Each destination visitor heads for a single feature, and the walk back is taken to follow the same corridor. A visitor who goes from the Hall to the lake and then the monument is not modelled as such.
- The terrain model is a snapshot
Slope is derived from LiDAR captured at a point in time and takes no account of vegetation change or ground conditions since.
- Lambda is a local calibration, and is presented as one
The exponential decay framework is well established in the literature; the specific value adopted here is a site calibration rather than a published finding. That is normal practice in applied spatial modelling, and it is said plainly rather than implied. It was re-checked against the model in October 2026, and should be revisited if systematic visitor tracking data ever becomes available.
- It should be re-run, not archived
The model needs recalibration if visitor numbers change materially, if a major new attraction opens, or if the path network is substantially altered.
Section ten
Client, sources and version
The model was developed for Holkham Estate as part of the Tree Risk Management Policy, which this practice originally authored, and revised in 2026. It is published here with the Estate's agreement, with visitor figures withheld at their request.
The wider policy work also included a LiDAR-derived, height-proportional safety buffer for event areas, replacing a blanket standoff distance with one that scales to the actual trees present. The same modelling approach is transferable to any property where public access varies significantly across the site: estates, parks, campuses, visitor attractions and long linear routes.
- National Tree Safety Group. (2024). Common sense risk management of trees: Guidance on trees and public safety in the UK for owners, managers and advisers (2nd ed.).
- Quantified Tree Risk Assessment (QTRA) practice note and target ranges, QTRA Ltd.
- Environment Agency LiDAR composite digital terrain model, Open Government Licence.
- Ordnance Survey and OpenStreetMap path network data, supplemented by on-site GPS survey.
Version 1.5 · October 2026 · attractors now routed (destination visitors and dwell), λ recalibrated, event corridors sampled across both polygons · earlier: version 1.4, version 1.3, version 1.2, version 1.1