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15 NOVEMBER 2006 A R O R A A N D B O E R 5875

The Temporal Variability of Soil Moisture and Surface Hydrological Quantities in a Climate Model

VIVEK K. ARORA AND GEORGE J. BOER Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, University of Victoria, Victoria, British Columbia, Canada

(Manuscript received 4 October 2005, in final form 8 February 2006)

ABSTRACT

The variance budget of land surface hydrological quantities is analyzed in the second Atmospheric Model Intercomparison Project (AMIP2) simulation made with the Canadian Centre for Climate Modelling and Analysis (CCCma) third-generation general circulation model (AGCM3). The land surface parameterization in this model is the comparatively sophisticated Canadian Land Surface Scheme (CLASS). Second- order statistics, namely variances and covariances, are evaluated, and simulated variances are compared with observationally based estimates. The soil moisture variance is related to second-order statistics of surface hydrological quantities. The persistence time scale of soil moisture anomalies is also evaluated. Model values of precipitation and evapotranspiration variability compare reasonably well with observationally based and reanalysis estimates. Soil moisture variability is compared with that simulated by the Variable Infiltration Capacity-2 Layer (VIC-2L) hydrological model driven with observed meteorological data. An equation is developed linking the variances and covariances of precipitation, evapotranspiration, and runoff to soil moisture variance via a transfer function. The transfer function is connected to soil moisture persistence in terms of lagged autocorrelation. Soil moisture persistence time scales are shorter in the Tropics and longer at high latitudes as is consistent with the relationship between soil moisture persistence and the latitudinal structure of potential evaporation found in earlier studies. In the Tropics, although the persistence of soil moisture anomalies is short and values of the transfer function small, high values of soil moisture variance are obtained because of high precipitation variability. At high latitudes, by contrast, high soil moisture variability is obtained despite modest precipitation variability since the persistence time scale of soil moisture anomalies is long. Model evapotranspiration estimates show little variability and soil moisture variability is dominated by precipitation and runoff, which account for about 90% of the soil moisture variance over land surface areas.

1. Introduction phasizes both the varying properties of the soil and the direct role of vegetation in determining the surface en- Land surface models (LSMs) provide the connection ergy and water balance, particularly by taking into ac- between the atmosphere and the land surface in general count the physiological properties of vegetation [leaf circulation models (GCMs). LSMs range in complexity area index (LAI) and stomatal resistance]. The SVAT from the simple “bucket” model with fixed water- approach may be enhanced to include the coupling be- holding capacity (Manabe 1969), to models of interme- tween photosynthesis and stomatal conductance (Sell- diate complexity, which implicitly represent some ef- ers et al. 1996b; Dickinson et al. 1998) and the dynamic fects of soil properties and vegetation (e.g., Noilhan treatment of vegetation (e.g., Foley et al. 1996; Arora and Planton 1989), to more sophisticated soil–vegeta- 2002). tion–atmosphere–transfer (SVAT) schemes that in- The role of LSMs is to mediate the fluxes of energy, clude explicit treatment of vegetation (e.g., Sellers et al. moisture, and momentum that connect the atmosphere 1986; Dickinson et al. 1986). The SVAT approach em- to the underlying land surface. Soil moisture is the dom- inant quantity affecting these surface fluxes. Shukla and Mintz (1982) highlight the role played by soil moisture Corresponding author address: Vivek Arora, Canadian Centre for Climate Modelling and Analysis, Meteorological Service of in the extratropics and make an analogy with energy in Canada, University of Victoria, Victoria, BC V8W 2Y2, Canada. the ocean. The ocean stores some of the radiational E-mail: [email protected] energy it receives in summer and uses it to heat the

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JCLI3926 5876 JOURNAL OF CLIMATE VOLUME 19 atmosphere in winter. The soil stores some of the pre- precipitation, evapotranspiration, and runoff and inves- cipitation it receives in winter and uses it to humidify tigate the connection between the variability of these the atmosphere in summer. The role of soil moisture in moisture budget components and that of soil moisture. influencing near-surface atmospheric variability (Del- Monthly values of moisture budget quantities from the worth and Manabe 1988, 1989; Manabe and Delworth second Atmospheric Model Intercomparison Project 1990), in affecting the persistence of atmospheric circu- (AMIP2) simulation made with the Canadian Centre lation (Namias 1952, 1959), and the effect of anomalies for Climate Modelling and Analysis (CCCma) third- of soil moisture and temperature on atmospheric circu- generation atmospheric general circulation model lation (Charney et al. 1977; Walker and Rowntree 1977; (AGCM3) are used. The SVAT scheme used in the Rowntree and Bolton 1983; Yeh et al. 1984; Dickinson CCCma AGCM3, the Canadian Land Surface Scheme and Henderson-Sellers 1988; Shukla et al. 1990; Koster (CLASS), explicitly models interactions between and Suarez 1995; Avissar and Liu 1996) have been in- canopy, snow, and ground (soil) moisture reservoirs. A vestigated by many researchers. Realistic spatial distri- brief description of AGCM3 and the land surface butions of soil moisture have been shown to improve scheme is given in section 2, which also describes the rainfall patterns, reduce errors in near-surface tempera- AMIP2 simulation. Comparisons of the variance of tures, and improve interannual variability in simulated simulated surface hydrological quantities with observa- climate (Fennessey and Shukla 1999; Dirmeyer 2000; tionally based variance estimates are presented in sec- Douville and Chauvin 2000). tion 3. The connection between the variability of soil While the role of soil moisture in affecting the near- moisture and other moisture budget components is in- surface atmosphere has been the focus of a number of vestigated in section 4, and the results are summarized studies, very few have focused on the nature and causes in section 5. of soil moisture variability itself. Delworth and Manabe (1988) describe the variability of soil moisture in a 2. Model and experimental design GCM (using a bucket LSM with a field capacity of 15 a. The CCCma third-generation AGCM cm) in terms of the variability of precipitation and the control of potential evaporation. In the light of stochas- The CCCma third-generation atmospheric GCM tic theory, they report that the forcing of the land sur- (Scinocca and McFarlane 2004) is the latest in the series face system by precipitation (a white noise input vari- of AGCMs described in Boer et al. (1984) and McFar- able) will yield soil moisture (the output variable) with lane et al. (1992). The results analyzed here are ob- a red spectrum, the redness of which is controlled by tained with a T47 L32 version of the model. Dynamic the dependence of evaporation on soil moisture and terms are calculated at triangular T47 spectral trunca- potential evaporation (the damping term). They con- tion, and the physical terms on a 96 ϫ 48 (3.75°) hori- clude that the increasing redness of soil moisture spec- zontal linear grid. The vertical domain extends to 1 hPa tra at high latitudes is a result of declining potential with the thicknesses of the model’s 32 layers increasing evaporation. Entekhabi and Rodriguez-Iturbe (1994) monotonically with height from approximately 100 m at derive an analytical expression for the space–time the surface to 3 km in the lower stratosphere. power spectrum of soil moisture that is related to the While many of the parameterized physical processes space–time power spectrum of the rainfall through a in the third-generation model are qualitatively similar hydrological gain function. They use a simple soil water to AGCM2, key new features include 1) a new param- balance model in which losses (combined evapotrans- eterization of cumulus convection (Zhang and McFar- piration, surface runoff, and drainage) are represented lane 1995), 2) an improved treatment of solar radiation as a linear function of soil moisture. The space–time that employs four bands in the visible and near-infrared power spectrum of rainfall is estimated by assuming region, 3) an “optimal” spectral representation of to- that rainbands arrive in space–time according to a ho- pography (Holzer 1996), 4) a revised representation of mogeneous Poisson process. As with Delworth and turbulent transfer coefficients at the surface (Abdella Manabe (1988), Entekhabi and Rodriguez-Iturbe and McFarlane 1996), 5) a hybrid moisture variable (1994) conclude that the hydrological gain function (Boer 1995), and 6) CLASS for treatment of the land (whose parameters depend on climate and surface hy- surface processes (Verseghy 1991; Verseghy et al. drological processes) acts as a low-pass filter that pref- 1993). erentially dampens high-frequency space and time fluc- b. The Canadian Land Surface Scheme tuations of rainfall to produce low-frequency and large- scale soil moisture variations. The CLASS land surface scheme processes heat and In this study, we evaluate the variability of modeled moisture via three reservoirs: the ground, the canopy,

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FIG. 1. The components of the land surface moisture budget: (a) The four subareas for which moisture and heat budget calculations are performed and (b) the direct precipitation inputs and evaporative outputs for all moisture reservoirs, and the exchanges between the reservoirs.

and the snow with fractional coverages, fg, fc, and fs, tween reservoir n and m (in practice we use subscripts respectively, as shown in Fig. 1a. A GCM grid cell is c for canopy, s for snow, and g for ground rather than further divided into four subareas: bare soil (fb), snow- numbers). covered ground (fgs), canopy-covered ground (fgc), and Here Inm represents the exchange as a loss from res- ϭϪ canopy-covered snow (fsc) for each of which heat and ervoir n and a gain by reservoir m so that Inm Imn moisture balances are evaluated separately. The soil is for nm. When n ϭ m, the term represents a loss (flow divided into three layers of depth 0.10 m, 0.25 m, and out of a grid cell) by some other process. For the ϭ 3.75 m, each with its own prognostic liquid and frozen ground moisture reservoir Igg R is the runoff and, ϭ soil moisture content and temperature. hence, river flow. For the snow moisture reservoir Iss The condensed moisture budget equation for a sys- C, the conversion of snow to glacial ice, which is pa- tem of N reservoirs applied to grid-averaged quantities rameterized in CLASS as a function of snow mass. The is written as net moisture budget equation,

dW N dW n ϭ Ϫ Ϫ ϭ ͑ ͒ ϭ Ϫ Ϫ ͑ ϩ ͒ ͑ ͒ Pn En ͚ Inm, n 1,...,N, 1 P E R C , 2 dt mϭ1 dt where Wn is the moisture content of reservoir n, Pn is is obtained by summing over all N reservoirs, where the gain of moisture by direct precipitation input into unsubscripted variables represent the sum; that is, W ϭ ͚N ͚N ͚N ϭ ϩ the reservoir, En is the loss of moisture in the form of nϭ1Wn and nϭ1 mϭ1Imn R C. vapor (the evaporative output including transpiration Figure 1b identifies the inputs, outputs, and ex- and sublimation), and Inm is the moisture exchange be- changes of moisture to, from, and between the snow,

Unauthenticated | Downloaded 10/02/21 08:25 AM UTC 5878 JOURNAL OF CLIMATE VOLUME 19 the canopy, and the ground moisture reservoirs. The model output variables, and establishment of new stan- exchange quantities Ics, Icg, and Isg refer to the falling of dards and protocols for data analysis. snow from the canopy onto the snow below, the drip- ping of rainwater from the canopy to the ground below, and the transfer of moisture from snow to ground due 3. Comparison with observations to snowmelt. Moisture input into a reservoir is the sum of direct precipitation input and any positive moisture In Arora and Boer (2002, 2003) the first-order statis- exchanges. For example, moisture input into the tics of moisture budget quantities from an AMIP2 ground moisture reservoir is the sum of direct precipi- simulation made with the CCCma AGCM3 are ana- tation that falls on the bare ground (Pg), rainfall drip lyzed and compared with observations. The mean an- from the canopy (Icg), and snowmelt (Isg). Evaporation nual values and the first harmonic of the annual cycle of loss from the ground moisture reservoir, Eg is made up simulated precipitation, runoff, and other primary wa- of two components: transpiration from the ground via ter budget components for the globe and selected major the canopy (Et) and direct evaporation from the soil river basins are considered and modeled mean annual

(Esoil). Runoff from ground (R) is also made up of two precipitation and runoff and their latitudinal structures components: 1) surface (overland) runoff (Ro), which is are shown to compare well with observations, although generated when the amount of ponded water exceeds a some discrepancies remain in the simulation of regional specified limit and ponds form when precipitation in- values of these quantities. Here the second-order sta- tensity exceeds infiltration capacity, and 2) drainage tistics (variances and covariances) of the model water

(Rg) from the bottommost soil layer, which is assumed budget quantities are analyzed. The variance of simu- equal to the saturated hydraulic conductivity of the soil. lated monthly precipitation is compared with observa- The rate of change of soil moisture in the ground res- tionally based estimates and the variance of simulated ervoir is the sum of the net moisture input (Gg), evapo- monthly evapotranspiration with estimates from Euro- transpiration (Eg), and drainage (Rg): pean Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis. Mean annual values of simulated

dWg soil moisture, and its monthly variance, are compared ϭ G Ϫ E Ϫ R , ͑3͒ dt g g g with estimates generated from the Variable Infiltration Capacity-2 Layer (VIC-2L) hydrological model. ϭ ϩ ϩ Ϫ ϭ ϩ where Gg Pg Icg Isg Ro and Eg Et Esoil. ϭ Similar equations can be written for the canopy dWc/dt a. Precipitation Ϫ Ϫ ϭ Ϫ Ϫ Gc Ec Rc and the snow dWs/dt Gs Es Rs ϭ ϭ ϩ ϭ In Fig. 2a the variance of simulated monthly precipi- moisture reservoirs, where Gc Pc, Rc Icg Ics, Gs ϩ ϭ ϩ tation values (calculated after removal of the climato- Ps Ics, and Rs Isg Iss. logical annual cycle) is compared with observationally based estimates from Xie and Arkin (1996). Xie and c. The AMIP2 simulation Arkin (1996) construct global 2.5° gridded monthly pre- The Atmospheric Model Intercomparison Project, cipitation estimates based on gauge data, satellite in- initiated in 1989, undertakes the systematic validation, formation from three difference sources, and results diagnosis, and intercomparison of the performance of from the ECMWF operational forecast model. Esti- atmospheric GCMs (Gates et al. 1999). In AMIP2 mates for the period from 1979 to–1997 are used. Model simulations, an atmospheric GCM is integrated for the precipitation variance compares well with that based on 17-yr period (1979–95) with specified lower boundary observations, except in Amazonia where the model conditions of observed monthly sea surface tempera- produces less precipitation (Arora and Boer 2002). The tures (SSTs) and sea ice concentrations (Fiorino 1996). variability of both model and observationally based AMIP2 is an extension of AMIP1, with improvements precipitation values is higher in the Tropics and lower in experimental design, diagnosis of an expanded set of at high latitudes, at least partially as a consequence of

→

FIG. 2. Comparison of variability of simulated water budget components with observationally based and other estimates: (a), (b) simulated precipitation variance and cv are compared with estimates from Xie and Arkin (1996); (c) cv for simulated evapotranspiration estimates is compared with estimates from ECMWF reanalysis; and (d), (e) simulated soil moisture in the top 1 m and its variance are compared with estimates from the VIC-2L model. The land average values exclude Greenland and Antarctica.

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Fig 2 live 4/C 5880 JOURNAL OF CLIMATE VOLUME 19 the large precipitation rates at low compared to high c. Soil moisture latitudes. The spatial correlation between the model Observationally based estimates of soil moisture con- and observationally based precipitation variance esti- tent at global scale are not readily available. Data in the mates is 0.52. The coefficient of variation (cv), given by Global Soil Moisture Data Bank (Robock et al. 2000) ␥ ϭ ␴ /X, where ␴ is the standard deviation and X is X X are mostly over Russia, China, and Mongolia. Model- the mean, characterizes the variability relative to the derived global soil moisture estimates are available mean. The cv represents the fact that the same level of from various sources (e.g., Mintz and Serafini 1992; precipitation variability is of less practical consequence Schemm et al. 1992; Willmott et al. 1985) typically es- in a region of high mean precipitation than in a region timated with a bucket hydrological model of field ca- of low mean precipitation. Values of cv over land are pacity 150 mm. These models do not, however, capture compared in Fig. 2b. Model values of the coefficient of the large observed high values of soil moisture because variation compare well with observations (spatial cor- of the limited depth of the bucket. This results in con- relation of 0.70). Although the precipitation variability stant soil moisture values in winter while observations is higher in the Tropics, the cv values are higher in areas that receive less precipitation on average such as Aus- suggest soil moisture varies as much in winter as in tralia, the Sahara Desert, the Middle East, and the other seasons (Robock et al. 1998). Soil moisture infor- southwestern United States. Precipitation variability is mation is also available from the Global Soil Wetness typically of more practical importance in these regions Project (GSWP) (Dirmeyer et al. 1999) in which the 10 of less precipitation (McMahon 1979). The land- participating land surface schemes are forced with me- averaged precipitation variance compares well with the teorological data from the International Satellite Land observationally-based estimate, 1.65 versus 1.59 (mm Surface Climatology Project (ISLSCP) (Sellers et al. dayϪ1)2 in Fig. 2a. The corresponding averaged values 1996a) for two years (1987–88). An assessment of of cv are 0.56 versus 0.68 in Fig. 2b, although averages GSWP data by Entin et al. (1999) over selected regions of ratios can be misleading. Here and throughout the (for which global soil moisture data are available) re- rest of the paper Greenland and Antarctica are ex- veals, however, that none of the models do a particu- cluded from the averages. larly good job of producing the observed soil moisture values for any of the regions. Of course, the 2-yr dura- tion of GSWP does not provide variability information. b. Evapotranspiration Soil moisture values are also available from various re- In the absence of an observed evapotranspiration analyses but these are nudged toward climatology using dataset, model evapotranspiration variance is com- an artificial moisture input term (e.g. see Roads and pared with estimates from the ECMWF reanalysis Betts 2000). (Gibson et al. 1997) for the period 1979–93. The land AGCM3/CLASS simulated soil moisture and its vari- surface scheme used in the ECMWF reanalysis consists ability is compared with the results of Nijssen et al. of four soil layers of thickness of 0.07, 0.21, 0.72, and (2001), who estimate daily soil moisture values for the 1.89 m (Viterbo and Beljaars 1995). Evapotranspiration period from 1980 to 1993 at 2° resolution using the displays much less variability than precipitation with VIC-2L model (Liang et al. 1994). VIC-2L is a some- variance values (not shown) of less than 0.20 (mm what more realistic hydrological model than the bucket dayϪ1)2 over most of the land area. The variance of model and predicts a larger range of soil moisture. Un- monthly evapotranspiration simulated over land is 0.19 like most land surface schemes, it includes an explicit (mm dayϪ1)2 in AGCM3, which is slightly higher than representation of spatial variability of infiltration ca- the value of 0.15 (mm dayϪ1)2 obtained from the pacity that is used for surface runoff generation. It as- ECMWF reanalysis. The coefficient of variation for sumes a 1-m soil layer with soil porosity values varying evapotranspiration is shown in Fig. 2c. The spatial cor- between 0.4 for coarse-textured to 0.48 for fine- relation between AGCM3 and ECMWF values is 0.50. textured soil. The maximum water-holding capacity of Evapotranspiration estimates show higher values of cv the soil column in the VIC-2L model averages about over areas characterized by low precipitation, implying 440 mm compared to 150 mm for bucket model. Nijssen that relative to the mean evapotranspiration is more et al. (2001) force the VIC-2L model with observation- variable in arid and semiarid areas, as is also the case ally based daily precipitation and temperature data, for precipitation. In Fig. 2c, the value of cv averaged wind speeds based on the National Centers for Envi- over land for the AGCM3 simulated evapotranspira- ronmental Prediction–National Center for Atmo- tion estimates (0.38) is slightly higher that that for the spheric Research (NCEP–NCAR) reanalysis data (Kal- ECMWF values (0.25). nay et al. 1996), and other meteorological variables (ra-

Unauthenticated | Downloaded 10/02/21 08:25 AM UTC 15 NOVEMBER 2006 A R O R A A N D B O E R 5881 diation and vapor pressure) derived from precipitation d 1 WЈ2 ϭ GЈWЈ Ϫ EЈWЈ Ϫ RЈWЈ. ͑5͒ and temperature. dt 2 The total depth of three soil layers in the CLASS land surface scheme is 4.1 m compared to1minthe Equation (5) is the same as that obtained by Albertson VIC-2L hydrological model. Soil moisture in the top 1 and Montaldo (2003) [their Eq. (7)] without the terms m of CLASS is obtained by combining the soil moisture describing the horizontal redistribution of water and by in the top two layers (of thicknesses 0.1 and 0.25 m, Teuling and Troch (2005) [their Eq. (9)] who, using respectively) with the soil moisture in the top 0.65 m of observationally based catchment data, attempt to un- the third layer assuming a uniform soil moisture profile derstand how the covariances of soil moisture with the ϭ ϩ ϩ ϫ input and output terms act to generate or damp soil [Wg,1m Wg1 Wg2 Wg3 (0.65/3.75), where Wgi (depth units) is the soil moisture content of the ith moisture variance. Not unexpectedly, the G term acts layer]. The resulting soil moisture values compare well to generate, and the E and R terms act to damp soil with those from the VIC-2L model in Fig. 2d, although moisture variability. the AGCM3/CLASS estimates are slightly higher in the Although Eq. (5) provides a connection between soil northern high latitudes and soil moisture estimates moisture variability and the other terms in the soil from VIC-2L are noticeably smoother. The average moisture budget, it is a differential equation involving values over land compare well (225 versus 219 mm) and the rate of change of soil moisture variability. We at- the spatial correlation (excluding Greenland and Ant- tempt a somewhat different connection between the arctica) is 0.58. variability of monthly soil moisture and other moisture Figure 2e shows that the AGCM3/CLASS soil mois- budget quantities. We rewrite (4) applied to daily val- ture variance, extracted for the top 1 m, is qualitatively ues, represented by lower case symbols, and averaged similar to that of the VIC-2L model although values are over a month (indicated by overbars) to get generally somewhat larger, except over the Tropics and wЈ͑t ϩ n⌬t͒ Ϫ wЈ͑t͒ the Sahara and the Mongolian deserts. The globally ϭ gЈ Ϫ eЈ Ϫ rЈ n⌬t averaged value of soil moisture variability in the top 1 m from the AGCM3/CLASS (376 mm2) compares ϭ GЈ Ϫ EЈ Ϫ RЈ well with that from the VIC-2L model (382 mm2). ϭ ͚Ј, ͑6͒ In summary, comparison of the variability of simulated precipitation and evapotranspiration with obser- where n ϭ 30 days and ⌬t ϭ 1 day. Here primes indicate vationally based estimates and reanalysis data, respec- deviations from the long-term mean, and uppercase tively, show that the model estimates of the variability quantities are monthly means. Squaring both sides of of these components are reasonable. The broad spatial Eq. (6) and averaging yields patterns of soil moisture variability, and its land- averaged value, are similar to those generated by the n2⌬t2 ␴2 ϭ ͑GЈ2 ϩ EЈ2 ϩ RЈ2 Ϫ 2GЈRЈ Ϫ 2GЈEЈ VIC-2L model although the AGCM3/CLASS values d 2͓1 Ϫ r͑n͔͒ are somewhat higher. In the absence of observed ϩ Ј Ј͒ ͑ ͒ monthly runoff estimates, comparisons for model run- 2E R , 7 off variance are not performed. Runoff data from other ␴ 2 ϭ Ј2 where d w is the daily soil moisture variance and models are available, but these data are not used given r(n), for n ϭ 30, is the lag 30-day soil moisture auto- the uncertainties associated with LSM’s runoff esti- correlation. Equation (7) formally relates the variances mates (e.g., see Gedney et al. 2000). and covariances terms of monthly averaged moisture budget quantities to the daily soil moisture variance. ␴ 2 4. Analysis of soil moisture variability The daily variance of soil moisture d is related to the ␴ 2 ϭ variance of monthly mean soil moisture W for W We approach the analysis of soil moisture variability ⌺w(t)/n as by writing Eq. (3) in terms of deviations (or anomalies, Ϫ indicated by prime) of a variable from its mean annual ͑1 ϩ C͒ n 1 ␣ ͒ ͑ ͒␣͑ ͪ ␴2 ϭ ؅2 ϭ ␴2 ϭ ͩ Ϫ cycle as W W d ; C 2͚ 1 r , 8 n ␣ϭ1 n Ј dWg ϭ GЈ Ϫ EЈ Ϫ RЈ. ͑4͒ where r(␣)islag␣-day autocorrelation. Then from (7) dt g g g and (8) the variance of monthly mean soil moisture is Multiplying Eq. (4) by WЈ on both sides, dropping the related to the variances and covariances of monthly subscript g for simplicity, and averaging yields moisture budget terms as

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␴2 ϭ ͚Ј2 GЈEЈ and EЈRЈ (Figs. 3e,f) are small, and only the GЈRЈ W B covariance term (Fig. 3d) is important. The land- ϭ B͑GЈ2 ϩ EЈ2 ϩ RЈ2 Ϫ 2GЈRЈ Ϫ 2GЈEЈ ϩ 2EЈRЈ͒, average values ͗GЈEЈ͘ and ͗EЈRЈ͘ are Ϫ0.03 and Ϫ0.05 (mm dayϪ1)2, respectively, which are an order of mag- ͑9͒ nitude smaller than the ͗GЈRЈ͘ value of 0.79 (mm ͚Ј2 Ϫ where involves variances and covariances as shown day 1)2. These variance and covariance terms scaled by and B are expressed as a percentage of the soil moisture n͑1 ϩ C͒⌬t2 variance in terms of global averages, in Fig. 3g, and B ϭ . imply that Eq. (9) may be reasonably approximated 2͓1 Ϫ r͑n͔͒ retaining only the G and R terms as Equation (9) symbolically relates moisture budget vari- ͚Ј2 ␴ 2 ϭ ͑ Ј2 ϩ Ј2 Ϫ Ј Ј͒ Ϸ ␴ 2 ͑ ͒ ance and covariance terms in and the “transfer ˆ W B G R 2G R W. 12 ␴2 function” B to monthly soil moisture variance W. The 2 ␴ 2 transfer function B, which has units of day , reflects a Simulated soil moisture variance in Fig. 3h ( W) is com- ␴ 2 time scale that is determined by the autocorrelation pared to that approximated by Eq. (12) in Fig. 3i ( ˆ W), structure of the daily soil moisture, and hence is a mea- and shows that (12) applies over most of the land sur- sure of soil moisture persistence. High values of soil face. The land average value of soil moisture variance moisture variance would be expected when values of from (12) is about 90% of the direct value. Figure 4 ͚Ј2 the transfer function B and/or values of ͚Ј2 are high. plots the transfer function B and as well as a mea- ␶ If daily soil moisture variability can be approximated sure of soil moisture persistence (discussed in the next as a first-order autoregressive [AR(1)] process, then section). Figures 4 and 3h indicate that in the Tropics r(␣) ϭ a␣ where a is the lag 1-day autocorrelation. In soil moisture variability is associated with variability in that case surface hydrological quantities, in particular precipitation and runoff as measured by ͚Ј2. At high latitudes, 2a͓n͑1 Ϫ a͒ Ϫ ͑1 Ϫ an͔͒ C ϭ , ͑10͒ however, soil moisture variability is associated with n͑1 Ϫ a͒2 large values of the transfer function B. Conceptually, large variability in moisture budget input/runoff terms n͑1 ϩ C͒⌬t2 ͓n͑1 Ϫ a2͒ Ϫ 2a͑1 Ϫ an͔͒⌬t2 B ϭ ϭ . is comparatively strongly damped in the Tropics as in- ͑ Ϫ n͒ ͑ Ϫ ͒2͑ Ϫ n͒ 2 1 a 2 1 a 1 a dicated by low values of ␶, while at high latitudes com- ͑11͒ paratively weaker variability in input/runoff is less strongly damped. The result is that large soil moisture The “inertia” of soil moisture as measured by a is large variance can result in both regions. and provides a long-term memory for the surface moisture and energy budgets. Over land the average of Soil moisture persistence and the transfer function B model values is ͗a͘ϭ0.985, while ͗a(30)͘ϭ0.60 Ϸ a30 ϭ 0.63, indicating that estimating B from Eq. (11) is rea- The transfer function B is a measure of soil moisture sonable on average. The average value of soil moisture persistence through the autocorrelation terms in (11). ͗␴ 2 ͘ 2 variance W (for the entire soil depth) is 1198 mm Persistence is short when anomalies are strongly when estimated using Eqs. (9) and (11), with r(␣) ϭ a␣, damped and long when they are weakly damped. There compared to value of 1152 mm2 evaluated directly. is a clear visual connection between B in Fig. 4a and soil Figures 3a–f display variances and covariances of the moisture persistence (␶) in Fig. 4c. Following Liu and moisture budget terms of Eq. (9). As expected, the spa- Avissar (1999), the soil moisture persistence (␶) is mea- tial structure of the variance of the moisture input term sured as the average run of months with the same sign GЈ2 in Fig. 3a is similar to that of precipitation (Fig. 2a) of the soil moisture anomaly. The spatial correlation but with somewhat smaller values since all precipitation between the transfer function B and soil moisture per- does not reach the ground because of canopy intercep- sistence is 0.72. The soil moisture persistence ␶ and the tion losses. The model evapotranspiration from the transfer function B are smaller at low latitudes and ground EЈ2 (which excludes evaporation of intercepted larger at high latitudes. The persistence varies from precipitation from canopy leaves) shows little spatial ϳ1–2 months in the Tropics to over 8 months at high structure (Fig. 3b), while the spatial structure of RЈ2 is latitudes. These results are generally similar to those similar to that of GЈ2 with small values over areas of obtained by Yeh et al. (1984), Gao et al. (1996), and Liu little runoff (including the Sahara Desert and southwest and Avissar (1999) although, because soil moisture is a United States). Since evapotranspiration variability is derived quantity, the results are not entirely uniform. comparatively weak, the associated covariance terms Our results differ from those of Liu and Avissar (1999),

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FIG.3.(a)–(f) Global plots of components of soil moisture variance for the ground moisture reservoir. (g) The contri- bution of moisture budget variance and covariance terms to soil moisture variance, expressed as a percentage. (h), (i) Simulated soil moisture variance, and the one approximated through Eq. (12).

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Fig 3 live 4/C 5884 JOURNAL OF CLIMATE VOLUME 19

the total rainfall is the same, with sufficient time between events so that soil moisture stays at a constant low (dry) value for long periods will yield long persistence times. The CLASS/AGCM3 results are consistent with the latitudinal dependence of soil moisture persistence on potential evaporation (Delworth and Manabe 1988). At low latitudes evaporation rates are high and soil moisture anomalies are quickly damped, in comparison to high latitudes. Koster and Suarez (2001) point out that the autocorrelation structure of soil moisture in climate models is also related to seasonality in the variance of atmospheric forcing, the dependence of evaporation and runoff on soil moisture, and correlation between the atmospheric forcing and antecedent soil moisture conditions, as perhaps induced by land– atmosphere feedbacks. We attempt to relate the transfer function B to soil moisture persistence assuming that soil moisture variability can be approximated by an AR(1) process. For a white noise time series, von Storch and Zwiers (1999) derive the expression P(l) ϭ 2Ϫ(lϩ1) for the probability of a run (i.e., a sequence of consecutive elements with the same sign) of length l. This formula does not apply to nonwhite AR(1) processes, however, and they estimate the percentage of runs of length l using Monte Carlo methods (their Fig. 10.2). We repeat the experiment for different values of the lag-1 autocorrelation and empirically fit the function

P͑l͒ ϭ ␪eϪ␪l ϩ ͑1 Ϫ ␪͒eϪ␤l for ␪ ϭ 0.63 Ϫ 0.53A, ␤ ϭ 1.5 ͑13͒

to the distribution of run lengths, where A ϭ r(1) is the lag-1 autocorrelation. Figure 5 shows the distribution of run lengths obtained from a Monte Carlo experiment with 200 000 realizations (shown as symbols) and the empirical function from (13) (shown as lines). Equation FIG. 4. (a) The transfer function B, (b) the variance and covari- (13) gives a very reasonable fit for r(1) Յ 0.6. The ex- ance term ͚Ј2, and (c) the soil moisture persistence ␶ measured as the average length of a run of months with the same sign of soil pected average run length, which is measure of the soil moisture anomaly. moisture persistence time scale ␶, is obtained from (13) as for instance, over the Sahara Desert (their Fig. 4) where ϱ 1 ͑1 Ϫ ␪͒ they find high soil moisture persistence while CLASS/ ␶͑A͒ ϭ ͵ P͑l͒ dl ϭ ϩ . ͑14͒ ␪ ␤2 AGCM3 gives lower values. Soil moisture persistence is 0 sensitive to rainfall frequency in arid regions where the The lag-1 autocorrelation A of monthly means is re- same amount of rainfall can yield different persistence lated to the lag-1 autocorrelation a of daily values as values depending on its temporal distribution, so persistence values must be interpreted with caution. Com- a͑1 Ϫ an͒2 A ϭ , ͑15͒ paratively frequent though small rainfall events, and n͑1 Ϫ a2͒ Ϫ 2a͑1 Ϫ an͒ the quick dissipation of resulting soil moisture anomalies due to high evaporative demand, will yield low per- as shown in the appendix. Taken together, Eqs. (11), sistence values and this is apparently the case for (14), and (15) yield a functional relationship between CLASS/AGCM3. Less frequent rainfall events, even if the soil moisture persistence time scale ␶ and the trans-

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Fig 4 live 4/C 15 NOVEMBER 2006 A R O R A A N D B O E R 5885

FIG. 5. The frequency distribution of the run lengths l derived from 200 000 realizations for AR(1) processes with lag-1 autocorrelations (A) of 0.0, 0.3, 0.6, and 0.9 (symbols), and the empirical function (lines) from Eq. (13). fer function B for an AR(1) process. This relationship is scatter in Fig. 6. The autocorrelation of soil moisture the curve plotted in Fig. 6. Actual values of B and ␶ depends on the manner in which evaporation and run- from the AGCM3 simulation are plotted as diamonds. off are parameterized as functions of soil moisture (Ko- Longer persistence time scales of soil moisture anoma- ster and Suarez 2001) and this is not explicitly ac- lies are related to larger values of the transfer function, counted for in Eq. (11). The fitted empirical relation- although not linearly, and the first-order relationship ship between probability of run length l and lag-1 can be approximated assuming an AR(1) process. Soil autocorrelation in Eq. (13), which is used to estimate moisture variability is approximated as an AR(1) pro- persistence (␶), is also a cause of scatter in Fig. 6. cess in Eqs. (10) and (11) and, although this approximation works well in a global average sense, this may 5. Summary and discussion not be the case for individual grid cells, leading to the Soil moisture and its variability play an important role in atmospheric anomalies that can persist for long periods. The role of potential evaporation (Delworth and Manabe 1988), the variation in evaporation and runoff with soil moisture, and land–atmosphere feedbacks in affecting soil moisture autocorrelation structure and thus its persistence has been highlighted in earlier studies (e.g., Koster and Suarez 2001). Here, we link soil moisture variance to the second-order statistics of precipitation, evapotranspiration, and runoff and evaluate terms using monthly data from an AMIP2 simulation made with the CCCma third-generation atmospheric general circulation model. The variance of monthly precipitation simulated in the model is compared with observationally based estimates from Xie and Arkin (1996) and the variance of FIG. 6. The relationship between soil moisture persistence time scale and the value of the transfer function B based on the as- evapotranspiration is compared to ECMWF reanalysis sumption of an AR(1) process (shown as the solid line). The results. Simulated values compare reasonably well with symbols are the values from the AGCM3 simulation. the observationally based estimates. In the absence of

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Fig 5 live 4/C 5886 JOURNAL OF CLIMATE VOLUME 19 observed gridded soil moisture values, we compare Acknowledgments. We would like to thank Slava model soil moisture variance with estimates from the Kharin and Steve Lambert for providing comments on VIC-2L hydrological model driven with observationally an earlier version of this paper. based meteorological data. AGCM3/CLASS soil moisture variance is qualitatively similar to that of VIC-2L APPENDIX although values are generally somewhat larger. Simu- lated evapotranspiration variance is small compared to Lag-1 Autocorrelation of Monthly Means Related that of precipitation and runoff and soil moisture vari- to Daily Values ance depends primarily on the precipitation and runoff Derivation of lag 1-month autocorrelation A as a terms. This approximation is acceptable over almost function of lag-1 day autocorrelation r for an AR(1) the entire land surface area and accounts for about 90% process is given as of the total soil moisture variance. Ј Ј Soil moisture variance is linked to the variance and WtWtϩ1 A ϭ , ͑A1͒ ␴2 covariance of source/sink terms in the moisture budget W via a transfer function. In this view, soil moisture vari- 1 1 a͑1 Ϫ an͒2 ance is connected to the variability of hydrologic quan- Ј Ј ϭ Խnϩ␣Ϫ␤Խ␴2 ϭ ␴2 WtWtϩ1 2 ͚ a daily 2 2 daily, tities and the persistence of soil moisture anomalies. n ␣,␤ n ͑1 Ϫ a͒ The transfer function is a measure of the persistence of ͑A2͒ soil moisture anomalies via lagged autocorrelation ͑ Ϫ n͒2 ␴2 ͑ Ϫ n͒2 terms. An expression linking the transfer function and 1 a 1 a daily 1 a 1 a n A ϭ ϭ . the persistence time scale of soil moisture anomalies is 2 ͑ Ϫ ͒2 ␴2 2 ͑ Ϫ ͒2 ϩ n 1 a W n 1 a 1 C developed, assuming soil moisture variability can be ͑ ͒ approximated by an AR(1) process. A3 Model results show that the soil moisture persistence Substitution of expression for C [Eq. (10)] in Eq. (A3) time scale and the transfer function are smaller in the yields Tropics and larger at high latitudes, as expected from ͑ Ϫ n͒2 the dependence on evapotranspiration. In the Tropics, a 1 a A ϭ . ͑A4͒ damping is comparatively strong and the persistence of n͑1 Ϫ a2͒ Ϫ 2a͑1 Ϫ an͒ soil moisture anomalies is short and values of the transfer function small. Nevertheless, high values of soil REFERENCES moisture variance may result because of high precipi- Abdella, K., and N. A. McFarlane, 1996: Parameterization of the tation variability. At high latitudes, characterized by surface-layer exchange coefficients for atmospheric models. low variability of precipitation and runoff, high soil Bound.-Layer Meteor., 80, 223–248. moisture variability is linked to comparatively weak Albertson, J. D., and N. Montaldo, 2003: Temporal dynamics of damping and long persistence time of soil moisture soil moisture variability: 1. Theoretical basis. Water Resour. Res., 39, 1724, doi:10.1029/2002WR001616. anomalies. Thus, large soil moisture variability can re- Arora, V. K., 2002: Modelling vegetation as a dynamic component sult in both regions but for different reasons. in soil–vegetation–atmosphere-transfer schemes and hydro- These results have some implications for soil mois- logical models. Rev. Geophys., 40, 1006, doi:10.1029/ ture initialization and the role of soil moisture memory 2001RG000103. for seasonal climate prediction. Despite the high pre- ——, and G. J. Boer, 2002: An assessment of simulated global moisture budget, and the role of moisture reservoirs in pro- cipitation variability in the Tropics that creates large cessing precipitation. Climate Dyn., 20, 13–29. soil moisture anomalies, the effect on seasonal climate ——, and ——, 2003: An analysis of simulated runoff and surface is likely not pronounced because anomalies are dissi- moisture fluxes in the CCCma coupled atmosphere land sur- pated quickly by high evapotranspiration and runoff face hydrological model. Proc. Int. Congress on Modelling and Simulation, MODSIM 2003, Vol. 1, Townsville, Queens- (Koster and Suarez 2001). In mid- and high-latitude land, Australia, Modelling and Simulation Society of Austra- regions, although the soil moisture anomalies are lia and New Zealand, 166–171. smaller because of low precipitation variability, their Avissar, R., and Y. Liu, 1996: A three-dimensional numerical effect on seasonal climate may be more pronounced study of shallow convective clouds and precipitation induced because of their longer dissipation time scales. Here, by land-surface forcing. J. Geophys. Res., 101, 7499–7518. Boer, G. J., 1995: A hybrid moisture variable suitable for spectral low evapotranspiration and runoff rates and soil mois- GCMs. Research Activities in Atmospheric and Oceanic Mod- ture freezing in winter cause soil moisture anomalies to elling, WGNE Rep. 21, WMO/TD-665, World Meteorologi- last longer. cal Organization, Geneva, Switzerland.

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——, N. A. McFarlane, R. Laprise, J. D. Henderson, and J.-P. Holzer, M., 1996: Optimal spectral topography and its effect on Blanchet, 1984: The Canadian Climate Centre spectral atmo- model climate. J. Climate, 9, 2443–2463. spheric general circulation model. Atmos.–Ocean, 22, 397– Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Re- 429. analysis Project. Bull. Amer. Meteor. Soc., 77, 437–471. Charney, J. G., W. J. Quirks, S. H. Chow, and J. Kornfield, 1977: Koster, R. D., and M. J. Suarez, 1995: The relative contributions A comparative study of the effects of albedo change on of land and ocean processes to precipitation variability. J. drought in semi-arid regions. J. Atmos. Sci., 34, 1366–1385. Geophys. Res., 100, 13 775–13 790. Delworth, T. L., and S. Manabe, 1988: The influence of potential ——, and ——, 2001: Soil moisture memory in climate models. J. evaporation on the variabilities of simulated soil wetness and Hydrometeor., 2, 558–570. climate. J. Climate, 1, 523–547. Liang, X., D. P. Lettenmaier, E. F. Wood, and S. J. Burges, 1994: ——, and S. Manabe, 1989: The influence of soil wetness on near- A simple hydrologically based model of land surface water surface atmospheric variability. J. Climate, 2, 1447–1462. and energy fluxes for general circulation models. J. Geophys. Dickinson, R. E., and A. Henderson-Sellers, 1988: Modeling Res., 99, 14 415–14 428. tropical deforestation: A study of GCM land-surface param- Liu, Y., and R. Avissar, 1999: A study of persistence in the land– eterizations. Quart. J. Roy. Meteor. Soc., 114, 439–462. atmosphere system using a general circulation model and ob- ——, ——, P. J. Kennedy, and M. F. Wilson, 1986: Biosphere– servations. J. Climate, 12, 2139–2153. Atmosphere Transfer Scheme (BATS) for the NCAR com- Manabe, S., 1969: Climate and the ocean circulation. I. The at- munity climate model. Tech. Note TN-275ϩSTR, NCAR, mospheric circulation and the hydrology of the earth’s sur- Boulder, CO, 69 pp. face. Mon. Wea. Rev., 97, 739–744. ——, M. Shaikh, R. Bryant, and L. Graumlich, 1998: Interactive ——, and T. Delworth, 1990: The temporal variability of soil wet- canopies for a climate model (BATS). J. Climate, 11, 2823– ness and its impact on climate. Climate Change, 16, 185–192. 2836. McFarlane, N. A., G. J. Boer, J. P. Blanchet, and M. Lazare, 1992: Dirmeyer, P. A., 2000: Using a global soil wetness dataset to im- The Canadian Climate Centre second-generation general cir- prove seasonal climate simulation. J. Climate, 13, 2900–2922. culation model and its equilibrium climate. J. Climate, 5, ——, A. J. Dolman, and N. Sato, 1999: The pilot phase of the 1013–1044. global soil wetness project. Bull. Amer. Meteor. Soc., 80, 851– McMahon, T., 1979: Hydrological characteristics of arid zones: 878. The hydrology of areas of low precipitation. Rep. 128, IAHS, Douville, H., and F. Chauvin, 2000: Relevance of soil moisture for Canberra, Australia, 105–123. seasonal climate predictions: A preliminary study. Climate Mintz, Y., and Y. V. Serafini, 1992: A global monthly climatology Dyn., 16, 719–736. of soil moisture and water balance. Climate Dyn., 8, 13–27. Entekhabi, D., and I. Rodriguez-Iturbe, 1994: Analytical frame- Namias, J., 1952: The annual course of month-to-month persis- work for the characterization of the space–time variability of tence in climate anomalies. Bull. Amer. Meteor. Soc., 33, 279– soil moisture. Adv. Water Resour., 17, 35–45. 285. Entin, J. K., A. Robock, K. Y. Vinnikov, V. Zabelin, S. Liu, ——, 1959: Persistence in mid-tropospheric circulations between A. Namkhai, and Ts. Adyasuren, 1999: Evaluation of global adjacent months and seasons. The Atmosphere and the Sea in soil wetness project soil moisture simulations. J. Meteor. Soc. Motion: Rossby Memorial Volume, Bert Bolin, Ed., Rocke- Japan, 77, 183–198. feller Institute Press and Oxford University Press, 240–248. Fennessey, M. J., and J. Shukla, 1999: Impact of initial soil wetness Nijssen, B., R. Schnur, and D. P. Lettenmaier, 2001: Global ret- on seasonal atmospheric prediction. J. Climate, 12, 3167– rospective estimation of soil moisture using the VIC land 3180. surface model, 1980–93. J. Climate, 14, 1790–1808. Fiorino, M., 1996: AMIP II sea surface temperature and sea ice Noilhan, J., and S. Planton, 1989: A simple parameterization of concentration observations. [Available online at http://www- land surface processes for meteorological models. Mon. Wea. pcmdi.llnl.gov/projects/amip/AMIP2EXPDSN/BCS_OBS/ Rev., 117, 536–549. amip2_bcs.htm.] Roads, J., and A. Betts, 2000: NCEP–NCAR and ECMWF re- Foley, J. A., I. C. Prentice, N. Ramankutty, S. Levis, D. Pollard, analysis surface water and energy budgets for the Mississippi S. Sitch, and A. Haxeltine, 1996: An integrated biosphere River basin. J. Hydrometeor., 1, 88–94. model of land surface processes, terrestrial carbon balance, Robock, A., C. A. Schlosser, K. Ya Vinnikov, N. A. Speranskaya, and vegetation dynamics (IBIS). Global Biogeochem. Cycles, J. K. Entin, and S. Qiu, 1998: Evaluation of the AMIP soil 10, 603–628. moisture simulations. Global Planet. Change, 19 (1–4), 181– Gao, X. G., S. Sorooshian, and H. V. Gupta, 1996: A sensitivity 209. analysis of the Biosphere–Atmosphere Transfer Scheme ——, K. Ya. Vinnikov, G. Srinivasan, J. K. Entin, S. E. Hollinger, (BATS). J. Geophys. Res., 101, 7279–7290. N. A. Speranskaya, S. Liu, and A. Namkhai, 2000: The global Gates, W. L., and Coauthors, 1999: An overview of the results of soil moisture data bank. Bull. Amer. Meteor. Soc., 81, 1281– the Atmospheric Model Intercomparison Project (AMIP I). 1300. Bull. Amer. Meteor. Soc., 80, 29–56. Rowntree, P. R., and J. A. Bolton, 1983: Simulation of the atmo- Gedney, N., P. M. Cox, H. Douville, J. Polcher, and P. J. Valdes, spheric response to soil moisture anomalies over Europe. 2000: Characterizing GCM land surface schemes to under- Quart. J. Roy. Meteor. Soc., 109, 501–526. stand their responses to climate change. J. Climate, 13, 3066– Schemm, J.-K., S. Schubert, J. Terry, and S. Bloom, 1992: Esti- 3079. mates of monthly mean soil moisture for 1979–89. NASA Gibson, J. K., P. Kallberg, S. Uppala, A. Hernandez, A. Nomura, Tech. Memo. 104571, 252 pp. and E. Serrano, 1997: ERA description. ECMWF Re- Scinocca, J. F., and N. A. McFarlane, 2004: The variability of Analysis Project Rep. Series 1, Reading, United Kingdom, modeled tropical precipitation. J. Atmos. Sci., 61, 1993–2015. 77 pp. Sellers, P. J., Y. Mintz, Y. C. Sud, and A. Dalcher, 1986: A simple

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biosphere model (SiB) for use within general circulation Viterbo, P., and A. C. M. Beljaars, 1995: An improved land sur- models. J. Atmos. Sci., 43, 505–531. face parameterization scheme in the ECMWF model and its ——, and Coauthors, 1996a: The ISLSCP Initiative I global validation. J. Climate, 8, 2716–2748. datasets: Surface boundary conditions and atmospheric forc- von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in ing for land–atmosphere studies. Bull. Amer. Meteor. Soc., Climate Research. Cambridge University Press, 484 pp. 77, 1987–2005. Walker, J. M., and P. R. Rowntree, 1977: The effect of soil mois- ——, and Coauthors, 1996b: A revised land surface parameter- ture on circulation and rainfall in a tropical model. Quart. J. ization (SiB2) for atmospheric GCMS. Part I: Model formu- Roy. Meteor. Soc., 103, 29–46. lation. J. Climate, 9, 676–705. Willmott, C. J., C. M. Rowe, and Y. Mintz, 1985: Climatology of Shukla, J., and Y. Mintz, 1982: Influence of land-surface evapo- the terrestrial seasonal water cycle. J. Climatol., 5, 589–606. transpiration on earth’s climate. Science, 215, 1498–1501. ——, C. Nobre, and P. Sellers, 1990: Amazon deforestation and Xie, P., and P. A. Arkin, 1996: Analyses of global monthly pre- climate change. Science, 215, 1498–1501. cipitation using gauge observations, satellite estimates, and Teuling, A. J., and P. A. Troch, 2005: Improved understanding of numerical model predictions. J. Climate, 9, 840–858. soil moisture variability dynamics. Geophys. Res. Lett., 32, Yeh, T. C., R. T. Weatherald, and S. Manabe, 1984: The effect of L05404, doi:10.1029/2004GL021935. soil moisture on short term climate and hydrology Verseghy, D., 1991: CLASS—A Canadian land surface scheme change—A numerical experiment. Mon. Wea. Rev., 112, 474– for GCMs. I. Soil model. Int. J. Climatol., 11, 111–133. 490. ——, N. A. McFarlane, and M. Lazare, 1993: CLASS—A Cana- Zhang, G. J., and N. A. McFarlane, 1995: Sensitivity of climate dian land surface scheme for GCMs. II. Vegetation model simulations to the parameterization of cumulus convection in and coupled runs. Int. J. Climatol., 13, 347–370. the CCC GCM. Atmos.–Ocean, 3, 407–446.

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