The earlier presented surface albedo parameterization is simplified by assuming that the reflectance of direct solar radiation is a simple function of solar zenith angle. The function chosen contains three parameters that vary with vegetation type, greenness, and leaf area index. Tables of parameter values are presented. Using these tables, SiB's (Simple Biosphere model) absorbances of direct solar radiation can be reproduced with an average relative error of less than 0.5 percent. Finally, the direct reflectance function is integrated over zenith angle to produce an equation for the surface reflectance of diffuse radiation

Koster, Randal D.

Suarez, Max J.

English

NASA Technical Reports Server

NASA Technical Memorandum 104538
A Simplified Treatment of
SiB's Land Surface Albedo
Parameterization
Randal D. Koster and Max J. Suarez
April 1991
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NASA Technical Memorandum 104538
A Simplified Treatment of
SiB's Land Surface Albedo
Parameterization
Randal D. Koster and Max J. Suarez
NASA-Goddard Space Flight Center
Greenbelt, Maryland
National Aeronautics and
Space Administration
Goddard Space Flight Center
Greenbelt, MD
1991

A Simplified Treatment of SiB's Land
Albedo Parameterization
Surface
Randal D. Koster and Max J. Suarez
Goddard Space Flight Center
Greenbelt, Maryland 20771
Abstract
The surface aJbedo parameterization presented by Sellers [1985] and Sell-
ers et al. [1986] is simplified by assuming that the reflectance of direct solar
radiation is a simple function of solar zenith angle. The function chosen
contains three parameters that vary with vegetation type, greenness, and
leaf area index. Tables of parameter values are presented. Using these ta-
bles, SiB's absorbances of direct solar radiation can be reproduced with an
average relative error of less than 0.5%. Finally, the direct reflectance func-
tion is integrated over zenith angle to produce an equation for the surface
reflectance of diffuse radiation.
1 Introduction
Koster and Suarez [1991] present a strategy for modeling land surface pro-
cesses in general circulation models (GCMs) in which the surface of each
grid box is assumed to consist of a "mosaic" of independent, homogeneous
vegetation "tiles." Each tile within a grid box is covered by a specified type,
amount, and state of vegetation (or by bare soil, permanent ice, or open
water), and each tile maintains its own state variables and budgets of heat
and moisture. The effects of vegetation within each tile are modeled using
a simplified version of SiB, the parameterization proposed by Sellers et al.
[1986].
The purpose of this report is to present the simplified version of SiB's
albedo formulation used by Koster and Suarez [1991] in the "mosaic" model.
In SiB, each GCM grid box is assumed to be covered uniformly by a
single biome consisting of a mixture of trees, ground cover, and bare soil.
For each biome, one may specify the fraction of one "type" of tree (say,
broadleaf deciduous, needleleaf, or some idealized mixed type), one "type"
of ground cover (such as grass), and of course, the fraction of bare soil. The
reflectance of the tree canopy is combined with that of the ground cover and
soil (through areal-weighted averaging) to produce a net reflectance for the
grid square.
In the "mosaic" model of Koster and Suarez [1991], each (non-ocean,
non-ice) tile consists of a single vegetation cover or bare soil. The current
version of the model selects the tile vegetation or soil type from the different
tree, ground cover, and soil types used to build the SiB biomes. The present
report concentrates on reproducing SiB's reflectance calculations for these
constituent types. By reproducing the constituent reflectances, the net grid
square reflectances calculated with either SiB or the mosaic strategy for a
given vegetation mixture will be the same. (Small differences will occur for
tree canopy and ground cover mixtures, because SiB allows the ground cover
to lie below the canopy and thereby affect the canopy reflectance.)
We used SiB's algorithm to compute the reflectances of direct radiation
for surfaces covered completely by each of six constituent vegetation types
employed by SiB. We then used these calculations to parameterize the re-
ftectances, as described in the next section. Tables of the relevant parameters
are presented below.
2 Calculation of Surface Reflectances
The calculation of the net incoming solar radiation requires reflectance values
for both the direct and diffuse components of both visible and near-infrared
solar radiation. In SiB, these reflectances depend only on vegetation type,
solar zenith angle, leaf area index (LAI), and the fraction g of leaves that
are alive (the greenness). The mosaic model reproduces SiB's reflectances
using the following parameterization of SiB's "two-stream approximation"
reflectance calculation [Sellers, 1985].
We found that for a given vegetation type and over reasonable ranges of
LAI and g, SiB's reflectances for the direct components of solar radiation
can be approximated very closely by
Tt(#) = a( LAI, g) -
/3(LAI, g)p
7(LAI, g)+p' (1)
where 7_(#) is the reflectance of the direct beam,/z is the cosine of the solar
zenith angle, and _, 8, and 7 are fitted parameters. (The visible and near-
infrared components of direct radiation require different sets of parameter
valuesfor (I).)
Reflectances7_forthe diffusecomponents oftheincidentradiation,which
are assumed in SiB to be independent ofp, may be obtained by integrating
(I) overthe hemisphere:
= 2 } cosO
Using (1), this gives
sinOdO. (2)
= a -/_ + 2/_ 7 (1 - 71n 1 +______7).
7
(3)
The parameters a,/_, and 7 for a vegetation type with given LAI and
g can be obtained through linear interpolation on the values provided in
Tables 1 through 6. Values are presented for six vegetation types: broadleaf
evergreen trees, broadleaf deciduous trees, needleleaf trees, ground cover,
broadleaf shrubs, and dwarf trees. The listed LAI values assume complete
(100%) coverage of the surface by the vegetation. Values used for the re-
flectance of the ground beneath the canopy are listed in Table 7.
When tested over realistic ranges of LAI and g, (1) used in conjunction
with Tables 1 through 6 reproduced SiB's direct radiation absorbances with
an average relative error of less than 0.3% and never with an error higher
than 10% for ground cover and 2% for the other vegetation types.
The diffuse refiectances computed with (3), however, do not match those
of SiB. Although the hemispherical integration (2) is consistent with SiB's
4
assumptionof isotropic incident diffuse radiation, the diffuse reflectances
produced with the two-stream calculation are somewhat higher than those
produced with (3). This does not result from inaccuracy in (1); careful
numerical integration of the two-stream direct reflectances from SiB repro-
duces the results of (3). We will use (3) in future GCM simulations and
recommend that it be substituted for SiB's diffuse results.
References
Koster, R. and M. Suarez, 1991: Modeling the land surface boundary in
climate models as a composite of independent vegetation stands, J. Geophys.
Res., in press.
Sellers, P. J., 1985: Canopy reflectance, photosynthesis and transpiration,
Int. J. Rein. Sens., 6, 1335-1372.
Sellers, P. J., Y. Mintz, Y. C. Sud, and A. Dalcher, 1986: A simple biosphere
model (SiB) for use within general circulation models, J. Atmos. Sci., 43,
505-531.
Table 1: Reflectanceparametersappearingin (1) and (3), for broadleaftrees. The
three numbersin eachbox are a, fl, and 7, in that order.
Broadleaf
Evergreen
Visible NIR
LAI
.5
1.0
1.5
2.0
2.5
3.0
3.5
g=.33 g=.67
0.0808 0.0788
0.0153 0.0135
0.0814 0.0760
0.0796 0.0775
0.0372 0.0354
0.1361 0.1336
0.0792 0.0771
0.0506 0.0487
0.2078 0.2034
0.0790 0.0769
0.0587 0.0568
0.2650 0.2622
0.0789 0.0768
0.0630 0.0611
0.2986 0.2969
0.0789 0.0768
0.0652 0.0633
0.3169 0.3159
0.0789 0.0768
0.0663 0.0644
0.3265 0.3259
.33
0.2867
0.1291
0.1582
0.2840
0.1707
0.2581
0.2828
0.1969
0.3227
0.2822
0.2125
0.3635
0.2819
0.2216
0.3882
0.2818
0.2267
0.4026
0.2817
0.2295
0.4108
.67
0.3564
0.1939
0.1934
0.3573
0.2357
0.3141
0.3577
0.2598
0.3818
0.3580
0.2735
0.4200
0.3581
0.2810
0.4415
0.3581
0.2851
0.4533
0.3582
0.2874
0.4598
Broadleaf
Deciduous
Visib_
.33
0.0803
0.0148
0.0834
0.0790 0.0770
0.0357 0.0342
0.1252 0.1235
0.0785 0.0765
0.0462 0.0446
0.1558 0.1531
0.0784 0.0763
0.0524 0.0508
0.1927 0.1912
0.0783 0.0762
0.0554 0.0539
0.2131 0.2122
0.0783 0.0762
0.0569 0.0554
0.2237 0.2232
0.0783 0.0762
0.0576 0.0560
0.2290 0.2286
.67
0.0782
0.0131
0.0789
NIR
.33 .67
0.2848 0.3544
0.1217 0.1781
0.1347 0.1440
0.2819 0.3550
0.1522 0.2067
0.1871 0.2217
0.2804 0.3553
0.1713 0.2221
0.2277 0.2629
0.2798 0.3555
0.1820 0.2301
0.2515 0.2839
0.2795 0.3555
0.1879 0.2342
0.2651 0.2947
0.2793 0.3556
0.1910 0.2363
0.2727 0.3003
0.2793 0.3556
0.1926 0.2374
0.2768 0.3031
6
Table 2: Continuation of Table 1.
Broadleaf
Evergreen
Visible NIR Visible
LAI g=.33 g=.67 .33 .67 .33 .67
0.0789 0.0768 0.2817 0.3582 0.0782 0.0762
4.0 0.0668 0.0650 0.2311 0.2885 0.0579 0.0564
0.3313 0.3309 0.4154 0.4633 0.2315 0.2312
0.0789 0.0768 0.2816 0.3582 0.0782 0.0762
4.5 0.0671 0.0652 0.2319 0.2892 0.0580 0.0565
0.3337 0.3333 0.4179 0.4651 0.2327 0.2324
0.0789 0.0768 0.2816 0.3582 0.0782 0.0762
5.0 0.0672 0.0654 0.2323 0.2895 0.0581 0.0566
0.3348 0.3346 0.4193 0.4662 0.2332 0.2330
0.0789 0.0768 0.2816 0.3582 0.0782 0.0762
5.5 0.0673 0.0654 0.2326 0.2897 0.0581 0.0566
0.3354 0.3352 0.4200 0.4667 0.2335 0.2333
0.0789 0.0768 0.2816 0.3582 0.0782 0.0762
6.0 0.0673 0.0655 0.2327 0.2898 0.0582 0.0566
0.3357 0.3354 0.4204 0.4671 0.2336 0.2334
0.0789 0.0768 0.2816 0.3582 0.0782 0.0762
6.5 0.0673 0.0655 0.2327 0.2898 0.0582 0.0566
0.3358 0.3356 0.4206 0.4672 0.2336 0.2335
0.0789 0.0768 0.2816 0.3582 0.0782 0.0762
7.0 0.0673 0.0655 0.2328 0.2898 0.0582 0.0566
0.3358 0.3356 0.4207 0.4672 0.2337 0.2335
Broadleaf
Deciduous
NIR
.33 .67
0.2792 0.3556
0.1935 0.2379
0.2790 0.3046
0.2792 0.3556
0.1939 0.2382
0.2801 0.3054
0.2792 0.3556
0.1942 0.2383
0.2808 0.3058
0.2792 0.3556
0.1943 0.2384
0.2811 0.3060
0.2792 0.3556
0.1943 0.2384
0.2812 0.3061
0.2792 0.3556
0.1944 0.2385
0.2813 0.3061
0.2792 0.3556
0.1944 0.2385
0.2814 0.3062
7
Table 3: Same as Table 1, but for needleleaf trees and ground cover.
Needleleaf Ground Cover
Visible NIR Visible
LAI g=.33 I g=.67 .33 .67 .33 .67 .33
0.0758 0.0683 0.2350 0.2474 0.2436 0.1637 0.5816 r'
.5 0.0108 0.0034 0.0846 0.0950 0.2050 0.1084 0.5256
0.0647 0.0258 0.1372 0.1435 0.3371 0.2634 0.4298
0.0746 0.0672 0.2311 0.2436 0.2470 0.1637 0.6157
1.0 0.0334 0.0272 0.1299 0.1410 0.2524 0.1404 0.7444
0.1342 0.1227 0.2368 0.2524 0.5762 0.4375 0.9651
0.0742 0.0667 0.2293 0.2418 0.2486 0.1637 0.6391
1.5 0.0478 0.0408 0.1614 0.1722 0.2799 0.1617 0.9908
0.2215 0.1999 0.3235 0.3370 0.7159 0.5532 1.6189
0.0740 0.0665 0.2285 0.2410 0.2494 0.1637 0.6556
2.0 0.0571 0.0501 0.1814 0.1921 0.2947 0.1754 1.2700
0.2968 0.2825 0.3839 0.3955 0.7927 0.6291 2.4084
0.0739 0.0665 0.2281 0.2406 0.2498 0.1637 0.6673
2.5 0.0624 0.0554 0.1935 0.2042 0.3022 0.1837 1.5680
0.3432 0.3339 0.4229 0.4332 0.8324 0.6763 3.2992
.... s
0.0739 0.0664 0.2280 0.2405 0.2500 0.1637 0.6758
3.0 0.0652 0.0582 0.2004 0.2111 0.3059 0.1887 1.8505
0.3696 0.3634 0.4465 0.4563 0.8526 0.7048 4.1928
0.0739 0.0664 0.2279 0.2404 0.2501 0.1637 0.6820
3.5 0.0666 0.0597 0.2043 0.2151 0.3076 0.1915 2.0767
0.3838 0.3794 0.4602 0.4697 0.8624 0.7213 4.9611
NIR
.67
0.5489
0.4843
0.4167
0.5770
0.6714
0.8974
0.5955
0.8577
1.4160
0.6079
1.0335
1.9414
0.6163
1.1812
2.4147
0.6221
1.2858
2.7803
0.6261
1.3458
3.0202
8
Table 4: Continuation of Table 3.
Needle&a/ Ground Cover
Visible NIR Visible NIR
LAI g=.33 g=.67 .33 .67 .33 .67 .33 .67
0.0739 0.0664 0.2279 0.2404 0.2501 0.1637 0.6866 0.6288
4.0 0.0673 0.0604 0.2064 0.2172 0.3085 0.1931 2.2211 1.3688
0.3912 0.3877 0.4679 0.4773 0.8671 0.7310 5.5095 3.1468
0.0739 0.0664 0.2279 0.2404 0.2502 0.1637 0.6899 0.6308
4.5 0.0677 0.0608 0.2076 0.2184 0.3088 0.1940 2.2808 1.3685
0.3950 0.3919 0.4722 0.4815 0.8693 0.7363 5.8085 3.1954
0.0739 0.0664 0.2279 0.2403 0.2502 0.1637 0.6924 0.6321
5.0 0.0679 0.0610 0.2082 0.2191 0.3090 0.1946 2.2774 1.3546
0.3968 0.3940 0.4745 0.4839 0.8704 0.7395 5.9069 3.1932
0.0739 0.0664 0.2279 0.2403 0.2502 0.1637 0.6943 0.6330
5.5 0.0680 0.0611 0.2085 0.2194 0.3091 0.1948 2.2362 1.3360
0.3978 0.3950 0.4758 0.4851 0.8709 0.7411 5.8726 3.1676
0.0739 0.0664 0.2279 0.2403 0.2502 0.1637 0.6956 0.6337
6.0 0.0680 0.0611 0.2087 0.2196 0.3091 0.1950 2.1779 1.3168
0.3982 0.3956 0.4764 0.4858 0.8710 0.7420 5.7674 3.1328
0.0739 0.0664 0.2279 0.2403 0.2502 0.1637 0.6966 0.6341
6.5 0.0680 0.0611 0.2087 0.2197 0.3091 0.1951 2.1160 1.2989
0.3984 0.3958 0.4768 0.4861 0.8712 0.7426 5.6346 3.0958
0.0739 0.0664 0.2279 0.2403 0.2502 0.1637 0.6974 0.6344
7.0 0.0680 0.0611 0.2088 0.2197 0.3091 0.1951 2.0564 1.2838
0.3985 0.3959 0.4770 0.4863 0.8712 0.7428 5.4944 3.0625
Table 5: Same as Table 1, but for broadleaf shrubs and dwarf trees (tundra).
LAI
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Broadleaf Shrubs
Visible NIR
g=.33 g=.67 .33
0.0807 0.0787 0.2845
0.0203 0.0184 0.1498
0.0971 0.0924 0.1959
0.0798 0.0777 0.2837
0.0406 0.0385 0.1930
0.1544 0.1470 0.3203
0.0794 0.0772 0.2832
0.0548 0.0526 0.2201
0.2511 0.2458 0.3985
0.0792 0.0771 0.2831
0.0632 0.0611 0.2364
0.3157 0.3123 0.4472
0.0792 0.0770 0.2830
0.0679 0.0658 0.2460
0.3548 0.3527 0.4766
0.0791 0.0770 0.2829
0.0703 0.0683 0.2514
0.3768 0.3756 0.4937
0.0791 0.0770 0.2829
0.0716 0.0696 0.2544
0.3886 0.3877 0.5034
.67
0.3532
0.2184
0.2328
0.3562
0.2656
0.3859
0.3578
0.2927
0.4734
0.3586
0.3078
0.5227
0.3590
0.3159
0.5498
0.3592
0.3202
0.5644
0.3594
0.3224
0.5720
.33
0.0802
0.0199
0.0970
0.0791
0.0388
0.1355
0.0787
0.0494
0.1841
0.0786
0.0554
0.2230
0.0785
0.0584
0.2447
0.0785
0.0599
0.2561
0.0785
0.0606
0.2617
Dwarf Trees
Visible
.67
0.0781
0.0181
0.0934
0.0771
0.0371
0.1337
0.0767
0.0476
0.1812
0.0765
0.0537
0.2213
0.0765
0.0568
0.2437
NIR
.33
0.2825
0.1369
0.1447
0.2812
0.1681
0.2244
0.2806
0.1860
0.2698
0.2803
0.1958
0.2953
0.2802
0.2010
0.3094
0.2801
0.2038
0.3170
0.0764
0.0583
0.2554
0.0764
0.0590
0.2613
0.2801
0.2053
0.3211
.67
0.3512
0.1969
0.1643
0.3538
0.2268
0.2624
0.3552
0.2416
0.3110
0.3559
0.2488
0.3347
0.3562
0.2521
0.3461
0.3564
0.2537
0.3517
0.3565
0.2544
0.3543
10
Table 6: Continuation of Table 5.
Broadleaf Shrubs Dwarf Trees
NIRVisib& NIR Visib&
LAI g=.33 g=.67 .33 .67 .33 ' .67
0.0791 0.0770 0.2829 0.3594 0.0785 0.0?64
4.0 0.0722 0.0702 0.2560 0.3235 0.0609 0.0593
0.3948 0.3942 0.5088 0.5761 0.2645 0.2642
0.0791 0.0770 0.2829 0.3594 0.0785 0.0764
4.5 0.0726 0.0?05 0.2569 0.3241 0.0611 0.0595
0.3978 0.3974 0.5117 0.5781 0.2658 0.2656
0.0791 0.0770 0.2829 0.3595 0.0785 0.0764
5.0 0.0727 0.0707 0.2574 0.3244 0.0612 0.0595
0.3994 0.3990 0.5134 0.5792 0.2664 0.2662
0.0791 0.0770 0.2829 0.3595 0.0785 0.0764
5.5 0.0728 0.0708 0.2577 0.3245 0.0612 0.0596
0.4001 0.3998 0.5143 0.5797 0.2667 0.2665
0.0791 0.0770 0.2829 0.3595 0.0785 0.0764
6.0 0.0728 0.0708 0.2578 0.3246 0.0612 0.0596
0.4006 0.4002 0.5147 0.5800 0.2669 0.2667
0.0791 0.0770 0.2829 0.3595 0.0785 0.0764
6.5 0.0728 0.0708 0.2579 0.3246 0.0612 0.0596
0.4007 0.4004 0.5150 0.5802 0.2669 0.2667
0.0791 0.0770 0.2829 0.3595 0.0785 0.0764
7.0 0.0729 0.0708 0.2579 0.3246 0.0612 0.0596
0.4008 0.4005 0.5152 0.5802 0.2669 0.2668
.33 .67
0.2801 0.3565
0.2060 0.2547
0.3233 0.3556
0.2801 0.3566
0.2064 0.2548
0.3244 0.3562
0.2801 0.3566
0.2066 0.2549
0.3250 0.3564
0.2801 0.3566
0.2067 0.2549
0.3253 0.3565
0.2801 0.3566
0.2068 0.2549
0.3255 0.3566
0.2801 0.3566
0.2068 0.2549
0.3256 0.3566
0.2801 0.3566
0.2068 0.2549
0.3256 0.3566
Table 7: Reflectances of the ground below the canopy.
Ground cover, dwarf trees
and broadleaf shrubs
All other vegetation types
Visible NIR
0.100 0.200
0.110 0.225
11
Report Documentation Page
F,_atoqal AE'K3n,au fC S and
Scace Adrr.n_t ralOn
1. Repo_ No. 2. GovernrnentAcce_ionNo.
NASA TM-I04538
4. TitleandSubtitle
A Simplified Treatment of SiB's Land Surface Albedo
Parameterization
7. Author(s)
Randal D. Koster and Max J. Suarez
9. Perfo_ing Organization Name and Addre_
NASA/Goddard Space Flight Center
Greenbelt, Md. 20771
12. Sponsoring Agency Name and Addre_
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
3. Recipient's Catalog No.
5. Repo_ Date
April 1991
6. Performing Organization Code
911
8. Performing Organization Report No.
91A01312
10. Work Unit No.
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
The surface albedo parameterization presented by Sellers (1985) and Sellers et
al. (1986) is simplified by assuming that the reflectance of direct solar
radiation is a simple function of solar zenith angle. The function chosen
contains three parameters that vary with vegetation type, greenness, and leaf
area index. Tables of parameter values are presented. Using these tables, SiB's
absorbances of direct solar radiation can be reproduced with an average relative
error of less than 0.5%. Finally, the direct reflectance function is integrated
over zenith angle to produce an equation for the surface reflectance of diffuse
radiation.
17. Key Wo_s(Suggested _ Author(s))
GCM Parameterizations
Surface albedos
Vegetation effects
18. Distribution Statement
Unclassified - Unlimited
Subject Category 47
19. SecuriW Cla_if.(ofthisrepo_)
Unclassified
NASA FORM 1626 OCT 86
_.SecuriW Cla_if,(ofthM pege)
Unclassified
21. No. of pages
11
22. Price




A simplified treatment of SiB's land surface albedo parameterization

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