aggregation of parameters for the land surface model class

ATMOSPHERE-OCEAN 37 (2) 1999, 157–178 0705-5900/99/0000-0157$1.25/0© Canadian Meteorological and Oceanographic Society

Aggregation of Parameters for the Land Surface Model CLASS

Yves Delage, Lei Wen* and Jean-Marc BélangerRecherche en prévision numérique, Atmospheric Environment Service

2121 voie de Service nord, route TranscanadienneDorval, Québec H9P 1J3

[Original manuscript received 21 April 1998; in revised form 5 January 1999]

abstract Land surface schemes are used in climate and weather forecasting models at vari-ous resolutions requiring the use of effective or aggregated parameters to adequately repre-sent each grid square. In this study we investigate the rules for aggregating the surfaceparameters for the Canadian Land Surface Scheme (CLASS). The method consists of runninga one-dimensional version of CLASS over a period of 105 days in summer using meteorolog-ical data observed at an agricultural site near Quebec City. The aggregation of parametersis tested by successively running the model with two homogeneous values (usually a smallone and a large one) of a chosen parameter and then with a mean or aggregated value ofthat parameter; the results of the latter run are then compared with the area-averaged resultsof the two homogeneous runs. Vegetation coverage, rooting depth, soil texture and roughnesslengths are the input parameters thus tested. Heterogeneity of soil moisture content due touneven distribution of precipitation is also discussed. The results indicate that the sub-areasof CLASS must have their own soil variables, that roots must occupy full soil layers and notpart of a layer, and that the aggregating rule for the roughness lengths (zo for momentum andzot for heat and moisture) should be changed from the current logarithmic averages to theblending height method for zo and to a new formula involving both roughness lengths for zot.The surface-layer scheme in CLASS was found inadequate and replaced. Results for soil tex-ture aggregation are not as clear; it seems difficult to obtain simultaneously a good averag-ing of atmospheric energy fluxes and a good averaging of soil moisture contents, runoff anddrainage. Horizontal variability of soil moisture due to uneven distribution of rainfall gener-ates an overestimate of evapotranspiration and an underestimate of runoff in an aggregatedmodel lacking this effect. Preliminary results indicate that, in order to effectively parametrizethis effect in CLASS, both surface ponding capacity and ground infiltration rate must bereduced over the grid square when convective precipitation occurs.

résumé Les schémas de surface sont utilisés dans les modèles de prévision du temps et de cli-mat pour différentes résolutions, mais celles-ci requièrent des paramètres efficaces et agrégésafin de représenter adéquatement chaque maille. Dans cette étude, on recherche, pour le

*Present affiliation: Centre de Recherche en Calcul Appliqué (CERCA), Montréal, Québec

158 / Yves Delage, Lei Wen and Jean-Marc Bélanger

schéma CLASS («Canadian Land Surface Scheme»), les règles pour l’agrégation desparamètres de surface. La méthode consiste à exécuter une version unidimensionnelle deCLASS pour une période d’été de 105 jours, en utilisant les données météorologiquesobservées à une station de météorologie agricole près de la ville de Québec. L’agrégation desparamètres est vérifiée par l’exécution successive du modèle, comprenant d’abord deuxvaleurs homogènes (d’habitude une petite valeur et une grande) d’un paramètre choisi et puisdans un deuxième temps comprenant une valeur moyenne ou agrégée de ce paramètre. Lesrésultats de cette dernière exécution du modèle sont alors comparés avec les résultatspondérés des deux passes d’exécution avec des valeurs homogènes. La fraction de végétation,la profondeur des racines, la texture du sol et les longueurs de rugosité sont autant deparamètres qui ont été testés. On a discuté aussi du contenu de l’hétérogénéité de l’humiditédu sol dû à la distribution aléatoire des précipitations. Les résultats indiquent que les sousdomaines de CLASS doivent posséder leurs paramètres de sol respectifs, que les racinesdoivent occuper des couches entières du sol et non une fraction de la couche. Ils indiquentaussi que la règle d’agrégation pour les longueurs de rugosité (zo pour la quantité de mouve-ment et zot pour la chaleur et l’humidité) devrait être modifiée, c’est-à-dire qu’il faudrait rem-placer les moyennes logarithmiques usuelles par la méthode de hauteur de mélange pour zo etpar aussi une nouvelle formule impliquant à la fois les deux longueurs de rugosité pour zot.On a trouvé que le schéma de couche de surface dans CLASS était inadéquat et on l’a rem-placé. Les résultats pour l’agrégation de la texture du sol ne sont pas aussi clairs. Il sembledifficile d’obtenir simultanément une bonne moyenne des flux énergétiques de l’atmosphère etune bonne moyenne du contenu de l’humidité du sol, de l’écoulement et du drainage. La vari-abilité horizontale de l’humidité du sol en raison de la distribution aléatoire des précipita-tions génère une surestimation de l’évapotranspiration et une sous-estimation del’écoulement dans un modèle agrégé qui ne tient pas compte de cet effet. Les résultats prélim-inaires indiquent que pour paramétriser efficacement cet effet dans le schéma CLASS, lacapacité de rétention de la surface et le taux d’infiltration du sol, doivent à la fois être réduitssur la maille pour des cas de précipitation de convection.

1 IntroductionThe importance of energy and momentum exchanges between the atmosphere andthe land surface for climate simulation and for weather forecasting is well estab-lished. Many schemes have been developed to model these exchanges; a list of themost well-known can be found, for example, in Chen et al. (1997). Land surfaceschemes (LSS) have to deal with the large heterogeneity of the earth’s surface andthis fact creates great complexity in LSS. The problem arises because climate mod-els by necessity deal with large grid squares, most of them containing many differ-ent vegetation species, soil types, surface slopes and several other surfacecharacteristics. Some averaging of the exchanges from all parts of the grid squaremust be done without biasing the results, and this usually implies aggregating thesurface parameters to generate effective values representative of the whole gridsquare or of specific sub-areas. Sometimes such a parameter aggregation is not pos-sible and the surface fluxes must be calculated separately for a number of sub-areasinside the domain (the mosaic approach). To reduce computational cost, it is impor-tant to determine the degree of complexity required to provide acceptable estimatesof areal averages. A great deal of work has already been done on aggregation

Aggregation of Parameters for the Land Surface Model CLASS / 159

research (see for example Michaud and Shuttleworth, 1997). The present paperstudies the impact of aggregating surface parameters in the Canadian Land SurfaceScheme, CLASS, used in the Canadian climate model (Verseghy et al., 1993).

Testing an LSS for scale aggregation can be done in several ways. The mostelaborate way consists of running a full atmospheric model at various scales,allowing two-way interactions at all scales resolved by the model. This approachhas been used by Noilhan and Lacarrère (1995), for example, but because of thecost of a full three-dimensional (3-D) simulation at high resolution, this method isnot appropriate for simulations extending to several weeks or months, as requiredto test the hydrological part of LSS. Various intermediate approaches have beenused to couple LSS to 3-D or 2-D boundary-layer models to study mesoscale circu-lations generated by the inhomogeneities of the land surface (Lynn et al., 1995),transitions at surface discontinuities (Blyth, 1995), or the variability of surface tex-ture (Schmid and Bünzli, 1995). Surface-layer models have also been used to studyfetch effects (Klaassen, 1992), but the simplest way to test the scale dependence ofan LSS is to force it with given atmospheric conditions at the top of the surfacelayer, the level where the coupling between the LSS and the driving model is usu-ally done, as for example in Sellers et al. (1997). The limitation of this method isthat different surface conditions would usually affect the meteorological variablesat that level, and care must be taken to ensure that this lack of feedback does notinvalidate the results. For the present study, which aims to reveal the most appar-ent difficulties in aggregating parameters for CLASS, we push the simplicity onestep further by running CLASS in a 1-D mode over various surface and soil condi-tions for a full season.

The general idea of the method is to consider the area of interest (typically a gridsquare of an atmospheric model) and assume that, for each parameter or situation tobe examined, 50% of its area is represented by parameter value A, and the other 50%is represented by parameter value B. Three runs of CLASS are made, forced by thesame meteorological inputs: one run with parameter value A, another run withparameter value B, and a third run with an effective parameter value attempting torepresent the full area. The true result is considered to be the average of the first tworuns (the mosaic approach), while the result of the third run is tested against thisaverage. A parameter for which the third run can reproduce the average of the firsttwo will be considered successful or well aggregated while aggregation problemswill be revealed when this is not the case.

In the next section, we describe the main features of the CLASS model and thesetup of the experiments. We then study the impact of averaging a number of inputparameters one at a time: fractional coverage of vegetation, rooting depth, soil tex-ture and roughness lengths. Spatial heterogeneity of soil moisture content is alsoaddressed by considering some aspects of the uneven distribution of rainfall.

2 Model description and experimental setupCLASS has been described in two main papers, Verseghy (1991) and Verseghy et al.


(1993). The version of CLASS used for this study is basically version 2.6, except forbare soil evaporation (the beta scheme of Wen et al., 1998), and in Section 7 where anew surface-layer module is introduced.

CLASS has three soil layers in which the mean temperature, the liquid water con-tent and the ice content evolve in time. The standard thicknesses of these layers are:0.10 m, 0.25 m and 3.75 m. In the soil, heat is transferred by conduction whilemoisture flux follows Darcy’s law. Infiltration of rain water as well as phasechanges are also modelled. The surface drives the soil variables by imposing bound-ary conditions. The interface between the surface and the soil for each grid point isdone on a maximum of four sub-areas: bare soil, vegetation, snow over bare soil andsnow with vegetation. Each of the above sub-areas shares the same soil variables.The simplest sub-area is bare soil; solar radiation is absorbed as a function of soilcolour and wetness, atmospheric resistance follows Monin-Obukhov’s similaritytheory, and water infiltrates the soil or is retained on the surface as ponding or isevacuated as runoff. The snow sub-area introduces an extra layer of variable thick-ness on top of the soil. In CLASS, vegetation has its own temperature, heat capacityand roughness, can hold water and snow, modifies the evaporation (transpiration),and can extract moisture from deeper in the soil than bare soil.

The two sub-areas containing vegetation (with and without snow) are themselvesa composite of four types of vegetation: needleleaf trees, broadleaf trees, crops andgrass. Each vegetation type gives rise to a particular treatment of certain processesor parameters; for example, needleleaf trees intercept radiation differently frombroadleaf trees. The input parameters refer to each of the above vegetation types;therefore, when entering CLASS, some aggregation of parameters has already beentaking place. For example in a given grid square, ‘crops’ may be composed of sev-eral crops with different albedoes, heights, leaf area indices, etc. This aggregation isdone outside CLASS. A second step of aggregation is done inside CLASS whenpreparing the composite vegetation (for example, the albedo, the roughness length,or the standing mass) from each of the four types. Finally a third stage of aggrega-tion is done on the results of the four sub-areas to produce a grid-point average ofatmospheric and ground fluxes.

The driving meteorological input for the experiment has been taken from adataset described in Wen et al. (1998). It was collected at an agricultural site nearQuebec City, from the beginning of June to mid-September 1993. The dataset con-tains downward solar radiation, precipitation, wind speed, temperature and specifichumidity of the air at 2 m above ground. Values of air variables so close to the sur-face are a limitation since most of the changes made to the surface parameters willaffect the 2-m values. To remove this limitation, we transposed the measurements toa height of 50 m; details of these calculations are shown in Appendix I. This is acompromise. Ideally, one would like to run CLASS with meteorological inputstaken as high as possible in the boundary layer. But another limitation comes intoplay; CLASS uses a standard surface-layer module whose accuracy decreases withthe height of the meteorological inputs. A compromise solution of 50 m balanced


these requirements. The resulting meteorological forcing given to CLASS is shownin Fig. 1.

The following outputs of CLASS were analysed:

Variable Symbol Units– sensible heat flux H W m–2

– latent heat flux LE W m–2

– soil moisture content in all three layers θ % by volume– surface runoff flux mm day–1

– bottom drainage flux mm day–1

– upward solar flux K↑ W m–2

– upward long wave flux L↑ W m–2

– momentum flux τ Pa– ground heat flux G W m–2

– temperature in all three layers.

The hourly outputs of these quantities have been averaged for daytime and night-time (the daytime group contains half of the total output hours with the largestincoming solar radiation) for the entire integration period (105 days). The results inthe text will be averages of daytime and night-time combined, unless specified oth-erwise. Not all outputs are relevant to each experiment and not all of them will bediscussed, but any interesting or unexpected features in any of these outputs will benoted.

For greater clarity we present here a summary of the experiments to be described:

Experiment Parameter, input, or process to be tested1 vegetation coverage2 rooting depth3 soil texture4a soil moisture (variable precipitation)4b soil moisture (impact of water reservoirs)5 roughness lengths.

3 Vegetation coverageThe first experiment attempts to verify the ability of CLASS to handle the partitionbetween bare soil and vegetation. As indicated above, CLASS computes a separateenergy budget for the bare soil portion of the grid square and for the vegetated por-tion, but the soil water contents and temperatures are shared by the two sub-areas.(Note that no experiment with snow or ice was done in this study.) In order to facili-tate the interpretation of the results, we minimized the number of differencesbetween the two areas, and set the roughness lengths and the albedos to the samevalues (0.01 m and 0.17, respectively, making the vegetated part a short grass). Theleaf area index of grass is 4.0 and the rooting depth is set at 0.30 m, extending well


Fig. 1 Meteorological variables from Wen et al. (1998) used to drive CLASS. The wind, temperatureand specific humidity have been corrected to represent conditions at a height of 50 m. a) Down-ward solar radiation, b) precipitation, c) wind speed, d) temperature and e) specific humidity.

a

b

c

d


into the second layer of the loamy soil. Initial soil moisture contents are set at 20%per volume for all three layers and for all experiments.

Experiment 1 is summarized as such: 50% of the area is covered by bare soil,50% by short grass. One run (A1) of CLASS is made with 100% bare soil. Anotherrun (B1) is made with 100% short grass. Finally a third run (C1) is made with 50%bare soil and 50% short grass. We want to verify that run C1 gives similar outputs tothe mean (M1) of run A1 and run B1.

We first compare runs A1 and B1. From results in Table 1, the grass evaporationrate is 4.9 W m–2 larger than for bare soil, because it has access through its roots tothe water in the second soil layer. Daytime values of LE (not shown) are about twicethe daily averages. One can verify that B1 has indeed a water content of 5.1% byvolume less than A1 in layer 2, whereas both runs started the season with the samewater content. Comparison of M1 and C1 shows that surface temperatures are rea-sonably close, with differences in L↑ of 0.4 W m–2. The surprising result is thatevapotranspiration is larger in C1 than in either A1 or B1, whereas we would haveexpected that a composite of bare soil and grass would evaporate at an intermediaterate between that of bare soil and that of grass. The reason for this unexpected resultis the following. In runs A1 and B1, all variables refer to a single type of surface,including the soil water contents; in run C1, the energy budgets are done separatelyfor both surfaces as in A1 and B1, but the soil water contents are shared by the two

e

Fig. 1 (concluded).

Table 1 Output variables for experiment 1 on vegetation cover, selected from the list in Section 2 ofthe text. M is the mean of A and B.

Run A1 B1 M1 C1 C1-M1description Units Bare soil Grass Mean Composite Error

L↑ W m–2 400.9 395.5 398.2 397.9 –0.4H W m–2 27.1 26.7 26.9 23.8 –3.1LE W m–2 62.4 67.3 64.9 68.7 3.8θ1 % by vol. 26.4 27.5 27.0 26.4 –0.5θ2 % by vol. 28.2 23.1 25.6 24.6 –1.0


sub-areas. The effect of this particular structure of CLASS is to allow water to betransferred horizontally from one area to the other: since the bare soil extracts all ofits evaporating water from layer 1 and the grass is capable of extracting water fromlayers 1 and 2 through the roots, the combination of the two is more effective thaneither one taken separately. This is illustrated by the water content of layer 1, θ1,which on average is the same in C1 as in A1 (and hence smaller than in M1) whileθ2 in C1 is 1% by volume less than in M1.

We can ask ourselves which of the two simulations M1 or C1 is more realistic.Our contention is that the only case for which C1 would give a realistic simulation iswhen the bare soil and the grass patches inside the grid square are very small andfinely interspersed, so that horizontal flow of water could indeed take place betweenthe two sub-areas. Since in general such transfer is minimal, the example shown inthis section indicates that the partial mosaic structure of CLASS (sub-areas forenergy budgets but common soil variables) is not always adequate to simulate theevapotranspiration of a mixture of bare soil and vegetated surface. The simplestsolution to this problem would be to allow CLASS to have independent soil vari-ables for its sub-areas. A similar conclusion has been reached by Mölders et al.(1996).

4 Rooting depthFrom the results above we see that rooting depth is important, allowing water reser-voirs to be available for plant transpiration. If in the above example the roots of thegrass are restricted to the first layer, the errors in the energy budget (not shown) areconsiderably reduced and run C1 becomes acceptable. A question naturally arises,What is the correct way to aggregate rooting depth from different plants in CLASS?

Since the sensitivity of an LSS to water availability is larger in dry conditions, wemake the present experiment with the same meteorological forcing as above butwithout precipitation. The situation is admittedly artificially exaggerated but notcompletely unrealistic since long dry spells can occur almost anywhere. For thisexperiment, vegetation coverage is 100% crops, the albedo is 0.20, zo = 0.08 m andthe soil type is loam as in experiment 1. In 50% of the area the rooting depth is 0.30m while in the other 50% it is 0.50 m; the rooting depths are chosen such that run A2has access to layers 1 and 2 only while runs B2 and C2 have access also to the thicklayer 3.

The results are shown in Table 2. They are so striking that only evapotranspirationneeds to be shown. Run A2 produces a mere 5.9 W m–2 while both runs B2 and C2yield over 30 W m–2, and the difference between B2 and C2 is only 0.9 W m–2. It is

Table 2 Results of experiment 2. The interface between layer 2 and layer 3 is at 0.35 m.

Units A2 B2 M2 C2 C2-M2

Rooting depth m 0.30 0.50 — 0.40 —LE W m–2 5.9 31.2 18.5 30.3 11.8


clear in this case that C2 is not a good simulation of M2. The reason for this behav-iour of CLASS is easy to understand. Inspection of the code reveals two roles playedby the rooting depth: firstly, it distributes the extraction of moisture for transpirationamong the layers according to a root density function (an exponential decrease withdepth), and secondly, it indirectly controls the stomatal resistance by labelling whichsoil layer is to be counted as a water source for transpiration. It is this second rolethat causes our problem: CLASS does not use the fractional penetration of roots intoa layer to determine the plant resistance, but only the presence or absence of roots inthe layer. For that reason run B2 and run C2 have virtually the same resistance sincethey are controlled in both cases by the wettest layer available to roots, layer 3,which contains enough water to sustain transpiration for many months. In contrast,A2 runs dry once the extractable water in layers 1 and 2 is exhausted. In reality, ofcourse, there should not be such a difference. B2 and C2 should not be so differentfrom A2, and C2 should be close to M2, because only water in the root zone is madeavailable to the plant, not the entire third layer.

We have attempted to use the fractional extent of roots in the layer to determinethe plant resistance to evaporation, but without great success. The reason is the highnonlinearity of the dependence between the resistance to transpiration and soil mois-ture content. A solution that had remarkable success involves adjusting the layerthicknesses such that roots occupy full soil layers and not parts of layers. When wereran experiment 2 with the interface between layer 2 and layer 3 set equal to therooting depth for each run, the evapotranspiration in this new run C2 reproduced runM2 within 0.01 W m–2. This solution appears reasonably easy to apply, but mayrequire the addition of one or two soil layers to accommodate deeper roots. An alter-native practical solution could be to keep the layer thicknesses constant but toincrease the number of layers so that the rooting depth coincides with full layers.

5 Soil textureDespite the fact that soil texture has been identified as the most sensitive parameterby Wilson et al. (1987) in stand-alone runs of the Biosphere-Atmosphere TransferScheme (BATS) model, the scaling and aggregation of soil hydraulic characteristicsfor mixed soil types remains largely unexplored (Kabat et al., 1997). One difficultyis that soils are more heterogeneous than the atmosphere, and soil variables thatcould apply to an area of the size of a grid square are not as realistic as in the atmo-sphere. Nevertheless the simplicity of Darcy’s equation (valid at a point) is veryattractive, and it is worthwhile trying to apply Darcy’s equation to a larger area. Inparticular, Kabat et al. (1997) suggest that sub-areas with similar hydraulic proper-ties could be treated as a single type of soil. Most of the variability in soil parame-ters can be related to the sand and clay fraction; in CLASS, these are used todetermine the soil hydraulic properties, following Clapp and Hornberger (1978) (seeAppendix II). Noilhan and Lacarrère (1995) define an aggregated soil by simplyaveraging sand and clay contents, but it is clear from (7) and (8) in Appendix II thatthe relationships between soil moisture and soil texture are highly nonlinear. Wen et


al. (1998) found that CLASS was particularly sensitive to parameter b, which rangesfrom 3 for sand to 12 for clay. In our experiment 3, we compare two extreme soiltextures, sand and clay, and a composite of sand and clay, with the same vegetation(see Tables 3 and 4 for the values of the input parameters) and the same meteorolog-ical forcing. Note that roots are restricted to the first two layers of soil (0.35 m) andthat precipitation is turned back on. Results are shown in Table 5.

In the example chosen, evapotranspiration is not greatly affected by soil type,ranging from 2.06 mm per day over clay to 2.37 mm per day over sand. Run C3 dida perfect job in producing the correct average in this case, a result comparable tothose of Noilhan and Lacarrère (1995) and of Kabat et al. (1997). Soil moisture con-tents, on the other hand, are very different in sand and in clay. For the first two lay-ers, sand holds less than half the amount of water than clay. Differences in the thirdlayer increase with time (not shown) and would eventually be of the same order as

Table 3 Common input parameters for experiment 3 on soil texture. Rooting depth andbottom of layer 2 are 0.35 m. The soil texture parameter values are shown inTable 4.

Needleleaf BroadleafUnits trees trees Crops Grass

Coverage % 22.5 22.5 22.5 22.5LAI 2 6 4 4zo m 1.5 2.0 0.08 0.08Albedo 0.12 0.17 0.20 0.18

Table 5 Results of experiment 3. The evapotranspiration is the same variable as LE expressed in dif-ferent units.

Units A3 (sand) B3 (clay) M3 C3 C3-M3

θ1 % by vol. 15.5 36.6 26.1 26.9 0.83θ2 % by vol. 13.1 31.5 22.3 26.3 3.98θ3 % by vol. 18.5 20.5 19.4 20.9 1.44Evapotranspiration mm day–1 2.37 2.06 2.22 2.22 0.00Bottom drainage mm day–1 2.26 0.00 1.13 0.00 –1.13Surface runoff mm day–1 0.00 0.40 0.20 0.01 –0.19

Table 4 Soil parameter values for the various runs or experiments.

Run/experiment C3type of soil A3 sand/clay 1, 2, 4 and 5 B3parameter Units sand composite loam clay

ksat m s–1 × 106 24 8 5 2ψsat m 0.05 0.14 0.2 0.4θsat 0.37 0.41 0.43 0.46b 3.4 7.8 5.8 12.1


the upper layers (it takes more than one season to drain the deep third layer). Run C3did reasonably well for layer 1 but not so well for layer 2, holding 4% by volumemore water than M3. However, the most striking differences are in the drainage andrunoff: sand drains almost as much water at the bottom of the third layer as it evapo-rates, while clay does not drain at all. The reverse is true for surface runoff, none forsand and 0.40 mm per day for clay. (The runoff is a small amount on the average,but runoff occurs only in a few events during the season and, in two of these,exceeds 15 mm day–1.) Run C3 with its composite of sand and clay has no drainageand virtually no runoff. Other runs not reported here convinced us that there is nosimple way to prepare a composite of sand and clay that would produce the sameeffect on all variables as the average of the two separate runs. These results confirmthose of Sellers et al. (1997) and of Kabat et al. (1997). When hydrological pro-cesses are an important modelling issue and the land area within a model grid cellcontains very different soil types, correct aggregation of soil types may requireusing a mosaic approach and treating these types separately in the LSS. In our exam-ple above we have used soil types that are vertically uniform, but this is often not thecase for real soils and the problem can be more complex.

6 Soil moisture content and precipitationThis section does not treat parameter aggregation but the impact of spatial heteroge-neity of soil moisture and precipitation. It is a well-documented fact that assuminguniform soil moisture content or uniform precipitation over a grid square tends tooverestimate evapotranspiration and underestimate runoff (see for example Wetzeland Chang, 1988; Johnson et al., 1993; Bonan, 1996; Noilhan et al., 1997). This iseasily understood since runoff is more likely to occur with larger precipitation rates(occurring over part of the grid cell) and over saturated soil, while evapotranspira-tion will be severely limited over the drier parts of the grid square, but usually notgreatly increased over the wetter parts due to limited energy supply. In addition, theincreased runoff will cause a drying of the soil. Wood (1997) presents a counter-example where taking into account the subgrid heterogeneity of soil moisture leadsto increased evapotranpiration (wet areas in an overall dry grid cell) but this case isuncommon. To illustrate the general case, several runs (experiment 4a) were madewith the same parameters as in experiment 3 except for the soil texture (see Table 4).These runs differ only in the factor multiplying precipitation, which varies from 0 to3. Figure 2 shows results of evapotranspiration, surface runoff and drainage flux atthe bottom of the third layer in the same units. No runoff or drainage takes placeuntil the daily average precipitation reaches ,3 mm day–1. At low precipitationrates up to ,1.8 mm day–1, nearly all the water goes into evapotranspiration. Forrates above 6 mm day–1 evapotranspiration stays steady and the excess water runsoff, increases the soil moisture content, or drains.

The message from Fig. 2 is that the ratios of evapotranspiration, runoff and drain-age vary with the precipitation rate and soil moisture content (both are related in ourexperiment), and consequently the linear averaging implicit in not considering spa-


tial heterogeneity will in general introduce biases. Several parametrizations of thiseffect have been proposed and evaluated. In Wetzel and Chang (1988), subgrid vari-ation in soil moisture is related to grid size; Wood et al. (1992) proposed a modelwith subgrid variability of infiltration capacity; Johnson et al. (1993) tested the run-off submodel of Entekhabi and Eagleson (1989), in which both the precipitation andthe soil moisture are assumed to vary within the grid cell; Eltahir and Bras (1993)modelled precipitation interception by the canopy and found significant reduction ininterception when horizontal inhomogeneity is taken into account; Bonan (1996)tested subgrid parametrization of infiltration and runoff in a General CirculationModel (GCM) and found for most basins the general behaviour shown by Fig. 2;Mölders et al. (1996) used an explicit subgrid strategy; more recently, Wood (1997)studied the effect of small-scale inhomogeneity of soil moisture on evapotranpira-tion with an analytical model.

Compared to the above references, the approach taken in this study is very limitedand serves only as an indication for future work. Since CLASS neglects subgridvariability in its canopy interception, in its surface ponding, and in its ground infil-tration submodels, we tested the interaction of these processes in preparation for the

Fig. 2 Results from experiment 4a, where the input precipitation (Fig. 1b) has been multiplied by a fac-tor ranging from 0 to 3. The observed precipitation is 4.3 mm day–1.


inclusion of a more realistic parametrization. In experiment 4b the two water reser-voirs and ground infiltration are selectively removed, and the impact on evapotrans-piration and on runoff is examined. The input parameters for this experiment are thesame as those for experiment 4a with the observed precipitation (4.3 mm day–1 onthe average). Eight runs are made with all combinations of the three processes; theruns and their results are summarized in Table 6.

The impact of removing the storage capacity on the canopy is to reduce theevapotranspiration (ET) by ,6%, except in the case of no ponding and no infiltra-tion where the impact is larger. The impact on runoff is small and not systematic(runoff can be reduced by removing canopy storage because the resulting increase insoil water content enhances infiltration in some cases). The impact of removingponding is negligible on ET if infiltration is maintained; it does, however, increaserunoff by a factor of three. Removing infiltration has very little effect on ET if pond-ing is retained, but runoff is increased by about a factor of five. The dramatic impactoccurs when both ponding and infiltration are removed: evapotranspiration consid-erably decreases and runoff considerably increases. In addition, when no canopystorage is allowed, all the precipitation goes into runoff. These results indicate that aparametrization of subgrid variability of precipitation and soil moisture for CLASSmust involve both the surface ponding and the ground infiltration in order to prop-erly affect evapotranspiration and runoff. Canopy storage also has an impact but it isless significant than ponding and infiltration in our experiment.

Although the need to introduce subgrid variability in the treatment of precipita-tion and soil moisture is clearly demonstrated, we felt that actually testing existingschemes or constructing new ones was beyond the scope of this study. Soil moisturevariability arises from horizontal transport inside the domain by gravity, fromunevenly distributed rainfall due to convective precipitation, and from variations inwater retention capacity of the soil. How to characterize the variability of soil mois-ture for a given grid cell must be addressed by including topographical information,but also by studying the interaction between the variability of soil types and that ofsoil moisture, and the influence of the variability of precipitation on soil moisture.

7 Roughness lengthThe roughness length is a surface parameter that determines the steepness of the log-

Table 6. Results of experiment 4b : impact of canopy storage, surface ponding and ground infiltrationon evapotranspiration and surface runoff. Units are mm day–1.

ProcessCanopy storage YES NO YES NO YES NO YES NOSurface ponding YES YES NO NO YES YES NO NOGround infiltration YES YES YES YES NO NO NO NO

VariableEvapotranspiration 2.31 2.18 2.31 2.18 2.30 2.17 0.65 0.18Surface runoff 0.13 0.12 0.40 0.40 0.63 0.67 3.97 4.32


arithmic profiles of wind, temperature and other scalar quantities near the surface,and hence, for given values of these variables at the surface and at a specified heightz, it determines the magnitude of the turbulent fluxes: the larger the roughnesslength, the larger the fluxes (see the logarithmic terms in (2) and (3) below). A dif-ferent roughness length is assigned to wind, zo, and to temperature and humidity, zot.To aggregate zo and zot, CLASS uses logarithmic averages, as suggested by Taylor(1987) for wind. In his analysis, Taylor (1987) investigates various approaches, allof them giving aggregated (or effective) values zo,eff larger than the logarithmic aver-age, and concludes that in most situations the simple logarithmic average is a goodapproximation, especially if one is concerned with the average wind profile ratherthan the average surface stress. Mason (1988) argues that Taylor’s conclusions applyto the layer near the surface affected by the changes in roughness, but that, if one ismainly concerned with the overall drag of the surface on the atmosphere, the aver-age of the drag coefficient should be used. This method involves a height, the blend-ing height zb, above which the flow is unaffected by horizontal variations of surfaceroughness: this height is related to the horizontal scale of the variations. In thismethod zo,eff is calculated using the following expression:

where fi is the fractional coverage for each of the sub-areas with their given zo,i. Otherstudies (among them Dolman and Blyth, 1997; Wood and Mason, 1991; Schmid andBünzli, 1995) found that zo,eff is weighted towards the larger-roughness elements inthe grid square, and is greater than the simple logarithmic average, as in (1).

We will not, in this study, provide novel results on the aggregation of zo, but thereis ample published evidence to prompt us to recommend the replacement of the log-arithmic average in CLASS by (1). The blending height should be determined fromthe horizontal scale of the variations as proposed in Mason (1988), or in other waysthat would be appropriate, since the expression (1) covers the complete range of val-ues from the logarithmic average (zb = 1) to the maximum value of zo inside thegrid square (zb = zo,max). In this section, the impact of this choice of zo,eff for the tur-bulent fluxes τ and H are examined. These fluxes are calculated as:

and

1

ln2 zb

zo,eff

�X fi

ln2 zb

zo,i

(1)

τ � ρ

264 κUz

lnz

zo

� ψm

� z

L

�+ ψm

� zo

L

�375

2

(2)

H � ρcp

264 κUz

lnz

zo

� ψm

� z

L

�+ ψm

�zo

L

�375264 κ(To � Tz)

lnz

zot

� ψt

� z

L

�+ ψt

� zot

L

�375 Ù (3)


where ρ is the air density, Uz is the wind speed at a height z (50 m in this study), Tz isthe potential temperature at the same height, To is the potential temperature at thesurface, κ is the Von Karman constant (0.4), cp is the specific heat at constant pres-sure, ψm and ψt are stability functions for momentum and heat, respectively, and L isthe Obukhov length, calculated with τ, H and the moisture flux. One can see that τdoes not depend on zot (except through L but this dependence is usually very smallcompared to the direct influence of zo) while H depends on both zo and zot. (Thelatent heat flux is governed by an expression similar to (3) with the specific humid-ity replacing T.) Therefore, zo,eff must be determined independently of zot,eff for itsimpact on the stress, but zot,eff should in principle be a function of the chosen valueof zo,eff. In this section, zo,eff will be given several values between the logarithmicaverage and the maximum zo, and the impact on the calculation of the energy fluxeswill lead us to choose a formula to determine zot,eff.

When attempting to find an aggregation rule for zot, we discovered a serious prob-lem in the surface-layer module. As discussed above, changing zot should have verylittle effect on the momentum flux, and the sign, if any, should be the same as for theheat flux, i.e., decreasing zot should decrease both fluxes. (We consider here the sea-sonally averaged fluxes where the daytime component dominates the night-timeone.) In our preliminary tests with the standard version of CLASS, we found thatchanging zot from 0.143 m to 0.00035 m while keeping zo = 1 m increased themomentum flux by 50%. This result is clearly unacceptable, especially in a study ofthe impact of roughness lengths, since large ratios of zo/zot such as the one in thisexample have been reported in the literature (Beljaars and Holtslag, 1991). Theproblem resides in the approximations that are made in the surface-layer module ofCLASS, which uses Abdella and McFarlane’s (1996) scheme to solve the system ofequations (2) and (3). Though corrections to this scheme are certainly possible,notably by introducing iterative solutions, we chose simply to replace the scheme bythe one used in the operational models of the Canadian Meteorological Centre,which is described in Delage and Girard (1992) and in Delage (1997). The aboveproblem completely disappears when using this new formulation.

For the experiments in the previous sections, forcing CLASS with variables at50 m without feedback from the LSS on these variables was not a serious limitationand the conclusions reached so far would not be changed if CLASS had been cou-pled to a boundary layer model. The impact of the roughness length, however, isdifferent since an increase in zo is expected to reduce the wind in the lower part ofthe boundary layer through an increase in the momentum flux. Keeping the wind at50 m unchanged when changing zo would exaggerate the impact of the modifica-tion, as explained by Taylor (1987). In an attempt to minimize this adverse effectwithout going into a full boundary-layer modelling, a simple correction scheme isapplied to the wind speed at 50 m. The correction logarithmically extends the windprofile upwards to a height zw using the zo of the dataset (0.05 m), and then, foreach run, recalculates a wind at 50 m, again logarithmically, using the zo assignedto the run:


Similar corrections should, in principle, be applied to the temperature and thehumidity but we have found none which were, at the same time, both simple andadequate. We believe that this has little effect on our conclusions because varyingthe surface roughness impacts much more on the momentum flux than on the heatand moisture fluxes, as revealed by our experiments. Wood and Mason (1991), andmore recently Ma and Daggupaty (1998), also report that temperature perturbationsdo not extend so far from the surface as those for momentum. We will do experi-ment 5 with zw = 500 m; with this rather large value, the effect of zo will certainlynot be exaggerated by the experimental setup.

Experiment 5 is done with the same soil and vegetation as experiment 2 exceptfor the roughness lengths. The rooting depth is set at 0.30 m and precipitation isturned back on. The surface-layer module is the new one and the wind at 50 m iscorrected according to (4). In run A5, zo is set to 0.0025 m while in run B5 it is set to1.0 m. The roughness lengths for heat and moisture for these two runs are set to 1/7of zo, the ratio provided by CLASS for crops. The results are shown in Table 7.Looking at the full day averages, the differences in surface stress between thesmooth and the rough surfaces are strikingly larger than those of the energy fluxes.The average τ for the rough surface is almost 4 times larger than for the smooth sur-face, while the largest change in any of the energy fluxes is 6 W m–2, a mere 2% ofthe incoming solar flux. The same result is found for daytime, except that the valuesare about twice the averages. Surface stress is the major dynamical link (the otherone being the drag exerted by mountains) between the atmosphere and the earth sur-face, and its magnitude determines, to a large extent, the wind regime. A GCM can-not hope to reproduce the correct climatology if its surface stress is incorrect. The

Table 7. Input parameters and results for experiment 5.

Variable orparameter A5 B5

Description Units Smooth Roughzo m 0.00248 1.0zot m 0.00035 0.143

Day and night Daytime Day and night Daytime

τ Pa 0.080 0.145 0.305 0.558H W m–2 23.1 53.0 26.9 64.0LE W m–2 64.6 127.9 67.3 134.6G W m–2 2.4 42.0 1.9 36.4L↑ W m–2 397.8 427.8 391.8 415.9

U50,run �ln

zw

0Ø05ln

50

zo,run

ln50

0Ø05ln

zw

zo,run

U50,dataØ (4)


aggregation rule for zo is therefore of prime importance for GCMs and the impact onenergy exchanges over land is relatively minor.

We show in Fig. 3 the results for stress with values of zo,eff spanning the wholerange of zb values using (1), from the logarithmic average of runs A5 and B5 (thestandard in CLASS) to the value used in B5. The graph also contains the corre-sponding values of zb. If we accept the blending height method, typical values of zbof the order of 100 m would yield values of τ about 50% larger than with the loga-rithmic average. We believe that these differences are very significant, in spite of thefact that daytime values of stress are an order of magnitude larger than night-timevalues. These differences may not affect the results of short term integrations ofatmospheric models but are bound to alter the circulation after a few days.

Taking a closer look at energy exchanges in Table 7, we see that the extra turbu-lent exchange over the rough surface increases the upward sensible and latent heatfluxes at the expense of the long wave flux (cooling of the surface must result sincethe energy supply is the same). The ground flux is downward during the day andupward during the night with about the same magnitude, and the net flux is therefore

Fig. 3 Surface stress from experiment 5 as a function of zo,eff in metres. The solid curve is for the aver-age stress, the upper curve is for daytime and the lower curve is for night-time. The blendingheights shown are the values of zb used to calculate zo,eff with (1). The x axis runs from the loga-rithmic average of runs A5 and B5 (–3.0) to the value of run B5 (0.0).


very small. We tried various scenarios (for example reducing the solar input or thesoil water content) to find out that the cooling of the surface is the most constanteffect of increasing surface roughness. Consequently L↑ will be used to measure thesuccess of an aggregation formula for zot. Two such formulae have been tried, one isthe logarithmic average of zot (currently used in CLASS), and the other one is givenby the following expression:

Equation (5) expresses that the product (zo,eff zot,eff) is obtained by logarithmic aver-aging. Results in Fig. 4 show that (5) is significantly better than the logarithmicaverage in keeping the error in L↑ to a minimum. This is especially so during theday, when the flux values are the largest. (The error is calculated by taking the dif-ference between L↑ from the runs with various values of zo,eff and zot,eff, and from themean of A5 and B5.) For the case where zo,eff is given by the logarithmic average,the two formulae for zot,eff give the same result, as expected. An important extensionof (5) is the case where zo,eff contains the effect of unresolved topography. It seems

Fig. 4 Error in L↑ in experiment 5 as a function of zo,eff in metres for two aggregation rules for zot,eff.

zot,eff �

Yi

(zo,izot,i)fi

zo,eff

Ø (5)


appropriate in this case to use a formula such as (5) to remove from the energy cal-culations the contribution of unresolved topography, which is believed not to affectthe energy fluxes.

In summary, correctly aggregating the roughness lengths was found to have moreimpact on the surface stress than on the energy fluxes. The current logarithmic aver-age for both roughness lengths is inadequate for the momentum flux, giving theminimum of the plausible range of values. The averaging formula based on theblending height method has the advantage of covering this range in totality, thoughthe proponents of this method have given a stricter meaning to the blending height.We therefore recommend the use of equation (1) for calculating zo,eff, and equation(5) for zot,eff, which has been found to be more accurate than the current logarithmicaverage of zot.

8 ConclusionsThis study addresses the problem of aggregating surface parameters for land surfaceschemes. The experiments are done with a particular model, CLASS, but the conclu-sions are applicable to other LSS using similar techniques. The method used in thisstudy involves running a one-dimensional version of CLASS forced with meteoro-logical data taken from a mid-latitude site during 105 days in summer. For each sur-face parameter to be tested, the model is run successively with two extreme valueseach corresponding to 50% of the grid area, and then with an average value repre-senting the composite for the whole area.

The first parameter tested, vegetation coverage versus bare soil, was expected toproduce good average fluxes with a composite run including both land surfaces,since each is treated separately in CLASS for the surface energy balance, but itturned out that the common soil variables shared by the two surfaces unrealisticallyenhance evapotranspiration. We therefore recommend separate soil variables, in par-ticular moisture contents, for each sub-area of CLASS.

The rooting depth presents the particular problem of the vertical resolution of thesoil layers. This study reveals that, if the vegetation roots penetrate a model soillayer, CLASS will have access to all of the water in this soil layer, irrespective of theactual fraction occupied by the roots. No easy solution using this fraction has beenfound. The effective way to eliminate this problem is to make the rooting layer coin-cide with actual model layers to avoid roots occupying a fraction of a layer.

Aggregating soil parameters with heterogeneous soil texture leads to almostinsoluble problems when trying to reproduce both the atmospheric fluxes and thesoil moisture contents. In particular, surface runoff and bottom drainage are difficultto average because soil properties controlled by texture are very nonlinear. The solu-tion to this problem is not as clear as for the other parameters. We recommend that,if large differences in soil texture are present in a grid point, separate calculationsshould be made for the main constituents (the mosaic approach). Also, if soil mois-ture measurements are to be assimilated, it is important to obtain information on soiltype, since the active range of soil moisture varies with soil texture.


One of our experiments with CLASS confirms the well-established fact thatignoring the heterogeneity of soil moisture contents within a grid cell, especiallythat arising from uneven distribution of precipitation, will overestimate evapotrans-piration and underestimate runoff. In order to account for such an effect in atmo-spheric models, information on precipitation type (convective or stratiform) shouldbe used. For CLASS it was found that, to be effective, such a parametrization mustreduce both the surface storage (ponding) and the ground infiltration rate.

The roughness lengths affect the surface momentum flux much more than theyaffect the heat and moisture fluxes. Based on other studies, we recommend theblending height method for averaging zo instead of the current logarithmic average.Using the blending height as a parameter to specify various values of zo,eff, we foundan aggregation rule for zot that involves zo,eff and the logarithmic average of theproduct of both roughness lengths. We also found that the surface-layer module inCLASS does not handle variations in zot properly and this scheme was replaced withthe one used in the operational models of the Canadian Meteorological Centre.

This study used a simple method designed to verify the basic reliability of anLSS. Such a test should be passed by all LSS. However, it is not a guarantee thatother problems will not be revealed by more sophisticated experimental setups. Webelieve that, in the case of CLASS, the solutions proposed here should be adoptedbefore CLASS is used in more complete studies with full atmospheric models.

AcknowledgmentsWe want to thank our colleague Nils Ek for helping us with the English. This studyhas been supported in part by the Canadian Climate Research Network.

Appendix IThis appendix describes the generation of the meteorological inputs for CLASS at aheight of 50 m from measurements at a height of 2 m. The solar flux and the precip-itation are unchanged. The wind speed is modified by adding a constant of 2 m s–1.Though arbitrary, this procedure maintains a fair amount of variability (see Fig. 1c)while eliminating the sometimes problematic low values. The downward long waveflux (not measured directly) is assumed to be 80% of the black-body radiation calcu-lated with the 50-m temperature. For temperature and humidity, the procedure isdescribed below.

The mean temperature and speciþc humidity ¼X are þrst calculated for each day

and then individual values at every 30 minutes at 50 m, X50, are calculated from

the measured value at 2 m, X2, according to the following formula:

X50 � ¼X + (X2 � ¼X)

�ln(1000) � ln(50)

ln(1000) � ln(2)

�Ø (6)

Equation (6) assumes that the differences between individual values and the current

daily mean decrease logarithmically with height and are zero at 1000 m.


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Appendix II

The soil hydraulic conductivity k and the water suction ψ are related to the soil

liquid moisture content θ as in Clapp and Hornberger (1978):

k(z) � ksat

�θ(z)

θsat

�(2b+3)

(7)

and

ψ(z) � ψsat

�θ(z)

θsat

��b

Ù (8)

where ksat, ψsat, and θsat are the saturated values and b is an empirical parameter.

The parameters ksat, ψsat and θsat are determined by the percentage of sand in the

soil while the b parameter is determined by the percentage of clay. The values used

in this study are given in Table 4.


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aggregation of parameters for the land surface model class

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