Modelling evapotranspiration in semi-arid terrains: Comparison of two schemes

Meteorol. Appl. 3, 229-242 (1996)

Model I i ng evapotranspiration in semi-arid terrains: comparison of two schemes C Fernindez, G Nieto and J A Prego, Departamento de Geofisicu y Meteorologh, Universidad Complutense de Madrid, 28040 Madrid, Spain

The importance of choosing a relatively detailed parameterisation for plant transpiration in semi-arid terrains is evidenced by comparison of model results and observations from a European field experiment recently performed in La Mancha (Spain). In severe drought periods the contribution of the vegetation cover to the total latent heat jlux is greater, since the evaporation from the bare soil fraction is small. Also, the observed heterogeneity of vegetation types in semi-arid regions, such as the Iberian peninsula, is an additional argument to recommend the inclusion of somewhat sophisticated parameterisations in mesoscale models. A set of sensitivity tests and different formulations for the stomatal resistance illustrates fairly well the importance of the vegetation properties in regions where plants are scarce.

I. Introduction

There is consensus that the parameterisation of soil, vegetation and planetary boundary layer processes needs to be improved in atmospheric models. Bou- geault (1991) gives a relatively recent review of this topic. He claims that physical-based parameterisations are required as an alternative to schemes that include artificial, non-physical parameters (such as those proposed by Zhang & Anthes, 1982), which have been widely used. Also, other classical physically based parameterisations, which include a lot of soil layers, are very expensive. Clearly there is a need to develop simple parameterisations which are physically realistic.

The earliest attempts to develop simple schemes, which included the textural characteristics of the soil as well as a canopy layer, were carried out by Dickinson (1984) and Sellers et al. (1986) among others. But perhaps the most simple, efficient and feasible parameterization was proposed by Noilhan & Planton (1989) (NP89, henceforth). It consists of two soil layers with prognostic equations for temperature and soil water content based on a force-restore method and a vegetation layer which controls evapotranspiration.

The NP89 parameterisation has been implemented in the Complutense University of Madrid (UCM) mesoscale numerical model (Fernindez et al., 1995). Initially, the aim of this implementation was:

(a) to achieve a correct coupling with the non-local scheme for daytime turbulence proposed by Black- adar (1978), and

(b) to compare the results against the observational database recorded during the European Field

Experiment in a Desertification-threatened Area (EFEDA, see Bolle et al., 1993) that took place in La Mancha (Spain) during June 1991.

This article deals with the results of that modelling effort. However, this work showed also that semi-arid terrains (vegetation fraction lower than 20% and low average amount of precipitation) exhibit some peculi- arities that are associated with the stornatal resistance properties of the plants. It is reasonable to assume that the characteristics of the vegetation become more important when the soil is dry than when the soil is nearly saturated: the transpiration from plants is expected to be greater than direct evaporation from the superficially dry soil. When the vegetation is sparse this argument begins to be weaker. However, it will be shown that even in this latter case the type of vegetation becomes more important with drier soils. Therefore, the importance of the vegetation species must be emphasised. It is claimed in this paper that a simplification of the vegetation part of the scheme is not advisable in these types of landscapes and an improvement of the NP89 scheme is proposed and compared with the original scheme.

2. Description of the experimental set-up

In order to test the model it was necessary to select a site and date from the EFEDA database for which, there was very weak synoptic and mesoscale atmospheric activity. The Intensive Observation Period (IOP) chosen for this purpose was 23 June 1991 in Tomelloso (La Mancha, Spain). The location of this site can be seen in Figure 1 . The experimental set-up corresponding to this IOP is described in Bolle et al. (1993). It consisted of five automated weather

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C Ferniindez, G Nieto and J A Prego

stations in a 5 km x 5 km square recording vertical gradients of wind and temperature, soil-atmosphere heat fluxes and soil and radiation fluxes at the surface (see Figure 5 in Bolle et al., 1993). Radiosonde launchings every 6 hours were performed in order to study the evolution of the planetary boundary layer. In the experimental area there was a vineyard with individual vines planted 2.5 x 2.5 m apart (see Figure 4 in Bolle et al., 1993).

I I I

Figure 1. Location of the EFEDA-Spain domain and measurement sites.

Some in rittr measured characteristics of the soil and the vegetation are available (Mascart et al., 1993; Droogers et al., 1993; Lacarrkre & Noilhan, 1993). These parameters and variables, together with the vertical profiles of atmospheric variables deduced from the 0600 UTC radiosonde, were prescribed as initial conditions for the one-dimensional model runs. A list of these initial values is shown in Table 1. Note that the value chosen for the minimum stomatal resistance was a typical value for agricultural sites (see Dorman & Sellers, 1989).

The extreme aridity of the terrain must be emphasised: 90% of the landscape is bare soil, and,

Table 1. Initial conditions for the one-dimensional model

Parameter Value

Percentage of sand (S) 45% Percentage of clay ( C ) 19% Initial soil surface temperature (T,) Initial mean soil temperature (TJ Roughness length (for momentum, 2,) Albedo 0.28 Long-wave emissivity 0.985 Soil depth 2 m Leaf area index (LAI) 0.23

Initial soil water content in the 10 cm

Initial mean soil water content (WJ Minimum stomatal resistance (Rs,i,) Maximum stomatal resistance (&,in)

19.5 "C 22.6 "C 0.025 m

Vegetation fraction (veg) 0.1

surface slab (W,) 0.158 m' m-3 0.2 m3 rn -' 30 s m-' 5000 s m-'

in addition, the soil water content is very low. The degree of aridity can be illustrated fairly well by comparing the mean soil water content against the so-called field capacity Wf, as defined by Jacque- min & Noilhan (1990): the value of the soil water content associated with hydraulic conductivity of 0.1 mm/day. The values of Wfc according to these authors are greater than 0.2 m3 m-3 (the measured value for the mean soil water content, W,, in this case) for all soil textural types except sandy soils, but this is not the type of soil analysed in the cam- paign site. This fact has two important implications when the NP89 scheme is used: evaporation from the bare soil fraction does not take place at the potential rate and also the stomata start to close. The low value of the soil water content is probably due to drought which is frequent in the Iberian peninsula. Indeed, certain regions of the southeast part of Spain must be categorised as small deserts. However, the most frequent landscape in the region does have some vegetation, though its fractional area is small. Even certain pine forests are hardly present. It must be emphasised that the semi-desertic landscape is not mainly due to a progressive, long-term regional climate change. Instead, the decrease in the vegetation cover is probably mainly attributable to irresponsible tree felling during the preceding five or six centuries.

3. Implementation of the NP89 scheme in t h e UCM model

The regional atmospheric numerical model of the UCM is described in Castro et al. (1993) and Fernin- dez et al. (1995). A one-dimensional version is used here and, in consequence, only a few components of the whole package will be described.

The original treatment of the soil-vegetation layer was proposed by Anthes et al. (1987). In the version used in this study, it has been replaced by the NP89 Soil- Vegetation-Atmosphere-Transfer (SVAT) scheme. The turbulence in the surface layer and the planetary boundary layer are parameterised following Zhang & Anthes (1 982), but some stability requirements recommended by Zhang (1985) are included in order to save computer time. In the iriitial versions of the model, radiative processes were parameterised according to Mahrer & Pielke (1977). However, both the turbulence and radiation routines had to be modified in order to obtain acceptable results. Specifically, two changes in the turbulence scheme were needed:

(a) in the non-local scheme for free convection the artificial 'convective velocity' reported in Anthes et al. (1987) was removed, and

(b) the distinction between a roughness length for momentum transfer and a roughness length for heat and vapour transfer in the surface layer was necessary.

Modelling evapotranspiration in semi-arid terrains

The stomatal resistance, Rs, is treated in the NP89 scheme as follows:

Following the recommendations of Braud et al. (1993), we have specified roughness length for heat transfer as Zoh=ZO/lO where Zo is the roughness length (for momentum). This means that Zo, is set equal to 2.5 mm. & = 4 m i n 4

LA1 F,F,F,

A disparity between measured and modelled values of the long-wave and short-wave radiative flux reaching the surface revealed the need for a modification of the radiation package. Therefore, the parameterisation proposed by Mahrer & Pielke (1977) was modified according to Paltridge & Platt (1976) and Veyre et al. (1980). Although several absorbers of both direct and ground-reflected short-wave radiation were taken into account and the calculation of long-wave atmospheric emissivities was modified, the results were not entirely satisfactory, as will be shown later. Some researchers of the Centre National de Recherches Mitiorolo- giques (CNRM) in Toulouse and our group have agreed that the lack of a parameterisation of the radiat-

where Rsmi, is the minimum stomatal resistance and LA1 is the leaf area index. The term RSmin F, / LA1 measures the influence of the amount of solar short- wave radiation flux, F2 accounts for the influence of soil water stress on stomatal resistance, F, represents the effect of atmospheric vapor pressure deficit and F, represents the influence of surface layer temperature. The formulation for these terms is described in Appendix B. As will be commented upon in the appendix and experimentally corroborated in section 5, this parameterisation implies an insensitivity of some factors influencing the stomatal resistance to the vegetation type.

ive properties of aerosols seems to be the main cause of that persistent disparity.

4. Control simulation results The SVAT parameterisation was implemented following the description of NP89 and Jacquemin & Noilhan (1990). As regards the soil part of the scheme, the continuous formulation for the main parameters of the soil proposed by Noilhan & Lacarrirre (1991) and Giordani (1993) was included. This formulation tries to over- come the handicap of having only 11 soil types by adjusting a curve with the 11 discrete values of the parameters reported in Clapp & Hornberger (1978). The adjusted functions are listed in the Appendix A (the graphical representation of these functions is depicted in Noilhan & Lacarrirre (1991) ).

A complete discussion about these parameters is given in NP89. As regards the soil part of the scheme, we want to point out the uncertainties inherent to this kind of formulation:

(a) As warned by Ye & Pielke (1993), a scheme that takes into account the soil porosity is preferable.

(b) Clapp & Hornberger (1978) claim that a large standard deviation exists for the hydraulic parameters within each textural soil type, so ‘a blind use of the reported average values may give erro- neous results’. Then, it is argued that a functional form dependent on both the sand and clay percentages (S and C) is always preferable.

(c) The wilting point soil water content WWiit must depend not only on the soil texture, but also on the vegetation species. This is the strongest drawback when the goal is to evaluate the evapotranspiration. As will be shown, the unsatisfactory results concerning the influence of soil water stress upon stomatal resistance was a motivation to try other schemes.

The one-dimensional model was run for 24 hours, although only the first 18 hours are considered for comparison. The initial conditions have been described in section 2. As regards the stomatal resistance species- dependent parameters, a value of 100 W m-* was chosen for R,, (as recommended by Dickinson, 1984, for grasslands and crops), which is the limiting value of the total incoming solar radiative flux. Also value of 0 hPa-’ for g which is a species dependent parameter (measured values for vineyards are not available, so we decided to allow the maximum evapotranspiration according to the scheme; see Appendix B).

Figure 2 shows the comparison between the observed diurnal evolution of the most significant variables as recorded at the five automated stations and the modelled evolution of these variables. I t can be seen that the peak of the modelled net radiation at the surface is near the lower limit of the range of the observed peaks. This can explain the fact that the modelled sensible and latent fluxes are somewhat under-estimated. However, another alternative explanation could be that the slight over-estimation of the soil conductive heat flux could be responsible for the under-estimation in the other two surface fluxes. The first explanation is consistent with the behaviour of the surface temperature. O n the other hand, the redistribution of the excessive conductive flux between the latent and sensible fluxes could improve the results at midday, but the latent heat flux would probably continue to be under- estimated near sunset, while the sensible heat flux would keep being under-estimated in the afternoon. We will try to shed light on this topic in the next sec- tions by means of performing sensitivity tests and changes in the formulation for stomatal resistance.

23 I

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Figure 2. Comparison of control simulation results versus observations. 4MO1, 4M02, 4M03, 4M04 and 4MOI correspond to measured data within a 5 k m x I km area. Solid line corresponds to model results. A: Net radiation (W m-'). B: Sensible heat flux (W m-2). C: Latent beat Pux (W &). D: Soil conductive f7u.x (W ni2). E: Surface temperature ("C). F: 2-metre tempw- ature ("C).

232


content. Jacquemin & Noilhan (1990) have also noticed this behaviour for bare soil (see Figure 3 in their article) and soil water contents corresponding to mid-saturation. We have repeated their experiments and obtained similar results. Also, another set of experiments (not shown here for brevity) using different procedures for determining a soil moisture initial value gives sufficient evidence for claiming that the cause of the ‘low-clay-fraction’ case is the difference in the values of the soil parameters, and this is inde- pendent of soil water content initialisation.

The determination of the temperature at the screen level (2 metres) is based on the formula proposed by Geleyn (1988). However, care must be taken with the roughness length, since it has different values for momentum and heat transfers. The results are acceptable, but an error can be noticed during night hours, in accordance with the evolution of the soil surface temperature.

After comparison with the radiosonde launchings during the daytime, we have verified that the evolution of the planetary boundary layer (PBL) is quite well simulated. The modelled structure and height of the PBL resembles the observations closely. As regards the PBL, the only noticeable imperfection is that the modelled mean PBL temperature is somewhat lower than the observed one, as would be expected. The results are not shown, since our main objective is to evaluate the importance of a good formulation for the stomatal resistance.

5. Sensitivity tests

In order to evaluate the relative importance of an accurate determination of soil texture and vegetation parameters, two sensitivity tests have been performed.

5. I . Clay and sand fractions

Keeping the other parameters unaltered, the percentages of clay and sand were varied within the range of observed soil textures in the neighbouring regions over the Iberian peninsula. The results of this sensitivity test are shown in Figures 3 and 4.

After inspection of the sensible and total (soil plus transpiration) latent heat fluxes in Figure 3, it is clear that changes in the clay percentage induces larger modifications than changes in the sand percentage. This behaviour could be expected, since the continuous formulation of soil hydraulic properties (Appendix A) has been expressed almost entirely as functions of clay fraction. As regards the evapotranspiration, perhaps the differences in the sensitivity tests for clay and sand is an indication of the severity of the Clapp- Hornberger warning we have quoted in section 3. In the next section, we will try to support this hypothesis.

We must also point out the apparently surprising daily evolution of the modelled latent heat flux when the clay percentage is lower than 10%. Such a small value for the clay fraction is uncommon in most countries. However, the result requires some discussion: it is clear that this ‘strange’ behaviour is a direct consequence of the continuous formulations for the parameters a and & (see Appendix A). As the clay fraction comes near to zero, these two parameters tend to become infinite. In the NP89 scheme, C2ref has a basic role in the force-restore equation for the soil water

On the other hand, Figure 4 illustrates fairly well that the decreased latent heat flux obtained when the clay fraction is higher is due to a change in evapotranspiration (while the latent heat flux from bare soil fraction (0.9) remains almost unaltered). This is an important result that we can summarise as follows:

(a) When the clay fraction is lower than 0.1, the direct evaporation from soil increases dramatically. This can be attributed to the continuous formulation of soil parameters. Indeed, the fact that C2rcf (which has a crucial role in the force-restore equation) tends to become infinite for low clay percentages does not have a physical cause. However, soils with clay fractions below 0.1 are marginal, so this fact is not very worrying.

(b) When the clay fraction increases, the changes in latent heat flux are mainly due to the transpira- tionby the vegetation, though the vegetation fraction, veg, is equal to 0.1. Additional experiments have been done with clay fractions as high as 0.43 in order to inspect the results for the range of observed soil textures in the Iberian peninsula; we have obtained nearly the same bare soil flux and zero evapotranspiration. These results are unsatisfactory because there are a variety of vegetation species that are capable of surviving during even more severe drought periods than that of the summer-1991 period in a region with an important fraction of clay. Therefore, it is important to focus our attention in this case.

(c) For the measured soil water content (a low value being very frequent in semi-arid terrain) and a clay fraction higher than 0.1, inaccuracies in the soil texture assignment have negligible influence upon latent heat flux. Such inaccuracies would lead to errors in latent heat flux due to evapotranspiration of plants. But it is crucial to realise that such flux mainly depends on the stomatal resistance which, in turn, significantly relies on the vegetable species (Sellers et al., 1986).

The results obtained after performing the sensitivity test with the sand fraction show that the differences in total latent heat flux are due both to changes in the bare soil part and in the vegetation part. Again, a comparison with the sensitivity test with clay reveals a somewhat unrealistic behaviour that can be attributed

233

C Fernindez, G Nieto and J A Prego

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2 200 L

E- 4 w X

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=l+-e--+ 2 4 6 8 1'0 12 14 16 18

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rn sand f r a c t i o n = 0.33 * sand f r a c t i o n = 0.45

sand f r a c t i o n = 0.57

Figure 3. Results of the sensitivity test for clay and sand fractions. Upper panels: sensible heat jlux. Lower panels: total (soil + vegetation) latent heat flux.

to the dependence of the wilting point moisture content, Wwiln on the clay fraction only (Appendix A). This result support the assertion that a functional form dependent on both the sand and clay percentages (S and C) is always preferable.

5.2. Vegetation parameters

In Figure 5, we show the results of model runs with the observed soil texture and different values for the parameters that influence the stomatal resistance in the NP89 scheme. The lower panel corresponds to a simulation with the initial soil water content value of the first soil slab level (10 cm) equal to the observed value. The upper panel corresponds to initial soil water con-

234

tents obtained after running the model for 24 hours (this value could be representative of a day later in that particular summer, since the amount of rainfall during summer in this region is very low).

In Figure 5, two lines linked with asterisks can be just distinguised. These correspond to two model runs with RGL=30 W m-' and RGL= 100 W m-'. The insensitivity of the NP89 scheme to this species- dependent parameter, at least in semi-arid terrain, can be seen. However, a considerable difference in the total latent heat flux is obtained after a change in the value of g (the second value for g corresponds to pine forest according to NP89) that determines the influence of atmospheric vapour deficit on stomatal resistance.


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clay fract ion = 0.07 a clay fract ion = 0.11

clay fract ion = 0.15 * clay fraction = 0.19 A clay fraction = 0.23 * clay fraction = 0.27 0 clay fraction = 0.31

- - - - , - , - . I 2 4 8 8 10 12 14 1% 18

SIMULATION HOUR

sand fract ion = 0.33 * sand fract ion = 0.45

sand fract ion = 0.57

Figure 4. As for Figure 3, but showing the partitioning between plant transpiration (upper panels) and direct evaporation from soil (lower panels).

Note that the sensitivity to changes in g is more noticeable than the sensitivity to changes in the sand fraction and it is also of the same order of that of changes in the clay fraction (higher than 0.1). Let us recall that changes in clay fraction induce changes in evapotranspiration (dependence of stornatal resistance on soil water stress). The insensitivity to R,, does not seem reasonable, since the importance of F2 and F, is evident. Besides, the less the soil water content the more important it is to determine accurately the vegetation type, even though it is sparse.

These results give sufficient motivation to develop and test some modifications to the NP89 scheme. These modifications and the subsequent results will be presented in the next section.

6. Implementation of Xue's evapotranspiration scheme in the NP89 parameterisation

6. I . The evapotranspiration scheme

The major drawback of the parameterisation of stornatal resistance in the NP89 scheme is the lack of a set of values for the parameters g, RGL, WA, Rs,;, and Rs,, corresponding to different species. Besides, these parameters are inherently difficult to estimate. This is quite evident as regards the terms F, and F2 that have been greatly simplified.

On the contrary, Dorman & Sellers (1989) and Xue et al. (1991) have proposed a classification which includes

235


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Wg = 0.158 m3/m3

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Figure 5. Sensitivity tests for NP89 vegetation parameters. Upper panel corresponds to an hypothetical drier soil. Lower panel corresponds to simulations with the same soil water content as used in the control run.

11 vegetation types and stomatal resistance parameters values corresponding to these types. Their parameterisation is somewhat complex, but those parameters are easy to measure. Our aim is to retain the relative simplicity of the two-layer soil model of ”9, while improving the parameterisation for plants according to the above-mentioned authors. So, the influence of soil water stress and photosyntetical activity on the stomatal resistance will be modified in the following manner.

Xue et al. (1991) obtained the empirical equation for the soil water stress term:

F, = 1 - exp (-C2 (C, - ln(v)))

where w is the soil water potential in centimetres. The soil water potential can be expressed as a function of

236

soil texture and soil water content following NP89:

where vsaI is the soil water potential at saturation, b is the slope of the retention curve on a logarithmic graph, W,, is the saturated soil water content and W, is the initial soil water content.

According to Clapp & Hornberger (1978), b must be estimated empirically for each specific soil type. At this point, the sole difficulty is how to relate wI., to soil texture. Again, the only way to achieve this is to use the data sample studied by Clapp & Hornberger (1978). According to these authors, the antilog of the mean log(vSat) is more representative, so we chose these values for each textural class. However, the warnings of Clapp and Hornberger when dealing with vSat are more severe than when dealing with the slope of the retention curve. Since the whole Clapp-Hornberger database is not available, there are principally two reasons for being careful with this topic: the large standard deviation of vsaI (and the subsequent need for a log transformation) and the fact that there is not a clear correlation between clay fraction (C) and wlal (while b increases uniformly as C increases).

The clear linear relation between b and clay fraction support the continuous formulation proposed by Giordani (1993) for this parameter. However, the standard deviation of b is also high. On the other hand, Clapp and Hornberger pointed out that the large standard deviation of wsSl is mainly due to a strong positive skew provoked by relatively few points separ- ated from the mean value. To quote these authors, ‘although both mean(vr,,,) and mean(y,,(log) ) increase with finer soils, neither is well correlated with the mean clay fraction; hence texture is not a good indic- ator of ws.,’. We propose the following alternative interpretation: once the strong skew has been over- came, it can be deduced that vsal is related both to the clay and sand fractions. This assertion can be supported by fitting a polynomial vial = P(C,S) by some mathematical methods.

First, the irregularly distributed points Pij = P( CJ,) must be used to construct a regular gridded dataset. This can be done by using some graphical software package. Next, a multivariate interpolation as described by Isaacson & Keller (1966) or a polynomial approximation of surfaces as presented by Gerald & Wheatley (1989) can be employed to program a sub- routine. We have verified that the two methods give similar results. In Figure 6, the surface wsat = w5., (C,S) is shown by using the second method. It can be observed that the values of the saturated soil water potential corresponding to the original 11 points can be retrieved with great accuracy by using that algorithm.


terrains). Other types of trees such as olive trees, ilexes and a variety of fruit trees, shrubs and vines are present in this zone even during the most severe dry periods. Therefore, we should point out that the classification of vegetation types given by Xue e t al. (1991) is incom- plete for mesoscale models and an additional measurement effort is needed. In our case study, the vines are in their initial stages in the early summer, so it is reasonable to think that they can transpire even with drier soils. Since the values of C, and C, are unknown, we can only elucidate in an indirect manner the imper- fections of the control simulation. It will be shown that performing sensitivity tests with the vegetation parameters is an excellent way to achieve that objective.

SATURATED SOIL MOISTURE POTENTIAL (em)

’:: F\

6.3. Sensitivrty test for vegetation parameters

CLAY PERCENTAGE

Figure 6. The saturated soil moisture potential as a function of clay and sand fractions using a polynomial approximation.

In this manner, values of ys.,, y and F2 can be calculated as functions of the soil texture. In our case study, the low soil water content determines that all vegetable species with C, < 7.52 close their stomata completely. In the classification of Xue e t al. (1991), only the needleleaf-decidious trees can transpire (C , = 7.8) under such circumstances. However, only 11 vegetation types are tabulated by these authors. In order to test the model with this alternative parameterisation, we have selected the values C, = 7.625 and C2 = 5.66 as a reference, since the simulated evapotranspiration with these values resembles quite well the results corresponding to the control simulation.

6.2. Sensitivity test for soil texture

The first test we have performed with the alternative formulation for F2 is to repeat the sensitivity tests for soil texture. The results are shown in Figure 7. As could be expected, the response of the bare soil part is almost identical to that in the previous scheme, while the plant transpiration shows different behaviour. For lower clay fractions, ySat is greater (see Figure 6), but the slope of the retention curve decreases (see Appendix A); if we remember that b appears as an exponent the behaviour of the evapotranspiration seems reasonable. As we increase the clay fraction the parameter b increases too in such a manner that ln(y) is greater than C,. Finally, if the sand fraction is 0.33, yla, increases and transpiration is not possible due to the higher value of ln(y).

Needleleaf deciduous trees (pines) are not the sole vegetation species that can survive during a drought in southeastern Spain (and other similar semi-arid

parameterisation for F2. For comparison, in these tests the control simulation would be the curve with asterisks in Figure 8; again, only the value of one parameter is changed while keeping the others unaltered. As could be expected, knowledge of the value of C, is essential; as mentioned, if C, <7.52 the plants close their stomata (though this does not imply the death of the plant). The lower panel in Figure 8 reveals a relative insensitivity to the value of C,. The great influence of g can also be observed (this fact was evident in the sensitivity tests with the original scheme). The curve with filled triangles in Figure 8 corresponds to the following hypothetical case: F2 = 1 (negligible soil water stress influence on stomatal resistance), F, = 1 (g = 0, as in the control simulation) and F4 = 1 (it is easy to verify that in the NP89 scheme the value of F4 is always close to I). Therefore, this curve represents the maximum evapotranspiration by using the NP89 scheme as well as the modified scheme in this case study. As commented before, the value of the species- dependent parameter RGL has a negligible influence on evapotranspiration. O n the other hand, the maximum evapotranspiration is achieved at 1400 UTC hour with this scheme. Therefore, we can argue that neither an improvement in the soil part of the scheme (i.e. a redistribution of the over-estimated conductive heat flux between the under-estimated latent and sensible fluxes) nor a change in the vegetation parameters can alleviate the noticeable under-estimation of the total latent heat flux after midday. In consequence, a more realistic formulation for the main contribution to the stomatal resistance (the influence of the short-wave radiation flux, since the majority of plants stop transpiration at night regardless of the other vegetation parameters) has been implemented.

6.4. Improvement to the stomatal resistance

Following the more sophisticated and physically based parameterisation proposed by Sellers et al. (1 986),

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v v

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clay fraction = 0.07 A clay fraction = 0.11

clay fraction = 0.15 * clay fraction = 0.19 A clay fraction = 0.23 Q clay fraction = 0.27 0 clay fraction = 0.31

sand fraction = 0.33 * sand fraction = 0.45

sand fraction = 0.57

Figure 7 . As for Figure 4, but after computing the stornatal resistance dependence upon soil water stress with the scheme of Xue et al. (1991).

Sellers et al. (1989) and Xue et al. (1991), the term (Rs,, F, / LA1 ) has been replaced by:

The parameters a, b and c are species-dependent constants, Fo is the flux of photosynthetically active radiation (PAR) above the canopy (55% of the total solar radiative flux), k is the extinction coefficient of PAR within the canopy and G is the leaf angle projection in (' ' pff+G ' the direction p. Following Tucker & Sellers (1986), we express k as follows:

pfe-"""I + G pf + R, = - -In

where N, is the greenness of the vegetation and is assumed to be equal to 1, p is the cosine of the solar zenith angle, and f is given by: k=(l-w*)"Z

where w, is the leaf scattering coefficient for PAR and is assumed to be equal to 0.2.

238


where x is the leaf angle distribution function, which is equal to 1 for horizontal leaves, O for spherical leaf angle distribution and -1 for vertical leaves. In order to make comparisons with the NP89 parameterisation, we suppose that F2 = F, = F4 = 1 . In the classification of vegetation types proposed by Dorman & Sellers (1989) only the ‘broadleaf-deciduous trees with wheat’ biome has F, = 1, so we choose the values of the parameters a, b and c corresponding to that vegetation type. It has to be mentioned that the above equation for Rs proposed by Xue et al. (1991) has been slightly modified; the Xue et al. formulation includes the vegetation fraction (teg’) in the denominator, but we have omitted this because in the NP89 scheme the evapotranspiration flux and the soil bare flux are computed separately.

SIMULATION HOUR

* C1 = 7.625 A comparison of the results with the NP89 para- 0 C1 = 8.00 meterisation and those obtained with the scheme of

c 1 = 7.55 Sellers e t al. (1989) is shown in Figure 9. This shows the importance of the specification of the mean leaf orientation, in contrast with the insensitivity of the NP89 scheme to the RGL value. Note also the relatively high value of transpiration in the afternoon when the leaves are not horizontal (indeed, the vine leaves tend to hang out vertically). We have omitted here the results of a sensitivity test with different values of a, b and c for brevity. Perhaps, a measurement of these time-invariant morphological parameters in the site would have lead to more satisfactory results. All the tests with the Sellers’s scheme reveal that a classification of vegetation types having different parameters influencing the stomata1 resistance is needed for mesoscale models in order to improve the calculation of surface fluxes. This urgency is more evident for mesoscale studies than for global climate models, since there exists a noticeable heterogeneity of land uses at the

a 2 10

‘ 0 2 4 6 8 10 12 14 16 18 regional scale, at least in semi-arid regions. SIMULATION HOUR

* CONTROL o g - - 0.027 hPa-’

C 2 = 6.4 a c 2 = 4.3 A F ~ = Fg = FA = 1

Figure 8. Sensitivity test for the species-dependent parameters of the vegetation using the scheme of Xue et a/. (1991).

Sellers et al. (1 989) recommended the following expression for G:

with:

$, = 0.5 - 0.633 x - 0.33 x2 $2 = 0.877 (1 - 2$, ),

7. Discussion

It has been shown that the treatment of plant transpiration in some SVAT schemes designed for mesoscale studies (Noilhan & Planton, 1989; Mihailovic et al., 1992) is very simple in comparison with other physically-based parameterisations used in General Circula- tion Models (GCMs). However, the opposite would be preferable in the state-of-the-art concerning this topic. The main reason for claiming this fact is the heterogeneity of vegetation types at the regional scale. O n the other hand, in GCMs there are sources of error growth more important than the inaccuracies in the vegetation (for instance, the horizontal diffusion and the duration of the temporal integration). These sources of error are inherently more controlled in mesoscale models.

Probably, further measurements would reveal the urgency for an improvement of transpiration schemes

239


F v

2 200 - cr,

t 16 ch

18

2 50 G 0 E

* VERTICAL LEAVES 0 S P H E R I C A L DISTRIBUTION rn HORIZONTAL LEAVES A NP89 PARAMETERIZATION

Figure 9. Sensitivity test for the distribution of leaf angles using Xue et al.’s (1991) scheme and assuming the ‘broadleaf deciduous trees’ biome (there are no measured parameters for vineyards). It is compared with the NP89 formulation.

on a small scale. It is obvious that the determination of vegetation parameters is essential when the vegetation fraction is 1 (i.e. the bare soil fraction is 0). Another case that reveals the need for a refinement in the transpiration scheme is the semi-arid terrain, though it would seem somewhat paradoxical. In the selected case study, the vegetation fraction was only 0.1. However, the importance of the plants is very significant as can be seen in Figure 5; specifically, in the lower panel the peak value for the evapotranspiration is 44.3 W m-’ and the peak value for soil evaporation is 122.5 W m-’, while in the upper panel these values are 47.5 W m-’ and 86.3 W m--’ respectively. Recently, Droogers et al. (1993) and Verhoef et al. (1996) have reported that the soil water content at the IOcm depth frequently decreased to values near 0.06m3m-’ during the

240

EFEDA study, while the mean soil water content remained almost constant and equal to 0.18 m3 m-3 (on the other hand, the vines were in a growth period and the leaf area index increased during the experiment, as showed by Bolle et al., 1993). We may conclude that in severe drought periods the knowledge of the plant parameters controlling transpiration is very important, even with low vegetation fractions.

In this case study, we have shown that the influence of plant morphological parameters is more important than that of the soil texture when the total latent heat flux is calculated. However, a different regime is observed when the clay fraction falls below about 0.1. This result is consistent with the results presented by Jacquemin & Noilhan (1990) and Mihailovic et al. (1992). These authors noted a clearly different behaviour in the soil evaporation for sandy soils, but this can be attributed to the soil hydraulic parameters in those marginal soil textures. Therefore, we argue that an accurate soil texture parameterisation is important for long-range simulations or when the drainage and run- off occurs (Wilson et al., 1987), but not so much for short-range forecasting in which soil water content is periodically reinitialised.

This study indicates that a continuous formulation of the soil hydraulic parameters as a function of both clay and sand fractions is always more reliable than a functional form depending on clay (or sand) fraction alone. In this latter case, it is likely to obtain the following result: insensitivity of the modelled evapotranspiration to changes in the textural fraction omitted in the formulation, a behaviour that seems to be very unrealistic.

There are some indications that the slight disparity between observed and modelled surface fluxes in the control simulation is due to an unsatisfactory specification of the vegetation cover. As can be observed in Figure 2, the conductive heat flux is clearly over- estimated. A simulation with a lower vegetation fraction (not shown) has revealed that the error in the conductive flux is greater in this case. O n the contrary, if we change the value of the vegetation fraction to 0.2, all fluxes are fairly similar to observations. However, in the simulations performed with greater evapotranspiration and ‘veg’ = 0.1 the conductive flux is reduced and the total latent heat flux is increased. This could be expected, since ‘Conductive flux = Net radiation - Sensible flux - Latent flux’. Therefore, we may conclude that the disparity between observations and simulation results is mainly due to inadequate specification of the vegetation parameters. This outcome has already been suggested by Ducoudrk et al. (1993) after their comparative study of General Circulation Models results: ‘Most of the discrepancies obtained between the models is due to the difference in the parameterization of evapotranspiration. The simulated fluxes and surface temperatures would probably


flux and RGI, is a limit value varying from 30 W m-’ for a forest to 100 W m-’ for a crop. It is easy to verify that the minimum stornatal resistance due to this factor takes place when PAR = ( R G L LAI)/2. O n the other hand, during the night hours PAR=O and, logically, the stomatal resistance due to this factor reaches a maximum. It is also easily verifiable that these limiting values for the stornatal resistance due to this one factor tend to converge in the case of small values for LA1 (for instance, in semi-arid terrains).

become more sensitive to the changes in the formulation of soil hydrology in a less vegetated area’.

Appendix A. Functions used to calibrate soil hydraulic properties

Giordani (1993) has proposed the following continuous formulation of soil hydraulic properties as functions of the clay and sand percentages (C and S, respectively):

b = 0.137 C +3.501 a = 0.73242 (C)4’.539 p=O.134C+3.4

CIS,, = lo-’ (5.58 C + 84.88) CZref = 13.815 (C)4.954 C,,,, = 10” (-0.015571 S- 0.01441 C + 4.7021) W,,, = lo-’ (-1.08 S + 494.305) W, = 89.0467 lo-’ (C)0.3496

WwilI = 37.1342 lo-’ (C)”’

where b is the slope of the retention curve, a andp are coefficients of the soil water content corresponding to balanced gravity and capillarity forces, Cis., and CZref are constants needed for the calculation of the two terms of the forcerestore equation for soil moisture, CGrat is the soil thermal coefficient at saturation, W,, is the saturated soil moisture content, Wf, the field capacity moisture content and Wwilt the wilting point moisture content.

Appendix B. Calculation of the stomatal resistance

The stomatal resistance is treated in the NP89 scheme as follows:

where RSmin is the minimum stornatal resistance and LA1 is the leaf area index. The term RSmin Fl / LA1 measures the influence of the amount of solar short- wave radiative flux on plant transpiration. Fl is expressed as:

4 = l+f f +Rs,,,

%,ax

(0.55& )*

R G L LA1 f =

where 0.55 RG is the photosynthetically active radiation (PAR), RG is the total incoming solar radiative

The term F, accounts for the dependence of stornatal resistance upon soil water stress. The formulation is as follows:

If W, > W, then F, = 1

If Wwilt I W, 5 W, then F, = w, --WwiII

w, - WWI, If W, c Wwilt then 8 = lo4

where W, is the soil water content, Wfc is the field capacity moisture content and Wwilt is the wilting point moisture content.

The main drawback of this formulation is the unrealistic independence of F, upon vegetation characteristics.

The factor F3 takes into account the effect of atmospheric vapour pressure deficit:

5 = 1 - g (em, (T,) - e,)

where esa,(TJ is the saturation vapour pressure at the temperature T, of the surface layer, e, is the partial vapour pressure in that layer and g is a species- dependent parameter.

Finally, F, represents the dependence of stomatal resistance upon air temperature:

4 = 1 - 0.0016 (298.0 - T,)

Aknowledgements

This study was supported in part by CEC ‘Human Capital and Mobility’ Grant, contract No. ERBCHBGCT920232. We are indebted to C. Gal- lardo and to Professor M. Castro for their valuable suggestions. C. Ferndndez greatly appreciates com- ments by Dr Noilhan, Dr Bougeault, P. Lacarrere and S . Amos.

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Documents

Modelling evapotranspiration in semi-arid terrains: Comparison of two schemes