The Parameterization of Sub-Grid Scale Processes in Climate Models

Transcription

1 Hydrological Interactions Between Atmosphere, Soil and Vegetation (Proceedings of the Vienna Symposium, August 1991). IAHS Pubi. no. 24, The Parameterization of SubGrid Scale Processes in Climate Models AJ. PITMAN School of Earth Sciences, Macquarie University, North Ryde, 219, NSW, Australia ABSTRACT Three methods of increasing subgrid scale heterogeneity in the representation of the land surface in AGCMs are described: a method of spatial aggregation of parameter data to AGCM resolutions which retains the original variability in the data in subsequent climate simulations; a parameterization of subgrid scale precipitation, interception and runoff; and an attempt at a model of subgrid scale lakes for climate models. The relative sensitivity of the land surface to these modifications is discussed. It is shown that the aggregation of data is likely to improve simulations while incorporating the precipitation or lake parameterizations will improve the level of realism in the land surface models, but may not improve the climate simulations. INTRODUCTION Atmospheric General Circulation models (AGCMs) are useful tools for predicting the effects of a variety of perturbations on the climate. However, their value is reduced by the coarse resolution necessary due to computational restrictions. AGCMs typically use grid resolutions of between 3 x 3 and 7 x 5 which is too coarse to represent many important land surface processes. The parameterization of the land surface in AGCMs has improved considerably over the last few years. The BiosphereAtmosphereTransfer Scheme (BATS, Dickinson et ai., 1986), the Simple Biosphere model (SiB, Sellers et al 1986), Ambramopolos et al.'s (1988) model and Bare Essentials for Surface Transfer (BEST, Cogley et al, 199) all represent the surfaceatmosphere exchange of moisture, heat and momentum with realism at reasonable levels of complexity. However, most of the development in land surface models has been directed towards improving the physical representation of surface processes. Hence detailed soil and vegetation models have been developed which represent quantities in the land surface system using prognostic variables. AGCM grid elements can be partially or completely covered by water, soil, vegetation or snow and submodels are developed to represent, at varying levels of complexity, the characteristics of each surface. Excluding ocean surfaces, it is rare for an area the size of an AGCM's grid element to be uniformly covered by one surface type. Hence, land surface models split :he grid element into fractions, which are treated separately, to calculate the temperature, wetness and turbulent energy fluxes. The quantities calculated for each 65

2 A. J. Pitman 66 fraction are then aggregated to give effective quantities for the entire grid element. Splitting an AGCM's grid square into soil, vegetation, water or snow fractions means, that quantities predicted for each fraction have to be parameterized since they are "subgrid scale" processes. This paper considers the implications of subgrid scale variability with respect to several processes. The distribution of precipitation within a grid element, and the resulting effects on interception and runoff is reviewed and the possible importance of representing small amounts of permanent fresh water within a grid element is discussed. Initially, however, mechanisms for representing the subgrid scale heterogeneity of soil and vegetation data are discussed with reference to techniques which provide a means to retain the spatial variability in these quantities for climate simulations. AGGREGATION OF LAND SURFACE DATA All land surface models require data for a number of soil and vegetation parameters (see Table 1). There are several basic sources from which these data can be derived, most of which are provided at 1 x 1 resolution (HendersonSellers et al, 1986). TABLE 1 Input parameters for the three simulations. Variable Tundra Fictitious Coniferous Variable Tundra Fictitious Coniferous SW,c LW,c SJU A * Zc s, d, /««. LAI^ Xvoid X fi"p X w ;u "/tap W w m b K h s w fcap is the volume ratio of water to porosity (X voii ) for a saturated soil, w w! is the volume ratio of water to the wilting point (X,. ) for a saturated soil and s is the soil colour. A vmax is the maximum vegetated fraction of the grid element, LAI max is the maximum leaf area index, S, is the seasonal range of L Ah S AI is the stem area index, d, is the lower soil layer depth (m), z c is the canopy roughness length (m), o^ is the visible canopy albedo, a LWc is the nearir canopy albedo and f roo, is the fraction of roots in the upper soil layer. AGCMs do not "recognise" the surface type represented at the surface. A classification based on names such as grassland or desert is merely a convenience since any broad classification will contain enormous inherent variability. Rather than "ecotype" or "soil type" a land surface model requires parameter values associated with the characteristics of the "effective" surface ("effective" is used to describe the entire AGCM surface which can be a combination of the characteristics of bare ground, vegetation, snow and water). Many AGCMs use a "most common" procedure for aggregating 1 x 1 data to

3 67 The parameterization of subgrid scale processes in climate models the resolution of the AGCM (e.g. Dickinson et al., 1986). Here, tests are performed to determin whether chosing "most common" (here assumed to be either tundra or coniferous forest) leads to significantly different results compared to using aggregated data. The aggregation of data simply involves averaging the input parameters (Table 1) according to the frequency of individual "ecotypes" of "soil types" prior to the simulation. This can lead to parameter values which do not have parellels in nature (hence termed "fictitious"). This technique involves piping 1 x 1 data through a lookup table and subsequent averaging, in contrast to chosing the "most common" in a grid element and then assigning values. The former technique thereby retains all the information provided in the input data sets. Three simulations have been performed using BEST to examine the model sensitivity to the aggregation procedures. These simulations were for "tundra", "coniferous forest" and a fictitious ecotype represented by an aggregation of these two ecotypes with 5/9ths tundra and 4/9ths coniferous forest. Table 1 shows the parameter values used in the simulations. ATMOSPHERIC FORCING In each simulation discussed here using BEST and BATS the climate forcing is prescribed. A reasonable amount of precipitation occurs but is distributed uniformly within the month with the frequency of events set at every 5 hours for tropical forest and every 5 days for other ecotypes. The solar radiation varies with latitude, season and time of day. The monthly mean air temperature is prescribed and a diurnal variation is imposed upon this value. Relative humidity, wind speed (3 m s' 1 ) and the atmospheric pressure (1 hpa) are all constant. Most of these data were derived from World Weather Records (1957). Although more realistic forcing could be derived, the method used here is considered satisfactory because the nature of standalone experiments reduces the value of sophisticated forcing due to the lack of surfaceatmospheresurface feedbacks. CONTROL SIMULATIONS Fig. 1 shows a set of surface wetness curves generated by BEST for an annual cycle. The parameter data used to produce the 9T:C (tundra), T:9C (coniferous forest) and 5T:4C (fictitious) curves was shown in Table 1. The remaining curves are represented by specified fractions of tundra and coniferous forest. The input data is averaged prior to the simulation and only one simulation is performed for each curve. Figure 1 shows two features: first small changes in the input parameters lead to significant changes in the results; second these differences are nonlinear. In particular, note how the T7:C2 curve is closer to the T5:C4 result than to the control simulation for tundra. The soil moisture changes lead to similar changes in the turbulent energy fluxes. These results show that aggregating data leads to different results compared to choosing the most common ecotype as representative of the grid element. Incorporating small amounts of coniferous forest into a grid element otherwise

4 A. J. Pitman 68 composed of tundra has profound implications as small amounts of coniferous forest affects spring snow melt, albedo, wetness and the surface energy balance. 1. </!.9 LU Z h UJ >.8 LU o < H.7 c/i < Q:.6 in LU ce Ê.5 h.4 T J T 1 i i i i i i % n i i \ J 1 / I \ /4'J \\ \\ /W J F M A M J J A S N D (Month) FIG. 1 Annual cycle simulation of soil moisture by BEST for 6 different aggregations of tundra and coniferous forest parameters. The key is explained in the text. Units are fraction of saturation. I! I 'rr 9T, C 7T, 2C 5T, 4C ' 4T, 5C _ 2T, 7C T, 9C I _j...l, If the "most common" ecotype is chosen, only the two control curves in Fig. 1 could be simulated. This leads to a loss of variability and a reduction in the spatial heterogeneity. The T5:C4 curve in Fig. 1 does appear to represent an average of the two control simulations, but the aggregation procedure suggested here seems most important when an AGCMs grid element is largely composed of one ecotype with small, but significant, amounts of another. Under these circumstances, the "most common" procedure could lead to very misleading results. The aggregation technique advocated here also provides the potential for further flexibility and realism in the prescription of input data for the land surface. Climate models usually only use the "primary" vegetation type from the 1 x 1 data sets. One advantage of the procedure discussed here is that since only parameters are aggregated, the methodology could utilise the "secondary" vegetation type for available data sets. It seems reasonable that the primary and secondary data could be aggregated to provide an improved estimate of the grid element effective value. The secondary data would have to be weighted, but Wilson and HendersonSellers (1985) provide information on the relative fraction of the primary and secondary vegetation type this need not represent a problem.

5 69 The parameterization of subgrid scale processes in climate models SUBGRID SCALE PRECIPITATION Variables predicted by AGCMs are assumed to be representative of an entire grid element. AGCMs predict whether precipitation occurred, and whether it was formed by large (e.g. frontal) or small scale (e.g. convective) processes. However, AGCMs currently simulate both large and small scale precipitation as a uniform depth of water over the entire grid element (i.e. the spatial distribution of precipitation in AGCMs does not differ as a function of precipitation type). Thus if a smallscale precipitation event, such as a cumulus shower is simulated, the precipitation is spread out, uniformly, over the entire grid element. Hence a widespread, less intense event occurs in the model instead of a localised and relatively intense one. In AGCMs which include vegetation the intensity of precipitation is especially important. A dense canopy might intercept and reevaporate virtually all the precipitation from a convective event which is spread out over a full grid element since the precipitation intensity is artificially reduced. In contrast, if the precipitation were to be spatially restricted, the higher precipitation intensity would result in throughfall or leafdrip reaching the soil moisture store or increasing runoff. The time difference of the evaporation of precipitation stored on the canopy, and that stored in the soil is considerable since canopies evaporate intercepted precipitation at the potential rate, while soils offer a high resistance to it (Rutter, 1975). The sensitivity of BATS to incorporating the parameterization suggested by Warrilow et al. (1986) and Shuttleworth (1988) for distributing precipitation nonuniformly within the grid element for both the canopy and soil components of the model was investigated by Pitman et al. (199). They showed that the assumption of Warrilow et al. (1986) and Shuttleworth (1988) that the local precipitation rate, over the rain covered fraction of the AGCM grid box (jo.) followed a probability distribution was reasonable, but that it led to a very different simulation of the surface hydrology. The results of changing JJ. were reported by (Pitman et al, 199) and are not repeated here. However, Fig. 2 sums up their results and shows that the hydrology predicted for tropical forest is very sensitive to the parameterization scheme used. These results indicate that the land surface is sensitive to certain subgrid scale processes and implies that experiments conducted with these types of parameterization must be clearly differentiated from those which do not since Fig. 2 shows that the results are largely incomparable. SUBGRID SCALE PARAMETERIZATION OF WATER Incorporating a model of open water into AGCMs is only worthwhile if it affects the simulation of the climate for which it has to be relatively common over significant spatial areas. Data derived by Cogley (199) provides the percentage cover of fresh water at 1 x 1 resolution and showed that over North America and large areas of Europe and Asia, open water surfaces make up 12% of many 5 by 5 grid elements. Furthermore, the occurrence of grid squares with > 1% open water are common associated with the Great Lakes, the Canadian shield and isolated grid squares in Africa and Asia.

6 A. J. Pitman 7 H = 1. M =.5 (1.1 M A M J J A S O N D Month J F M A M J J A S O N D Month FIG. 2 The seasonal variation in the precipitation, runoff and evaporation rates (mm month" 1 ) for (a) the control simulation (BATS without the \l parameterization), (b) for BATS with the (i parameterization with i = 1., (c) with (X =.5 and (d) with (. =.1. Precipitation, in each case, is identical, and is plotted downward from the top 'X' axis. Runoff is plotted downward form the lower 'X' axis, while evaporation is plotted upwards from the lower 'X' axis, and is shaded (after Pitman et al, 199). AGCMs which fail to account for subgrid scale permanent lakes underestimate the overall wetness of many grid elements. However, the overall frequency of small lakes is generally quite low (i.e. small lakes generally cover < 2% of a grid element). This leads to limitations in the computational effort available to represent small lakes in AGCMs where they only cover small fractions of the grid element. Over areas which are partly open water and partly soil or vegetation, the computational expense of simulating each element with realistic, physicallybased models is probably prohibitive suggesting that physical lake models are probably inappropriate for AGCMs at present.

7 71 The parameterization of subgrid scale processes in climate m METHODOLOGY In most AGCMs the land surface is split into its component parts so A + A + A = 1 (1) g ' v where A is the fractional cover of bare soil, A s is the fractional cover of snow and A v is the fractional cover of vegetation. Each component lies in the range» 1. In the scheme proposed here a further factor, A w, is added to represent the fractional cover of small lakes (from Cogley, 199). Equation (1) is rewritten as A+A+A+A=l (2) g S V W The addition of a further surface type requires a pro rata reduction in the areas of the existing types. Ratios A g^s and A v are reduced by multiplying by the fraction la w so the ratio A g :A s :A v remains constant but the absolute amount of the grid element covered by each component is reduced. In AGCMs a p factor is often used to describe "how wet the surface is" for the calculation of the latent heat flux. Since the atmosphere simulated by an AGCM has no knowledge about individual surface elements and only requires grid means of temperature, roughness and wetness, in the presence of open water the (3 factor must be redefined. Here, for fraction A g a _ r u u Pw w /iv ' ~ A + A u w where (3, is the mean wetness of the soil and open water surfaces, P is the soil wetness and (3 W = 1.. Although parameterizations for p vary (e.g. Carson, 1987) the methodology described here is independent of the exact definition of P and can be used in any AGCM. This approach is limited in a number of ways. There is no effort to model lake temperature, heat storage, lake overturn, etc. The methodology described here is intended as a free adjustment to land surface schemes to account for a general underestimation of P where there are significant amounts of open water. Modifying P to incorporate A w is reasonably straightforward. For consistency, the roughness length and albedo of the grid element must also be modified to account for the characteristics of open water (see Pitman, 199). All land surface models calculate a e and z c irrespective of their individual complexity hence incorporating A w does not require significant modifications to existing schemes. TROPICAL FOREST RESULTS Using prescribed atmospheric forcing four simulations were performed for a tropical forest: a control with the standard version of BEST, then with 1%, 2% and 3% open water. The results discussed here are restricted to mean monthly water balance

8 A. J. Pitman 72 results. Fig. 3 shows the results for a tropical forest ecotype for runoff and evaporation simulated by BEST. In each case, the precipitation forcing is identical. The basic pattern shown here is that evaporation increases and runoff decreases as A w increases. Fig. 3a shows the control results where evaporation is relatively constant through the year with runoff increasing during the summer as the soil gets wetter and precipitation intensities increase. Fig. 3b shows that by increasing A to 1%, evaporation increases but the seasonal pattern remains similar to the control. Runoff is reduced to compensate for the increased evaporation and because incorporating A w reduces the area of A (a) Trop cai forest Av». J F M A M J J A S N D 11 ' i (b) g 1 E 2 Ë a. 5 Ul t1 i2 S 4 Trop ica fores! Aw =.1 J F M A M J J A S O N D i i i f i ' 1 i i (c) Tropical forest, Aw =.2 (d) Tropical forest, Aw =.3 \ 1 ; 2 I J F M A M J J A S O N D F M A M J J A S O N WWsMr?** alii ^ZZXZZi FIG. 3 The seasonal variation in the precipitation, runoff and evaporation rates (mm month" 1 ) for (a) the control simulation (BEST with A w = ) (b) for BEST with A w = 1%, (c) best with A M = 2% and (d) with BEST with A w = 3%. Bars as for Fig. 1.

9 73 The parameterization of subgrid scale processes in climate models Fig. 3c shows the simulation for A w = 2%. Runoff is reduced to approximately 5% of the control value. Evaporation is generally increased by ~5 mm month" 1 although during February and March evaporation is increased by ~75 mm month" 1 leading to a different seasonal pattern. Fig. 3d (A w = 3%) shows both a general increase in evaporation throughout the year, and markedly higher evaporation in the spring. This pattern is related to the precipitation forcing used to drive BEST. Fig. 3 shows minimal precipitation in winter which leads to a relative drying which restricts evaporation even though the potential evaporation rate is very high in the spring and autumn (due to seasonal variations in the available energy). Increasing A w forces more water to be available for evaporation and spring is the season when a greater proportion of this available water can be evaporated. Fig. 3d also shows that runoff is greatly reduced due to the higher evaporation and since less of the grid element is covered by soil. The parameterization of subgrid scale open water described here is obviously highly simplistic. More complex lake models do exist (see review of by Henderson Sellers and Davies, 1989), and have been shown to perform well for specific regions. However, AGCMs require a generic model which can be embedded into existing models with minimal computational cost and site specific data. These results show that the model hydrology is sensitive to incorporating A w with decreasing runoff and increasing evaporation as A w is increased. Increasing A w to 1% did not lead to a dramatic change but evaporation did increase by 12 mm month" 1 and runoff decreased by > 15% in most months. This sensitivity to small increases in A w shows that although the methodology may be flawed it does demonstrate that more careful consideration of open water in AGCMs may be necessary. Larger increases in A w lead to more dramatic results as expected, but it is the changes due to small increases in A w which have the greatest implications. SUMMARY AND DISCUSSION This paper has highlighted three generally ignored processes in the land surface of AGCMs. The method of aggregating 1 x 1 data to AGCM resolutions by assuming the "most common" ecotype is flawed for areas where significant natural variability exists. By aggregating the original 1 x 1 data by specifying the parameter values for a soil or ecotype at 1 x 1 and then averaging into a "fictitious" ecotype leads to more appropriate data being used to build land surface schemes. The two subgrid scale sections discussed precipitation and lakes. The parameterization of subgrid scale precipitation in AGCMs is important but great care is needed unless (J. can be predicted by the AGCM. The land surface hydrology is very sensitive to the magnitude of [J. and simulations will be meaningless if it is miscalculated. The lakes section identified a regionally significant omission in AGCMs which leads to large differences in evaporation and runoff if incorporated. Overall, incorporating (J. or lake schemes is likely to be a factor once BATS type schemes are standard in AGCMs. There are inappropriate unless the land surface is physically represented and a canopy parameterized. The aggregation of land surface data is a more general problem of greater concern. The surface responds in nonlinear ways to an addition of small amounts of forest to a tundra ecotype while the

10 A. J. Pitman 74 effects of small amounts of forest on snow melt is considerable. An examination of data aggregation techniques and the discarding of the "most common" procedure for chosing the ecotype represented for a grid point is recommended. ACKNOWLEDGMENTS A.J.P is a Macquarie University Research Fellow. This research was, in part, supported by a grant from the Australian Research Council. REFERENCES Abramopoulos, F., Rosenzweig, C. & Choudhury, B. (1988) Improved ground hydrology calculations for global climate models (GCMs): Soil water movement and évapotranspiration. J. Climate i, Carson, DJ. (1987) An introduction to the parameterization of landsurface processes Part 2. Soil heat conduction and surface hydrology. Meteorol. Mag. 116, Cogley, J.G. (199) GGHYDRO: A terrestrial hydrographie data set (In preparation). Cogley, J.G., Pitman, AJ. & HendersonSellers, A. (199) A land surface for largescale climate models. Trent Climate Note, 91, Trent University, Peterborough, Ontario, Canada. Dickinson, R.E., HendersonSellers, A., Kennedy, P.J. & Wilson, M.F. (1986) Biosphere Atmosphere Transfer Scheme (BATS) for the NCAR Community Climate Model, NCAR Tech. Note, NCAR, TN275+STR. HendersonSellers, A., Wilson, M.F., Thomas, G. & Dickinson, R.E. (1986) Current global land surface data sets for use in climate related studies, NCAR tech. note, TN272+STR. HendersonSellers, B. & Davies, A.M. (1989) Thermal stratification modelling for oceans and lakes. Ann. Rev. Num. Fl. Mech. and Heat Transf. 2, Pitman, A.J., A simple parameterization of subgrid scale open water for climate models, submitted to Climate Dynamics, September, 199. Pitman, A.J., HendersonSellers, A. & Yang, Z.L. (199) Sensitivity of regional climates to localized precipitation in global models. Nature, Lond., 346, Rutter, AJ. (1975) The hydrological cycle in vegetation, in Vegetation and the Atmosphere, 1_, Monteith, J.L., (éd.), Academic Press. Sellers, P.J., Mintz, Y., Sud, Y.C. & Dalcher, A. (1986) A Simple Biosphere model (SiB) for use within general circulation models. J. Atmos. Sci. 43, Shuttleworth, WJ. (1988) Macrohydrology the new challenge for process hydrology. J.Hvdrol. 1, Warrilow, D.A., Sangster, A.B. & Slingo, A. (1986) Modelling of land surface processes and their influence on European climate. Dynamic Climatology Tech. Note No.38, Meteorological Office, MET O 2. (Unpublished), Bracknell, Berks, UK. Wilson, M.F. & HendersonSellers, A. (1985) A global archive of land cover and soil data sets for use in general circulation climate models. J. Climatol. 5, World Weather Records, (1957) U.S. Dept. Commerce, Superintendent of documents, U.S. Govt. Printing Office, Washington.