Roughness length estimation along road transects using airborne LIDAR data

Authors


L. Chapman, School of Geography, Earth and Environmental Sciences, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. E-mail: l.chapman@bham.ac.uk

Abstract

Roughness length (Z0) is traditionally used as the primary measure of the aerodynamic roughness of a surface, but is notoriously difficult to estimate. This study takes a new approach to the estimation of Z0, using high resolution LIDAR data coupled with spatial processing techniques to provide estimates of effective roughness length (Z0eff) based upon the prevailing wind direction and the height of the surface elements (e.g. buildings, trees) within a defined area of upwind fetch. The range of roughness values obtained using this new technique is consistent with published values obtained from detailed boundary layer experiments, and is shown to distinguish between a variety of landuse categories, ranging from high density urban areas to rural farmland. Indeed, comparisons in Z0eff values between different landuse classes using a detailed land-cover dataset have revealed significant differences in surface roughness between landuse classes, giving confidence not only in the technique itself but also to the validity of the land-cover dataset used in the study. Copyright © 2011 Royal Meteorological Society

1. Introduction

Obtaining real-world values of surface roughness for application in boundary layer models can be problematic. Typically the roughness length (Z0) is used, which is a measure of the aerodynamic roughness of a surface defined using the height at which the neutral wind profile near to the ground extrapolates to zero (Oke, 1992). Z0 is related to the height of the surface elements (ZH) by the empirical coefficient f0 derived from observation, whereby:

equation image(1)

The length Z0 is related, but not equal to, the height of the surface elements and is also a function of the shape and density of the elements. As such, Z0 is difficult to calculate in the heterogeneous conditions found in the real world, and practical estimation of Z0 at a particular locality is often based on published values for roughness of similar terrain elsewhere (Wieringa et al., 2001). A detailed review of roughness data from boundary-layer experiments conducted in the 1970s and 1980s was undertaken by Wieringa (1993), who found that the Davenport (1960) classification of effective terrain roughness most reliably described the effective roughness of realistic landscape types. The original Davenport classification has since been updated at both ends of the classification scale (Wieringa, 1992; Wieringa et al., 2001), providing arguably the best field-validated roughness classification to date (Table 1).

Table 1. Davenport classification of effective terrain roughness (Wieringa et al., 2001)
ClassZ0 (m)Landscape description
1. Sea0.0002Open sea or lake (irrespective of wave size), tidal flat, snow-covered flat plain, featureless desert, tarmac and concrete, with a free fetch of several kilometres.
2. Smooth0.005Featureless land surface without any noticeable obstacles and with negligible vegetation; e.g. beaches, pack ice without large ridges, marsh and snow-covered or fallow open country.
3. Open0.03Level country with low vegetation (e.g. grass) and isolated obstacles with separations of at least 50 obstacle heights; e.g. grazing land without wind breaks, heather, moor and tundra, runway area of airports. Ice with ridges across-wind.
4. Roughly Open0.10Cultivated or natural area with low crops or plant covers, or moderately open country with occasional obstacles (e.g. low hedges, isolated low buildings or trees) at relative horizontal distances of at least 20 obstacle heights.
5. Rough0.25Cultivated or natural area with high crops or crops of varying height, and scattered obstacles at relative distances of 12–15 obstacle heights for porous objects (e.g. shelterbelts) or 8–12 obstacle heights for low solid objects (e.g. buildings).
6. Very Rough0.5Intensively cultivated landscape with many rather large obstacle groups (large farms, clumps of forest) separated by open spaces of about eight obstacle heights. Low densely planted major vegetation like bush land, orchards, young forest. Also, area moderately covered by low buildings with interspaces of three to seven building heights and no high trees.
7. Skimming1.0Landscape regularly covered with similar-size large obstacles, with open spaces of the same order of magnitude as obstacle heights; e.g. mature regular forests, densely built-up area without much building height variation.
8. Chaotic8.0 ≥ 2.0City centres with mixture of low-rise and high-rise buildings, or large forests of irregular height with many clearings.

This paper outlines a new method for approximating surface roughness (along road transects) using high resolution LIDAR data obtained from airborne surveys. The range of roughness values obtained using the proposed method is compared to published roughness values for similar terrain based on the updated Davenport classification of effective terrain roughness (Table 1). Statistical comparisons are then undertaken to assess whether the new roughness values distinguish between various landuse classes, using a comprehensive land-cover dataset developed by Owen et al. (2006). Potential applications, improvements and limitations of the technique are also discussed.

2. Re-parameterizing effective roughness length

2.1. Methods for calculating effective roughness length

Equation (1), which ignores the shape and spacing of elements, can be used as a simple rule of thumb for estimating Z0 (Oke, 1992; Grimmond and Oke, 1999). Both Garratt (1992) and Hanna and Chang (1992) estimate the value of f0 to be ∼0.1, which is a commonly quoted value for surfaces in general (Grimmond and Oke, 1999). Such a simple rule of thumb ignores the fact that Z0 should intuitively show maximum values at intermediate densities of surface elements due to the smothering of surface roughness at high densities. This smothering effect causes an increase in the zero-plane displacement length (Zd) until the surface elements are so densely packed that they merge to form a new surface (i.e. ZH = Zd) with Z0 returning to its background value. Thus, the expected form of Z0/ZH, with a peak at intermediate densities, means that this simple rule of thumb increasingly overestimates Z0 at very high and very low densities and fails to identify the roughness peak, but across the range it does yield reasonable values for Z0 (Grimmond and Oke, 1999). Z0, however, is a local value and well defined only for homogeneous terrain. In the case of heterogeneous terrain, where surface roughness can vary over short distances due to the varying height and spacing of surface elements, it is more appropriate to calculate an effective roughness length (Z0eff) from the distribution of local Z0 values (Vihma and Savijärvi, 1991). Whilst taking an areal average (denoted 〈〉) of a local parameter is far from an ideal solution, it does provide a simple method to calculate Z0eff from the available local Z0 values within a defined area, i.e.:

equation image(2)

Under normal circumstances the logarithmic wind profile would typically be incorporated into such an analysis by taking the logarithmic average of Z0 within the defined area (Vihma and Savijärvi, 1991). However, using the natural logarithm of height in Equation (2) would naturally lessen the influence of taller surface elements and weight the calculated Z0eff values towards the lower end of the roughness scale. Given the significant control that taller surface elements have on the local wind regime in urban areas (Oke, 1992), and in order to maintain rather than reduce the disparity between urban and rural areas, it was decided to use the arithmetic average of local Z0 values as shown in Equation (2).

2.2. Using LIDAR data to estimate Z0eff

The simple height-based rule of thumb outlined in Equation (1) was applied to a LIDAR dataset of the West Midlands, UK, to provide local estimations of Z0 at 50 m points along a mixed urban and rural study route consisting of a network of adjoining road transects that traverse through Birmingham city centre before passing through the southwest Birmingham suburbs and north Worcestershire countryside, covering a range of landuse classes (Figure 1). The LIDAR dataset consists of a 2 m resolution Digital Terrain Model (DTM) giving elevation measurements of the natural terrain features and a 2 m resolution Digital Surface Model (DSM) which together with the natural terrain features included additional features such as buildings, vegetation and roads. Hence, subtracting the DTM from the DSM produces a dataset containing height measurements of all surface objects, which can be utilized within the simple height-based Z0 calculation in Equation (1) to provide local Z0 estimations. This step is optional as in many circumstances it will be advantageous to calculate the additional impact of topography, although for this study this additional calculation was included for completeness to demonstrate how a building heights database can be derived.

Figure 1.

Mixed urban and rural study route with Birmingham city centre located in the north-east section of the route and the rural Worcestershire countryside to the south-west. Land-classes of 1 km2 (Owen et al., 2006) used for statistical analysis of the LIDAR based technique are shown overlain with the study route. Base mapping courtesy of EDINA Digimap http://edina.ac.uk/digimap/ chemical structure image, villages/farms; chemical structure image, suburban; chemical structure image, light suburban; chemical structure image, dense suburban; chemical structure image, urban/transport; chemical structure image, urban; chemical structure image, light urban/open water; chemical structure image, woodland/open land. This figure is available in colour online at wileyonlinelibrary.com/journal/met

To account for the prevailing wind and the effect of upstream surface elements on the surface roughness at each 50 m point along the route, Z0eff values for each point were calculated by taking the areal average of all local Z0 estimations (Equation (2)) contained within a wedge shaped area spanning away from each point. The wedge subtends a 45° angle from 247.5–292.5° to account for the prevailing southwesterly wind direction experienced in the UK. Five different wedges were calculated in ArcMap for various lengths of upwind fetch (100, 150, 200, 250 and 500 m) using a 45° focal mean wedge neighbourhood function. A series of fetches was chose for analysis as no standard recommendation exists, although the literature does suggest the fetch requirement to be a function of obstacle height (Wieringa, 1993; Bottema and Mestayer, 1998; Grimmond and Oke, 1999). To overcome a combination of intensive processing requirements and the limitation of single core processing on individual ArcMap tasks, a buffer (zone of specified interest around the point) with distances equal to the fetch requirements were created around each 50 m point and used as an analysis mask on the LIDAR dataset, from which the required LIDAR data within the buffer mask could be extracted and used to calculate the Z0eff values along each road transect.

3. Comparison with published values for similar terrain

The newly calculated Z0eff values at each point were compared against the Davenport classification of effective terrain roughness (Table 1) to assess whether the roughness values obtained using LIDAR data are typical of the values we would expect based on good quality observational data. Figure 2 shows the percentage distribution of Z0eff values over the study route, revealing how the roughness values are positively skewed towards the lower end of the roughness scale as might be expected given the predominantly rural to suburban nature of the study route. Maximum roughness values occur with an upwind fetch of 100 m (Figure 3) and are mainly located in the urbanized city centre where Z0eff values up to 3.1 m are found. This compares well with the Davenport classification for ‘chaotic’ terrain such as city centres containing a large mixture of low and high-rise buildings, where a Z0 value ≥ 2.0 m would be expected. When the distance of upwind fetch increases, the range of roughness values around the route decreases (Figure 3), most likely due to the damping of average surface element heights by an increasing proportion of low-rise surface elements within the defined neighbourhood area over larger fetches. With a fetch of 500 m the range of roughness values along the route decreases by approximately 55% to a peak value of 1.38 m in the city centre, which are still realistic values for terrain roughness in a densely built-up area.

Figure 2.

Histogram showing the percentage frequency distribution of Z0eff values over the five distances of westerly upwind fetch used in the analysis

Figure 3.

Hi-low plots showing the range of Z0eff values over the five distances of upwind fetch

At the opposite end of the roughness scale, a few Z0eff values as low as 0.0004 m are found on the westerly rural side of the route that fall within the ‘smooth’ category of the Davenport classification, typical of a featureless land surface without any noticeable obstacles and negligible vegetation, such as beaches or fallow open country (Wieringa et al., 2001). Such Z0eff values are particularly low but are also plausible given their location on the rural section of the route within the rural Worcestershire countryside. At this point, it is worth mentioning the influence of the local road environment as a complicating factor. Roads by their very nature are smooth surfaces which undoubtedly have a damping effect on the average surface element heights calculated within a defined neighbourhood area. However, the presence of traffic on roads will offset this thus affecting localized values and mixing, particularly in rural areas. Indeed, the vast majority of the rural and semi-rural points along the route, however, have roughness values that place them firmly within the ‘Open’, ‘Roughly Open’ or ‘Rough’ categories of the Davenport classification scale, with roughness values ranging from approximately 0.03 m up to around 0.25 m (Figure 4). Likewise, most of the points located within the suburban and urban areas of the route have roughness values of between 0.25 and 0.5 m (Figure 4), placing them within the ‘Rough’ and ‘Very Rough’ categories of the Davenport roughness scale. Thus, the overall range of roughness values seems typical of the values that would be expected for the general landuse classes around the route.

Figure 4.

Z0eff values (greyscale: dark = high, light = low) along the study route based on an upwind fetch of 100 m, categorized using the Davenport roughness classification. LIDAR data © 2009 landmap

4. Statistical analysis

To test for significant differences in the newly calculated Z0eff values between landuse categories, Kruskal–Wallis rank-order tests (Dytham, 1999) were performed on the Z0eff values calculated for the five distances of upwind fetch using an urban land-cover classification (OWEN) derived by Owen et al. (2006) for the UK West Midland metropolitan area. The OWEN land-cover dataset consists of eight land-cover classes at 1 km2 resolution (villages/farms, suburban, light suburban, dense suburban, urban/transport, urban, light urban/open water and woodland/open land) derived from dimensionality reduction of 25 spatial land-cover attributes using principal components analysis. The results from the Kruskal–Wallis analyses were highly significant (p < 0.001) over all five distances of fetch for the OWEN land-cover classifications. This indicates that significant differences exist in the Z0eff values between at least two of the OWEN land-cover classes, but does not reveal where these differences occur. Hence, post-hoc Wilcoxon rank-sum tests were performed on the Z0eff values within each independent OWEN land-cover class, comparing each class against each other to reveal where the significant differences occur. Table 2 displays a Wilcoxon p-values matrix for the OWEN land-cover classification.

Table 2. p-values matrices for Wilcoxon rank-sum tests comparing Z0eff values between each landuse class in the OWEN land-cover classification
OWEN 100 m fetchOWEN 150 m fetch
Land use1234567812345678
10.0000.0000.0000.0000.0000.0000.7510.0000.0000.0000.0000.0000.0000.468
20.0000.2120.0000.0000.2610.0000.0190.0000.1020.0000.0000.0000.0000.008
30.0000.2120.0010.0000.0480.0320.0490.0000.1020.0000.0000.1620.0000.023
40.0000.0000.0010.0000.0000.0000.0170.0000.0000.0000.0000.0000.0000.027
50.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000
60.0000.2610.0480.0000.0000.0000.0080.0000.0000.1620.0000.0000.0000.004
70.0000.0000.0320.0000.0000.0000.0020.0000.0000.0000.0000.0000.0000.000
80.7510.0190.0490.0170.0000.0080.0020.4680.0080.0230.0270.0000.0040.000
OWEN 200 m fetchOWEN 250 m fetch
Land use1234567812345678
10.0000.0000.0000.0000.0000.0000.7300.0000.0000.0000.0000.0000.0000.290
20.0000.0520.0000.0000.0000.0000.0010.0000.0160.0000.0000.0000.0000.000
30.0000.0520.0000.0000.0170.0000.0050.0000.0160.0000.0000.0020.0000.001
40.0000.0000.0000.0000.0000.0000.0010.0000.0000.0000.0000.0000.0000.000
50.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000
60.0000.0000.0170.0000.0000.0000.0010.0000.0000.0020.0000.0000.0000.000
70.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000
80.7300.0010.0050.0010.0000.0010.0000.2900.0000.0010.0000.0000.0000.000
OWEN 500 m fetch
  1. Land use classification: 1 villages/farms; 2 suburban; 3 light suburban; 4 dense suburban; 5 urban/transport; 6 urban; 7 light urban/open water; 8 woodland/open land.

  2. Italic values represent statistically non-significant results from the land use comparisons.

Land use12345678
10.0000.0000.0000.0000.0000.0000.002
20.0000.9020.0000.0000.0000.0000.000
30.0000.9020.0000.0000.0000.0000.000
40.0000.0000.0000.0000.0000.0000.000
50.0000.0000.0000.0000.0000.0000.000
60.0000.0000.0000.0000.0000.0000.000
70.0000.0000.0000.0000.0000.0000.000
80.0020.0000.0000.0000.0000.0000.000

To account for the problem of inflated error rates when conducting multiple Wilcoxon tests (Field, 2005), the Bonferroni Correction factor was applied to the standard 95% significance level, giving a new independent test level of 99.8% (0.002) for the OWEN dataset. Without this correction factor, the probability of rejecting the null hypothesis when it is actually true (Type 1 error) for at least one comparison increases from 5% to 76% (based on a total of 28 comparisons) when comparing all the land-cover classes. The Wilcoxon p-values for the OWEN classification (Table 2) reveal that up to 96% of the landuse comparisons are statistically significant at the 95% level using a Bonferroni corrected significance level of 0.002 on each comparison. This indicates that significant differences exist in the Z0eff values between the majority of the land-cover comparisons over all five distances of upwind fetch. The greatest similarities in surface roughness occur between the suburban and light urban land-cover classes, where no significant differences in surface roughness are found (p-value ≥ 0.016) over any distance of upwind fetch. With a fetch of just 100 m, only 68% of the roughness comparisons between all the land-cover classes are statistically significant, with over half of the non-significant comparisons (55%) resulting from individual comparisons with the woodland/mixed open land category (p-value ≥ 0.008). With a 500 m fetch, however, 96% of the roughness comparisons are statistically significant, revealing how the distance of upwind fetch used to calculate surface roughness has a significant effect on the resulting roughness values, which supports previous findings in the literature and increases confidence in the proposed LIDAR based technique. Hence, in summary, statistical differences are evident for calculated Z0eff values between the different land cover types, with the significance level increasing at larger fetches.

5. Conclusions

A new method for calculating surface roughness in neutral conditions using high resolution LIDAR data coupled with spatial processing techniques has been presented. Results from this pilot study have shown that the range of Z0eff values this method produces is consistent with published values for similar terrain based on good quality observational data from detailed boundary-layer experiments. Such a technique enables the roughness characteristics at numerous points to be modelled based on the height and spacing of surface elements within the prevailing upwind fetch, which is an improvement on the current ordinal parameterizations used in many models (e.g. route-based road weather models which require roughness length data for the many thousands of sites forecasted in the model: Chapman et al., 2001; Chapman and Thornes, 2006).

It is acknowledged that the proposed technique is not perfect. A local parameter can, at best, only be approximated by an areal average and as such it assumes that each portion of the upstream surface is an equal contributor to the aerodynamic character at a given point. In reality certain patches within this upstream area will be greater source contributors, and others less so, due to variations in the height and spacing of the surface elements. Furthermore, the most appropriate distance of upwind fetch to use in calculating roughness values is somewhat debatable, particularly for city centres which typically display greater spatial variability in surface character. For operational use, it is necessary to consider additional wind directions other than the prevailing. This is potentially computationally intensive and hence the recommended approach would be to use the technique to assimilate a real-time lookup table of Z0eff values for various directions of upwind fetch, with the appropriate roughness values selected based on the forecast wind direction.

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