This section will discuss a series of issues relating to the role of water in the SEB: both the impact at the surface on evapotranspiration, and the role of clouds on the surface radiative fluxes, as well as the part played by precipitation in the coupling between atmosphere and BL. Over land (in contrast to over the ocean), the availability of water essentially determines evaporative fraction
Figure 7 illustrates the primary role of soil water in the surface energy partition, and the impact on the diurnal cycle of 2-m temperature and humidity. Twenty-eight days with nearly clear skies during July and August, from the 1987 FIFE grassland prairie experiment near Manhattan, Kansas [Betts and Ball, 1995, 1998] have been stratified into three roughly equal groups, based on the 0-10cm volumetric soil moisture (which was measured gravimetrically). The left panel shows the mean diurnal cycle of Rnet (left-hand-scale) and daytime evaporative fraction EF (right-hand-scale). Rnet is almost the same for each group of days, peaking around 615 W m-2 at local noon (about 1820 UTC), because they were chosen for nearly clear skies. However the partition of Rnet into λE and H, represented by EF is radically different. As mean soil moisture increases from 14.7% (when the vegetation is stressed) to 29.9% (when the vegetation is unstressed), near-noon EF increases from 0.54 to 0.75. The right panel shows the large impact of these different surface fluxes on the diurnal cycle of 2-m temperature, T, and relative humidity, RH. We see the typical mirror opposites of RH falling as T rises (because diurnal changes of mixing ratio are relatively small) for all the data. However, with drier soils, there is a systematic shift to higher temperature and lower RH.
 From wet to dry soils, the afternoon RH minimum drops from 53% to 30%. This corresponds to an increase in PLCL, the pressure height of the LCL above the surface, from 134 to 239 hPa in the afternoon. I use PLCL extensively as measure of the LCL, because it can be computed easily from parcel T and pressure p, as
where p* is the parcel saturation pressure: the pressure at the LCL, when a parcel lifted dry adiabatically reaches water vapor saturation. Saturation temperature and pressure (T*, p*) define the properties conserved in reversible adiabatic processes [Betts, 1982], and the properties of parcels as they cross cloud boundaries. Over land, when there are BL clouds in the afternoon, PLCL gives a good estimate of mixed layer depth.
3.2. Diurnal Cycle on Vector Diagrams
 Two-dimensional vector plots are helpful for visualizing and quantifying the balance of processes involved in the diurnal cycle [Betts, 1992; Santanello et al., 2009]. Figure 9 is a remapping from Figure 7 of the daytime 2-m diurnal cycle (from 1115 to 2245 UTC) of the three FIFE soil moisture composites into a conserved parameter reference frame. The left panel is a (θ, Q) plot (potential temperature and mixing ratio): with a duplicate (Cpθ, λQ) scale in J kg-1. The right panel is the same data on a (θE, PLCL) plot (equivalent potential temperature, pressure height to LCL). The left panel has auxiliary dotted lines, corresponding to saturation pressure, p* = 900hPa, and virtual potential temperature, θv = 298K. The p* isopleths are roughly parallel, so one can visualize the rise of LCL along the daytime surface trajectories on the (θ, Q) plot.
Figure 9. Daytime 2-m diurnal cycle for three FIFE composites, partition by soil moisture: (left) a (θ, Q) plot, showing vector budget from 1415 to 2045 UTC, and (right) a (θE, PLCL) plot.
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 The triangle, superimposed on the left panel, is a schematic BL vector budget for the high soil moisture composite for the period 1415 to 2045: representing the vector time-change as the sum of a surface flux vector and an entrainment flux vector. This is constructed as follows [see Betts, 1992. The simplified mixed layer (ML) budget can be written for a time-step, Δt, when the mean depth of the mixed layer is ΔZi, as
where Δξm is the vector Δ(Cpθ, λQ)m, that is the change in ML values between 1415 and 2045 (heavy dashes), Fs is the surface flux vector and Fi is the entrainment flux vector, representing the mixing down of warm, dry air from above the ML. We approximate the ML change with the 2-m change of (Cpθ, λQ) in Figure 9. The length of the surface flux vector (heavy line) is calculated [setting θ/T ≈ 1] from the relation
using the scaling ‘velocity’
The entrainment vector, Fi, is the third (dotted) leg of the triangle, which can be found as a residual, using (13) to convert the dotted vector to a flux. Thus the ML step from 1415 to 2045 can be regarded as the sum of the surface flux vector, which warms and moistens, and the entrainment vector that warms and dries the ML. We have of course ignored advection in the simplified (11), so the advection of (Cpθ, λQ) in time Δt is also a vector contribution to the residual. Warm, dry advection will have a similar impact on the ML as the entrainment of warm, dry air from above. Using a large time-step (here 6.5h) in (11) introduces a small approximation, but for the case shown it is only a few %.
 The slope of the surface flux vector on Figure 9 is related to the surface Bowen ratio, BR = H/λE: it is actually (θ/T)(H/λE), since the figure is plotted in terms of potential temperature. For this high soil moisture case, the surface flux vector is slightly less than the slope of p* = 900 hPa, meaning that the surface fluxes alone would tend to lower cloud-base. It is the entrainment fluxes therefore that are responsible for the rise of cloud-base. For this high soil moisture composite, we have an estimate of mixed layer depth, ΔZi(t), from sequential sondes [Betts and Ball, 1994], launched during intensive periods. We do not show the corresponding vector figures for the drier soils, because there is no sonde data. However as EF falls, BR increases and the surface flux vector becomes steeper (that is it rotates anti-clockwise), which contributes to the greater rise of PLCL. In addition, entrainment of dry air from above the ML (which has a lower saturation pressure) also increases as H increases.
 The right panel showing (θE, PLCL) gives a reference for moist processes. Also shown (open circle) is the equilibrium state over a tropical ocean corresponding to the same daily mean surface flux, H+λE, as these FIFE composites, from the solutions of Betts and Ridgway ; and the 24-h mean surface 2-m states for our FIFE composites (solid circles). The picture here is that, although the mean state over land has a lower θE than over the oceans, the superimposed diurnal cycle over land gives a higher θE in the afternoon; and the highest values (favoring deep convection) for the wettest soils for which evaporation is the highest. Afternoon cloud-base is the lowest over wet soils, although not as low as over the ocean.
3.3. Water Availability, Evaporation and LCL
 The fundamental reason why the LCL is higher over land than over the ocean is that water is less available for evaporation. In physiological terms the resistance to transpiration means there is a drop in the RH across a leaf, and this translates into a lower mean RH in the ML. In Figure 7, differences in soil moisture for this grassland prairie change the EF, and the diurnal cycle of RH with corresponding differences in the diurnal rise in the LCL. Model parameterizations, which link vegetative resistance and therefore evapotranspiration to soil moisture, reproduce this behavior in the land-surface climate.
 Figure 10 (left panel) shows the warm season diurnal cycle in ERA-15; an average over the Missouri river basin binned in 2% ranges of 0-7cm soil moisture. The four soil-layer land-surface model at that time was Viterbo and Beljaars . There is a monotonic increase in PLCL (with a corresponding decrease in RH) for drier soils. This is characteristic of this type of land-surface model, although it is an over-simplified representation. For example, over the boreal forest with extensive regions of wet organic soils, soil moisture is a much weaker control on EF and LCL. However, there are extensive moss layers on the surface in spruce forests, which store substantial water after rain (in addition to the water storage in the canopy). After heavy rain, evaporation falls on sequential days as this surface vegetation layer dries out. The right panel shows the diurnal cycle of PLCL in summer for the BOREAS northern study site. The data has been binned by a wet surface index, based on recent past rainfall [Betts et al., 2001b]. For an index of 5, which means more than 5mm of rain fell the previous day, LCL is low. After five days without rainfall, an index of zero, afternoon PLCL has increased from 75 to 195 hPa.
Figure 10. Warm season diurnal cycle of PLCL for the Missouri river basin as a function of 0-7cm soil moisture (left) and (right) for boreal forest site in Thompson, Manitoba.
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 RH is a routine measurement (although accurate measurement is often a challenge) and PLCL can be calculated from p, T and RH (and when BL clouds are present, lidar ceilometers give an independent measure of LCL). So we can think of PLCL as an observable, linked to the availability of water for evaporation, which can be used to evaluate the impact of model parameterizations on surface climate in the model.
3.4. Land-surface-BL Coupling
 In the coupled land-surface-BL system, evapotranspiration is just one factor. Figure 10 shows that the 24-h mean PLCL shifts with the availability of water for evaporation, so it is useful to look at the relationships between daily mean parameters. The day and night-time boundary layers differ, but in a sequence of undisturbed days, a quasi-equilibrium is established. The BL equilibrium of RH and LCL on daily timescales depends on atmospheric processes as well as surface processes.
 Figure 11 shows for ERA-40 for the Madeira river the joint dependence of PLCL (with RH plotted on right-hand-scale with slight approximation) binned by precipitation rate (in mm day-1) and first-layer soil moisture index, SMI-L1 (left panel) and EF (right panel). SMI-L1 is computed for the first 0-7cm soil layer as
where SM is the model soil water fraction, the model soil permanent wilting point is 0.171 and the model field capacity is 0.323. SMI-L1 is not only a useful index on the daily time-scale for the availability of water for evaporation (although transpiration depends also on soil water in deeper layers), but it also responds to precipitation on this time-scale. A representative set of standard deviations of the daily mean data are shown. Not surprisingly as SMI and EF increases, mean cloud base descends and RH increases; but RH also increases as precipitation increases. This is a highly coupled system. When the LCL is lower, more precipitation is likely; but the converse is also true: the evaporation of precipitation as it falls through the sub-cloud layer will lower the LCL, and increase SMI-L1 on daily time-scales.
 Figure 11 links one key observable (PLCL) with several important but poorly measured processes in the land-surface-atmosphere coupling. Over the diurnal cycle of the boundary layer the atmosphere integrates over much larger spatial scales, so that the diurnal cycle of PLCL and its daily mean represent processes on scales of order one day's advection (432 km at 5 m s-1). Soil moisture is an important parameter in the model system, but in the real world, in-situ measurements of soil moisture represent quite local processes. Satellite microwave measurements may give us useful estimates of near-surface soil moisture. EF can be measured on towers, but these are representative only of a local footprint. On basin-scales we can make estimates of the land-surface fluxes using hydrologic models [Maurer et al., 2002]. Evaporation of falling precipitation plays a fundamental role in the model surface interaction, because evaporation of water above the surface cools and moistens the BL, which increases the surface Bowen ratio; while evaporation off a wet canopy reduces the Bowen ratio. The structure shown in Figure 11 for ERA-40 is broadly consistent with observations, but models in general show a wide range of behavior [Dirmeyer et al., 2006].
Figure 11. Stratification of PLCL by soil moisture index and precipitation (left) and (right) EF and precipitation. Daily-mean ERA-40 data for Madeira River.
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3.5. Separating Cloud and Surface Controls on the SEB and EF
 Figure 12 gives a conceptual split of the surface energy balance in terms of the atmospheric and cloud processes that primarily determine Rnet; and the surface processes, soil moisture and temperature that primarily determine EF (the partition of Rnet). We use ERA-40 data, averaged over the Missouri river basin [Betts, 2007], so the figures reflect the physical parameterizations in that reanalysis.
Figure 12. Dependence of Rnet (clear-sky) and cloud forcing on αcloud (left) and (right) EF on temperature and soil moisture index.
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 The left panel is the partition of Rnet into the clear-sky Rnet(clear) and the cloud forcing CF = SWCF + LWCF.
 We have chosen May-August, so the variations in the top-of-the-atmosphere solar flux are small. We have added the partition with soil moisture, SMI-L1, but this has no impact on CF, which depends almost solely on αcloud (see (3) and Figure 5). Rnet(clear) also has little dependence on SMI-L1. Surface albedo, not shown, has little variability in summer. So we can think of surface Rnet being the sum of the clear-sky flux with little variability in summer and the atmospheric cloud forcing, which has a linear dependence on αcloud.
 EF shown in the right panel determines the partition of Rnet; and this is a strong function of soil moisture, represented here by SMI-L1, but also of temperature. The slope with temperature is close to the slope of the classic ‘equilibrium evaporation’ relation [Priestley and Taylor, 1972; McNaughton, 1976], defined as
where β(T) = (λ/Cp) (∂qs/∂T)p is related to the slope of the Clausius-Clapyron equation at constant saturation pressure, plotted here for the mean surface pressure, 900hPa for the Missouri river basin. The slope of the saturation pressure line, p* = 900hPa, in Figure 9 is just (θ/T)β. The slope of (16) on Figure 12 just comes from the non-linearity of the Clausius-Clapyron equation. There are of course many other non-linear processes influencing the surface fluxes in the model (ERA-40), but we can loosely interpret the right panel as conceptually splitting the thermodynamic impact of increasing temperature on EF (at constant p*) from the impact of decreasing soil moisture (and increasing vegetative resistance), which by dropping the RH across the leaf, reduces mixed layer RH and p*, and increases PLCL and mean cloud-base.
3.6. Coupling Between Cloud Albedo and Surface Fluxes
 Stratifying surface fluxes by cloud albedo changes our perspective on the SEB. Figure 13, adapted from Betts et al. , stratifies surface flux data in summer by cloud albedo; comparing BERMS observations from three forest types, stands of old aspen, black spruce and jack-pine (abbreviated on the Figure as OA,OBS and OJP), with ERA-40 data from the nearest grid-point. On panels (a) and (b) the heavy lines are the ERA-40 data. The left panel (a) shows the radiation fluxes and RH stratified by αcloud. All three flux sites and ERA-40 show a similar structure: quasi-linear behaviour of the net fluxes with αcloud, consistent with our earlier Figure 5 (also BERMS data) and Figure 12 (ERA-40, Missouri basin). The lower surface albedo of the conifer sites give slightly larger net SW fluxes with low cloud cover, but model and observations broadly agree, and show the surface radiation fluxes are largely determined by the surface SW cloud forcing. Note the increase of mean 2-m RH with αcloud.
Figure 13. αcloud stratification of (a) radiation fluxes and RH; (b) H, λE and EF; (c) Net CO2 flux and precipitation.
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 The center panel (b) stratifies H, λE and EF by αcloud. For the conifer sites (the dominant landscape cover) and for ERA-40, the slope of sensible heat flux with αcloud is much steeper than the slope of λE: that is variations in cloud cover and Rnet are projected more onto H than λE; so that EF increases with reflective cloud cover. For the deciduous aspen site, which has the highest EF in summer, changes in Rnet from αcloud are projected roughly equally onto H and λE. Traditional hydrologic models link evaporation to Rnet, but in the fully coupled system, it is H not λE that is more tightly coupled to Rnet for these conifer sites and in ERA-40 [Betts, 2004]. In ERA-40, model errors in cloud cover are largely projected onto H [Betts et al., 2006].
 The right panel (c) shows the stratification of the net CO2 flux for the BERMS sites by αcloud, and the corresponding distribution of mean precipitation for the aspen site (point precipitation is a noisy field and the standard deviations, which we do not show, are as large as the mean). All the BERMS sites show a weak maximum in their net ecosystem exchange at an intermediate αcloud ≈ 0.35, characteristic of a typical cumulus cloud fraction. This is probably due to a combination of factors: vapor pressure deficit stress under clear skies and the higher photosynthetic efficiency for diffuse radiation (scattered by the cloud field). Clearly there are many processes involved in the coupled system, and integrated analyses of the BL coupling between the carbon and water cycles are needed.