CASANZ2015 Conference, Melbourne, 20-23 September 2015 1

TECHNICAL CONSIDERATIONS OF ADOPTING AERMOD INTO AUSTRALIA AND NEW ZEALAND

Tiffany Gardner, Brian Holland, Weiping Dai (PhD, PE, CM), Qiguo Jing (PhD)

Trinity Consultants, Inc.

Dallas, Texas, 75251 USA

Abstract

The AERMOD model has been the preferred near-field dispersion model by the United States Environmental Protection Agency (US EPA) for air quality impact assessment since 2006. US EPA also continues to update and improve the model. The latest update to AERMOD was released in 2014, with another update expected mid-2015. AERMOD is a steady-state Gaussian dispersion model that represents the current state-of-science, including advanced planetary boundary layer (PBL) parameterizations. Due to this advanced science, good match between modelled and observed results, and reasonable computational demands, more and more regulatory agencies across the globe have started promulgating AERMOD for these assessments including EPA Victoria (EPA Vic). EPA Vic has adopted AERMOD in place of AUSPLUME as of January 2014. AUSPLUME is also a Gaussian model, but is limited by the inability to model complex terrain and the use of older PBL parameterizations (model last updated in 2004) than AERMOD. To ease the adoption of AERMOD into Australia and New Zealand, several technical aspects will be discussed in this paper that are important to the use of the model. These technical aspects will include mixing height calculation techniques, land use input sensitivities, urban option applicability, and terrain data selection. By discussing these technical aspects of AERMOD, including how they are handled in the model and the sensitivity of results to changes in the parameters, existing and future AERMOD users in Australia and New Zealand will be provided with information and tips that they may employ moving forward when using the AERMOD model for their own environmental impact assessments. Keywords: AERMOD; AUSPLUME; Victoria; AERMET

1. Introduction

The AERMOD model has been the preferred near-field dispersion model by the United States Environmental Protection Agency (US EPA) for air quality impact assessment since 2006 (US EPA 2005). US EPA also continues to update and improve the model. The latest update to AERMOD, executable 15181, was released in mid-2015. AERMOD is a steady-state Gaussian dispersion model that represents the current state-of-science, including advanced planetary boundary layer (PBL) parameterizations. Due to this advanced science, good match between modelled and observed results, and reasonable computational requirements, more and more regulatory agencies across the globe have started promulgating AERMOD for these assessments including Victoria EPA (EPA Vic). EPA Vic has adopted AERMOD in place of AUSPLUME as of January 2014 (EPA Victoria 2013). AUSPLUME is also a Gaussian model, but is limited by the inability to model complex terrain and the use of older PBL

parameterizations (updated in 2004) than AERMOD. To ease the adoption of AERMOD into Australia and New Zealand, several technical aspects will be discussed in this paper that are important to the use of the model. These technical aspects include mixing height calculation techniques, land use input sensitivities, and several other aspects that AERMOD users should be familiar with.

First, when using AERMOD, hourly convective mixing heights, which are derived in part from upper air observational data taken at or near sunrise, are required by the model. Depending upon location, however, this meteorological parameter can be difficult to obtain. Some areas do not have nearby upper air data available. Even areas with available data can run into issues with AERMOD due to the timing of the upper air observations. Typically, observations are taken from radiosondes (weather balloons) launched at 0000 and 1200 UTC. In Western Australia, the time zone (UTC+8) puts the 0000 upper air sounding close enough to local

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sunrise to generally be usable. For Eastern Australia though, some of the upper air soundings are launched a couple hours after local sunrise at 2300 UTC while others are launched a few hours before local sunrise around 1700 UTC. While it may be possible to use these upper air data in Eastern Australia as they are launched a few hours before or after local sunrise, modellers run the risk of not being conservative enough in doing so because these data could feed the “sunrise time” mixing height information into the model when in reality the data are coming from a time significantly before or after sunrise. As a result, in Eastern Australia and other locations, such as New Zealand and the United Kingdom where the radiosonde launch times are not close to the sunrise time as required by AERMOD, various alternative techniques can be used to best estimate the mixing heights for use in AERMOD. These techniques are discussed and evaluated.

Second, when using AERMET to process meteorological data for input into AERMOD, three land use parameters must be identified: surface roughness, albedo and Bowen ratio. To define these three micrometeorological parameters in the area surrounding a facility, a detailed land use analysis is required. While guidance is provided by regulatory agencies, such as the US EPA and EPA Vic, for determining these land use values, caution must be exercised when doing so as variations can lead to significant changes in AERMOD results. To better understand the sensitivity of AERMOD results to changes in these three land use inputs, a comparison of AERMOD modelling results using different land use settings was performed and is presented in this paper.

In addition to these considerations, the applicability of AERMOD’s urban option and issues related to terrain data selection will be discussed. By discussing these technical aspects of AERMOD, including how they are handled in the model and the sensitivity of results to changes in the parameters, existing and future AERMOD users in Australia and New Zealand will be provided with information and tips that they may employ moving forward when using the AERMOD model for their own environmental impact assessments.

2. Mixing Height Techniques

2.1. Background

When processing meteorological data into an AERMOD-ready format, both surface and upper air data are required. While surface data is obtained through weather stations on the ground, most upper air observations are obtained when a radiosonde (an instrument package suspended below a weather balloon) is launched. These launches occur daily in

about 800 locations worldwide around 0000 and 1200 UTC, 365 days a year. As the weather balloon ascends through the atmosphere, sensors on the radiosonde measure profiles of pressure, temperature, and relative humidity, and the wind speed and direction are also recorded by tracking the position of the radiosonde. These parameters are used in AERMET, the meteorological pre-processor to AERMOD, to determine atmospheric turbulence and mixing height, which in turn affects the computed pollutant concentrations in AERMOD.

In AERMOD, the preferred upper air sounding used is one just before or at sunrise. For locations in North America, this generally means the 1200 UTC sounding (~0500 to 0800 local time). In other parts of the world, this means the 0000 UTC sounding. When AERMOD is used for a location in parts of the world where 0000 and 1200 UTC are not near sunrise, like New Zealand, and the United Kingdom, or in locations like Eastern Australia where using the upper air data may not be the most conservative modelling approach, the question of how to accurately and appropriately determine for the local mixing height arises. There is currently no regulatory standard method used to address this issue, but various techniques have been developed and are in widespread use.

One such method, based in part on the work of Holtslag and Van Ulden (1983) is described below. This technique, which utilizes the fact that hourly mixing height data can be used by AERMET in place of upper air data, has been utilized for regulatory modelling applications in countries around the world for more than fifteen years, with broad acceptance. This technique can be used if upper air data are unavailable, or when local times that correspond to radiosonde ascents do not occur near sunrise. This technique relies on calculation of mixing heights using semi-empirical models to estimate the surface similarity parameters of friction velocity, sensible heat flux, temperature scale, and Monin-Obukhov length via the routinely collected surface meteorological variables of cloud cover, ceiling height, wind speed, and temperature, as well as estimates of surface roughness.

2.2. Technique to Estimate Mixing Depths from Surface Observations

2.2.1. Daytime Mixing Depth Estimate

Daytime refers to the period from one hour after sunrise to one hour before sunset. The daytime mixing depth is estimated using sensible heat flux, friction velocity, and Monin-Obukhov length. The Monin-Obukhov length is used to determine whether daytime mixing depth estimates will be calculated using a neutral or unstable mixing depth equation. If the absolute value of the Monin-Obukhov length is greater than 100 metres, the

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neutral mixing depth equation is used; otherwise, the unstable mixing depth equation is used. To determine the Monin-Obukhov length and then estimate the daytime mixing depth, the sensible heat flux and friction velocity will need to be estimated.

The sensible heat flux, QH, is a critical parameter required to estimate the buoyant production of turbulent energy and resulting daytime mixing depth. The convergence or divergence of sensible heat flux produces warming or cooling of the air in the boundary layer. The vertical exchange of heat occurs primarily through turbulent motions or mixing in the boundary layer. This process influences the vertical profile of air temperature and resulting atmospheric stability. Since no method exists for directly measuring the sensible heat flux, it is determined from the surface energy balance expression that may be found in Appendix A. The equation is solved using cloud cover data and temperature values to parameterize Q* and solve for QH, as proposed by Holtslag and Van Ulden (1983). The latent heat flux and soil heat flux are parameterized using the soil moisture availability parameter and techniques proposed by Holtslag and Van Ulden (1983). The soil moisture availability parameter is assumed to be 0.5, which is the midpoint in the range between saturated (1) and arid (0). The anthropogenic heat flux is not accounted for.

There are two additional methods to solve the surface energy balance equation for QH using Q*: (1) using a net radiometer to collect Q* measurements, or (2) using a pyranometer to collect incoming solar radiation measurements and parameterize Q*.

After the sensible heat flux has been estimated, the friction velocity needs to be estimated. There are two separate equations used to estimate friction velocity in neutral versus unstable conditions, which may be found in Appendix A.

Once the sensible heat flux and friction velocity are estimated, the Monin-Obukhov length can be determined using the equation below:

𝐿 =−𝑢∗

3𝑇𝜌𝐶𝑝

𝑘𝑔𝑄𝐻

Using the Monin-Obukhov length, the estimation of the daytime mixing depth is possible. For unstable conditions (when |L| < 100), the daytime mixing depth (Zi) is calculated using the sensible heat flux and friction velocity as proposed by Farmer (1991). The integrated sensible heat flux is calculated by summing the values for each hour (h) after sunrise:

𝑍𝑖 = √𝑍𝑛2 + 1400 ∑ 𝑄𝐻

ℎ

0

Where: Zn = 𝑢∗𝑛

4𝑓

f = Coriolis Parameter

If the absolute value of the calculated Monin-Obukhov length is greater than 100 metres, the following expression is used to determine the neutral mixing depth:

𝑍𝑛 =𝑢∗𝑛

4𝑓

2.2.2. Night time Mixing Depth Estimate

Night time refers to the period from one hour before sunset to one hour after sunrise. Night time mixing depths are estimated using friction velocity, sensible heat flux, and Monin-Obukhov length. During stable conditions, the temperature scale 𝜃∗ is used to calculate the stable friction velocity, sensible heat flux, and Monin-Obukhov length, which are subsequently used to determine night time mixing depth. If the absolute value of the Monin-Obukhov length is greater than 100 metres, the neutral mixing depth equation is used.

First, two estimations are made for the temperature scale. The first estimate is based upon the method proposed by Holtslag and Van Ulden (1983) and the second is based upon the temperature profile equation. These equations may be found in Appendix B. The smaller of the two temperature profile estimates is used for subsequent calculations.

After the temperature scale estimates are made, the friction velocity is calculated which is then used to estimate the sensible heat flux (see Appendix B).

The Monin-Obukhov length is then determined using:

𝐿 =𝑇𝑢∗

2

𝑘𝑔𝜃

The night time mixing depth is estimated using the sensible heat flux and friction velocity during stable conditions (|L| < 100) as proposed by Farmer (1991). The depth of the turbulent layer (ZS) is defined as:

𝑍𝑆 =21500𝑢∗

2

√|𝑄𝐻|

Where: 𝑍𝑛 =𝑢∗

4𝑓

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If the absolute value of the calculated Monin-Obukhov length is greater than 100 metres, then the following expression defines the neutral mixing depth:

𝑍𝑛 =𝑢∗

4𝑓

After the daytime and night time estimations for all parameters above are made, a file should be generated using the data as required by our proprietary mixing height tool (a CD-144 file) and then a computer utility called ADMS is run to generate an .ADM file from the data. The .ADM file is then input into AERMET to run the ADMS job type and upon completion, the .SFC (surface) and .PFL (upper air) files will be created that may be used in AERMOD.

Using this method, locations where the 0000 and 1200 UTC soundings do not align with sunrise, such as New Zealand, or where using the existing upper air data may not be the most conservative approach as is the case in Eastern Australia, will be able to generate and use mixing heights and atmospheric turbulence parameters in AERMOD that are representative of the site location. As was mentioned above, it should be noted that for Western Australia, the time zone (UTC+8) puts the 0000 UTC upper air sounding close enough to local sunrise to generally be usable instead of this method.

3. Surface Parameter Considerations

To define turbulence in AERMOD, especially in the absence of direct on-site measurements, the surface roughness, Bowen ratio, albedo, wind speed and direction, and temperature are used in AERMET. Unlike wind speed, wind direction, and temperature, the other three surface micrometeorological parameters can be difficult to quantify. Guidance is provided by regulatory agencies, such as the US EPA and Victoria EPA, for determining these land use values. However, caution must be exercised when doing so as variations of these values in AERMET can lead to significant changes in AERMOD results.

3.1. Surface Roughness

The surface roughness length is a measure of how smooth or rough a surface is, with lower values corresponding to smoother surfaces (e.g., open water) and higher values corresponding to rougher surfaces (e.g., high intensity residential areas). When determining the surface roughness around the meteorological surface station being used in AERMOD, the US EPA (US EPA 2008) and Victoria EPA (EPA Victoria 2013) requires that modelers consider land-use types within a 1 km radius. To ease the process of determining surface roughness, a surface roughness length table (see Appendix C

for an example) may be used, which contains predetermined values for land use types. However, in order to accurately estimate the surface roughness, the circular area centered on the site location should be broken down into up to 12 sectors (30° each) and an inverse-distance weighted average should be used when multiple land use types are present within that 1 km radius. In addition to varying by direction, the surface roughness can vary seasonally, so it is important exercise caution when determining these values, taking into account the time of year and land use. AERMET allows for seasonal or even monthly variation in land use parameters to account for this.

3.2. Albedo

The albedo is the measure of a surface’s ability to reflect incoming solar radiation with values ranging from 0 to 1, where light-colored and reflective surfaces (e.g., snow) will have higher albedo values because more light is reflected and dark surfaces (e.g., forest) will have lower albedo values. To accurately account for albedo in AERMOD, the US EPA (US EPA 2008) and Victoria EPA (EPA Victoria 2013) require modelers to consider land-use types within a 10km by 10km area around the meteorological station site. A simple average of all land use types within the area may be used instead of determining a value per sector, and the values for albedo may be found in the seasonal and land use variability tables available from US EPA and other sources (similar to the Surface Roughness table in Appendix C).

3.3. Bowen Ratio

The Bowen ratio, which ranges from 0.1 to 10, represents the ratio of sensible heating (in which solar radiation increases temperature) to latent heating (in which solar energy is used in evaporating water). Higher Bowen ratios represent arid regions whereas low Bowen ratios represent moist regions. Like the albedo, land use types within a 10km by 10km area around the meteorological station site should be considered (EPA Victoria 2013; US EPA 2008), as should variations by season, and a simple average of all land use types within the area may be used.

3.4. Considerations

In order to provide appropriate surface roughness, albedo, and Bowen ratio values for the surrounding area to AERMET, a detailed land use analysis is required. It is important to point out that according to the guidance of US EPA, the area over which these values are obtained and averaged should be centered upon the meteorological station site, so it is important to make sure the land use coverage is similar to that around the actual site being modelled.

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AERMET and AERMOD do not currently offer the ability to adjust meteorological data to account for land use differences between a meteorological station and source location.

Land use maps and aerial photographs are essential resources to determine the types, amounts, and relative locations of vegetation, urban, and other land uses and covers. Additionally, the US EPA AERSURFACE utility may be used as an aid in determining realistic and reproducible surface characteristic values for input to AERMET. AERSURFACE requires a land use dataset based on the format of the US 1992 National Land Cover Database.

3.5. Sensitivity Analysis in AERMOD

A simple comparison of AERMOD results with varying land use inputs was performed to illustrate the effects of land use on the model. Four uniform land uses were considered: grassland, desert shrubland, open water, and urban. A one-year model run was conducted using two sources: a 25 m stack and a ground-level area source. Maximum ground-level concentrations from 1-hour and 24-hour averaging periods were examined. The results are shown in Figure 1, with concentrations normalized based on the grassland case results to allow easier comparison of the variations between land use types.

1-Hour Averaging Period

Land Use Type

Normalized Concentration

25m Stack Ground-level

Grassland 1.00 1.00

Desert 1.08 1.06

Water 1.32 1.19

Urban 1.32 0.99

24-Hour Averaging Period

Land Use Type

Normalized Concentration

25m Stack Ground-level

Grassland 1.00 1.00

Desert 1.56 1.14

Water 0.51 0.79

Urban 2.17 1.23

Figure 1. Maximum ground-level concentrations from 1-hour and 24-hour averaging periods normalized based on the grassland case results.

As is shown in the results in Figure 1, varying the land use inputs can have an impact on AERMOD results. While the impacts of varying land use inputs

on the 1-hour averaging period concentrations in this analysis are visible, the impacts on the 24-hour averaging period results are much more significant.

In the 24-hour averaging period results, the land use effect has more impact on the stack than it does on the ground-level source. This is likely due to the fact that higher Bowen ratio in the desert and urban cases, and a higher surface roughness in the urban case, help to mix the plume down to the surface sooner, whereas the low surface roughness and low Bowen ratio in the water case means that the plume does not get mixed down quickly. Even for the ground-level source though, the 24-hour averaging period normalized concentrations show significant impacts due to varying the land use parameters. For example, the concentration for the urban land use case is about 56% higher than the water concentration for the ground-level source.

All in all, this analysis shows the impacts that varying land use inputs can have on AERMOD results. As such, it is important to ensure the most representative land use inputs are used when performing a land use analysis.

4. Urban Option Applicability and Considerations

When processing meteorological data in AERMET and using the surface roughness, Bowen ratio, and albedo, the surrounding land use types are taken into account as described above. However, if a facility is located within the influence of a large city, an additional portion of the AERMOD model algorithm may be needed to account for the urban heat island effect.

In cities, surfaces such as concrete and asphalt absorb and store radiation to a greater degree than typical rural surfaces. This effect, combined with anthropogenic waste heat and reduced wind speeds due to large buildings, can cause an increase in surface temperature in urban areas relative to rural areas, particularly at night. The warm night time temperatures within the city create enhanced turbulence relative to that which is expected in an adjacent rural, stable boundary layer. The result is an urban heat island; a city or metropolitan area that is significantly warmer than its surrounding rural areas. This effect extends beyond what is captured by the surface roughness, Bowen ratio, and albedo parameters, and thus must be accounted for separately by a model.

In AERMOD, users may turn on the Urban Option (URBANOPT) to account for the urban heat island effect (US EPA 2004). By doing this, AERMOD assumes higher surface temperatures in urban areas compared to rural night time conditions, and will make adjustments to the convective velocity scale, heat flux, and temperature gradient to

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compute an adjusted urban mixing height. The magnitude of the urban heat island effect in AERMOD is driven by the urban-rural temperature difference that develops at night, so this adjustment of the mixing height will be based on temperature difference, roughness, and population.

By default, the Urban Option is turned off in AERMOD because it is only applicable for use in large cities. Because many smaller cities do not experience this urban heat island effect, before turning it on in AERMOD, a local regulatory agency should be consulted. If permission is granted by the regulatory agency to use this option, US EPA guidance is available to help determine which sources should be modelled as urban and which should be modelled as rural (US EPA 2009). This approach is consistent with the fact that the urban heat island is not a localized effect, but more regional.

5. Terrain Selection

5.1. How Terrain is Handled in AERMOD

In many older Gaussian models, such as the ISTSC3 model and AUSPLUME, a pollutant plume can either rise above a terrain feature or travel around the terrain feature; not both (Ministry for the Environment 2004). This results in a sharp discontinuity in behaviour – a miniscule increase in stack height could completely change the terrain response of the plume. AERMOD, however, utilizes a terrain algorithm that enables a portion of the plume to travel over the terrain while the remainder travels around the terrain, eliminating the discontinuity. Using a dividing streamline height, which is calculated based on stability, wind speed, and plume height, AERMOD is able to account for this not-purely-Gaussian behaviour of a plume (see Figure 2).

Figure 2. To determine the flow of the plume when terrain is present, AERMOD uses the dividing streamline height to calculate the weighted sum of the horizontal plume state (e.g., portion that wraps around the terrain) and the terrain

responding plume state (e.g., portion that rises above the terrain). (US EPA 2004)

As is illustrated in Figure 2, the portion of the plume that is below the dividing streamline height wraps around the terrain feature, while the portion of the plume that is above the dividing streamline height rises up and over the terrain feature.

5.2. Terrain Data Selection

The terrain files accepted by AERMAP, the terrain pre-processor of AERMOD, are Digital Elevation Model (.DEM) data and National Elevation Dataset (NED) GeoTIFF files. AERMAP tends to be “US-specific” in terms of the terrain data formats it processes, so CISRO and the Australian Government Bureau of Meteorology (BoM) are currently undertaking the One-second DEM Project, during which they will be developing one-second (30 metre resolution) DEM for Australia based on SRTM data (EPA Vic 2013a). SRTM data include the heights of obstacles (e.g., buildings; trees), however, because SRTM data is based on reflective surfaces, there are gaps in the data. EPA Vic states though that gap filled and filtered topography data with vegetation and obstacles removed is available from Geo Science in Australia in high resolution (EPA Vic 2013a).

Using the terrain data files, AERMAP imports model object elevations into AERMOD using the UTM coordinate system. It is important to note that if a new model object is added after AERMAP has already been run, it is necessary to rerun AERMAP so the elevation for the new model object is also imported.

5.3. 10% Slope Rule

AERMOD requires that the DEM or NED data files that are imported into the model encompass every model object and also satisfy the 10% slope rule. In other words, if a 10% slope is drawn from the most distant receptors, then the DEM or NED terrain data files should include every terrain feature that rises above this slope.

Estimating the number of DEM or NED files that are necessary to include in the terrain analysis performed by AERMAP is not straight forward because there is no standard distance for which terrain data should be provided; it varies case by case. Because of this, many modellers simply obtain terrain data that surrounds the extents of their receptors. In areas with significant topography, this will not be enough to compute the correct critical scale height required by AERMOD though, which is used to calculate the critical dividing streamline height. As a conservative estimate, it is good practice to estimate on the higher end to ensure the correct number are included instead of

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underestimating the number of DEM or NED data files required.

6. Conclusion

With the recent promulgation of AERMOD in Victoria and the potential future promulgation of the model in other Australian states and New Zealand, certain aspects of AERMOD should be considered as they differ from the previously promulgated model, AUSPLUME. The topics covered in this paper bring light to and discuss a few of those aspects and provide suggestions and considerations on how to handle them when setting up a model run in AERMOD.

References

Environmental Protection Authority Victoria, 2013a, ‘Construction of Input Meteorological Data Files for EPA Victoria’s Regulatory Air Pollution Model (AERMOD)’, 1550.

Environmental Protection Authority Victoria, 2013b, ‘Guidance Notes for Using the Regulatory Air Pollution Model AERMOD in Victoria’, 1551.

Farmer, S.P.G 1991, ‘Outline of Smith and Blackall’s (1979) methods of estimating boundary layer depth,’ Private communication to M.D. Miller.

Holtslag, A. A. M. and Van Ulden, A. P. 1983, ‘A simple scheme for daytime estimates of the surface fluxes from routine weather data’, J. Climate Appli. Meteorol., 22: 517-529.

Ministry for the Environment, 2004, Manatu Mo Te Taiao, New Zealand, 2004, Good Practice for Atmospheric Dispersion Modeling.

US Environmental Protection Agency, 2008, ‘AERSURFACE User’s Guide’.

US Environmental Protection Agency, 2004, ‘AERMOD: Description of Model Formulation’.

US Environmental Protection Agency, 2005, ‘Revision to the Guideline on Air Quality Models: Adoption of a Preferred General Purpose (Flat and Complex Terrain) Dispersion Model and Other Revisions; Final Rule’ 40 CFR Part 51.

US Environmental Protection Agency, 2009, ‘AERMOD Implementation Guide’.

Wang, I.T. and Chen, P.C. 1980, ‘Estimation of heat and momentum fluxes near the ground’, Proc. 2nd Joint Conf. on Applications on Air Pollution Meteorology, AMS, 764-769.

Appendix A

The following equations are used in Section 2.2.1 to estimate the sensible heat flux and friction velocity, which are in turn used to estimate the Monin-Obukhov length and mixing depth.

The sensible heat flux is determined from the following surface energy balance expression:

Q* = QH + QE + QG - QA

Where: Q* = Net Radiation

QH = Sensible Heat Flux

QE = Latent Heat Flux

QG = Soil Heat Flux

QA = Anthropogenic Heat Flux

For friction velocity, the following equations are used in neutral and unstable conditions, respectively:

Neutral Conditions: 𝑢*n =𝑘𝑢

ln (𝑧

𝑧𝑜)

Where: u*n = Neutral friction velocity (m/s)

k = von Karman’s constant (0.4)

u = wind speed (m/s)

z = wind measurement height (m)

zo = surface roughness length (m)

Unstable Conditions (Wang and Chen 1980):

u* = 𝑘𝑢

ln(𝑧

𝑧𝑜)

[1 + 𝑑1 ln(1 + 𝑑2𝑑3)]

Where: u* = Friction Velocity (m/s)

d1 = 0.128 + 0005 ln (z/zo) if (z/zo) <= 0.01

= 0.107 if (z/zo) > 0.01

d2 = 1.95 + 32.6 (z/zo)0.45

d3 = (𝑄𝐻

𝜌𝐶𝑝) (

𝑘𝑔𝑧

𝑇𝑢∗𝑛3)

Where: QH = Sensible Heat Flux (W/m2)

𝜌 = Atmospheric Density (kg/m3)

Cp = Specific Heat at Constant Pressure

(J/K kg)

g = Acceleration due to Gravity (9.8m/s2)

T = Ambient Air Temperature (K)

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Appendix B

The following equations are used in Section 2.2.2 to estimate temperature scale and friction velocity.

The first estimate of temperature scale is based on the method proposed by Holtslag and Van Ulden (1983):

𝜃∗ = 0.09[1 − 0.5(𝑇𝑂

10)2]

Where: TO = Total Opaque or Total Sky Cover in tenths

The second estimate is based upon the temperature profile equation:

𝜃∗ =𝑇𝐶𝑑𝑛𝑢2

18.8𝑧𝑔

Where: 𝐶𝑑𝑛 = 𝑘/ln (𝑧

𝑧𝑂) (Neutral Drag Coefficient)

For the night time friction velocity, the following calculation is used:

𝑢∗ = (𝐶𝑑𝑛𝑢

2) [ 1 + √1 − (

2𝑢0

√𝐶𝑑𝑛𝑢)2 )

Where: uo = √4.7𝑔𝑧𝜃∗

𝑇

The sensible heat flux is estimate using the friction velocity and temperature scale for the turbulent heat transfer using the following formula:

𝑄𝐻 = −𝜌𝐶𝑝𝑢∗𝜃∗

Appendix C

The following chart shows an example of the Surface Roughness Length chart that may be utilized when defining the surface roughness for an area:

Table 1. Surface roughness length, in metres, by land-use and season