7. Model Parameters¶

Land surface models use parameters to describe the surface. For example to model the latent heat flux using the Penman Monteith equation the following parameters are needed.

7.1. Albedo¶

From the short-wave radiation (K), within the Eq.3.1 Radiation balance the albedo (\(\alpha\)) is calculated:

(7.1)¶\[\alpha= K_{\uparrow} / K_\downarrow\]

using the incoming (\(\downarrow\)) and outgoing (\(\uparrow\)) shortwave radiation (K) fluxes.

7.1.1. Typical Values¶

Note

The table below is based crowd-sourced dataset at Albedo Collection. Please report issues there if any found.

Table 7.1 Calculated values of albedo at selected AMF sites¶
site	location	land cover type	day of year	time of day	value	reference	remarks
US-SRG	Santa Rita Grassland	Grassland	27	12:00	0.24	Moore (1976)	summer value of grassland
US-VAr	Vaira Ranch-Iona	grasslands	10	12:00	0.45	Ryu et al. (2008)
US-MMS	Morgan Monroe State Forest	Deciduous Broadleaf Forest			0.13	Liu (2017)	value has seasonal variability-approximated from summer values
Crop field	UK	Cropland	25	13:00	0.2	Page (2012)	a short growing crop
CA-Qsu	Quebec-Eastern Boreal	Black Spruce / Jack Pine Cutover	15th December	12:00	0.907	Betts and Ball (1997)	winter time
CA-Qfo	Quebec	Eastern Boreal - Mature Black Spruce	196	12:00	0.081	Betts and Ball (1997)	none
40-50N	40-50N	Deciduous Broadleaf Forest	74	12:00	0.142	Gao et al. (2005)
Saskatchewan	Western Boreal	Mature Black Spruce	annual mean	daily mean	0.145	Rosbjerg (1997)
US-MOz	Missouri USA	Deciduous Broadleaf Forest		Midday	0.15+/-0.02	Moore et al. (1996)	Valid for summer days (a case study of a Deciduous forest)
US-Oho	Oak Openings USA	deciduous broadleaf forest	July		0.159	Strugnell et al. (2001)
CA-Obs	Saskatchewan	ENF			0.260	Bright et al. (2014)	January average

7.2. Roughness length (\(z_0\)) and displacement height (\(d\))¶

If the displacement height is known, or is negligible, the logarithmic law equation can be rearranged with observed \(z_0\) and mean wind speed to allow \(z_0\) to be determined. As this may vary we normally take median of a minimum of 20 results for a wind direction sector. If you have a period with a lot of neutral conditions you may be able to get a lot of samples rapidly.

\[𝑧_0 = (𝑧−𝑑) exp ⁡[−(𝑈_𝑧 𝜅)/𝑢_∗ ]\]

Table 7.2 Literature values of roughness parameters collected by students of BLM class¶
group	land cover	z0	zd	ra	reference
1-1
1-2
2-1
2-2
3-1	Grasslands		0.25m	10-20	de Miguel and Bilbao (1999)
3-2	Suburban Neighbourhood Park	0.03	0.2		Kent et al. (2017)
4-1
4-2	Boreal, Mature Black Spruce	0.22	9.66	50	Kettridge et al. (2013)
5-1
5-2	Broadleaf Deciduous Forest	2.9	20.1		Maurer et al. (2015)
6-1
6-2	Cropland	0.062		77.0	Liu et al. (2007)
7-1
7-2
8-1
8-2	Grasslands	0.026	0.1	40	Dunin et al. (1978)
9-1
9-2
10-1
10-2

Table 7.3 Calculated values of roughness parameters at selected AMF sites¶
site	z0	zd	ra	site description
CA-Obs
US-Blk
US-MMS
US-MOz	1.48	15.40	9.02	Deciduous Broadleaf Forest
US-Dia	0.04	0.65	19.1	Grassland
US-KUT	0.03	0.049	159.6	Temperature grassland
CA-Qcu	0.24	8.4	27.7	Boreal Black Spruce/Jack Pine Cutover
CA-Qfo	1.86	9.66	8.55	Boreal Mature Black Spruce
US-Slt
US-UMB	2.32	15.4	3.4	Deciduous Broadlead Forest
US-Br3
US-Bo1	0.04	1.37	50.1	Croplands
US-NC1	0.38	3.5	23.5	Young pine forest
US-Whs
US-SRG
US-Var	0.09	0.03499	58.0899	Grasslands
US-Bo2
US-Br1
CA-TPD
US-Oho	2.66	1.75	5.63	Deciduous broadleaf forest

7.2.1. How does it vary with wind direction?¶

A rule of thumb for calculating d is to assume it is ~0.7 \(h\) where \(h\) is the height of the canopy. As the heights may vary with direction you can determine how much this may vary. What are expected to be consistent sectors?

The wind profile can also be used to determine \(z_0\) and \(d\) if there are more than 2 levels in the profile. This requires fitting a straight line (linear regression) through the data to determine the intercept, which provides the \(z_0+d\) value. See equations 1-2 in [9].

For References see list