1. Introduction
The ability to estimate grapevine water use is important for worldwide production (Mullins et al. 1992) in climates where water resources are limited. Vineyard architecture is variable because the trellis systems utilized to produce the grapes depend both on the final product desired (wine, raisins, or table grapes) and the method of harvest (by hand or machine). The spacing between rows and vines is adjustable, with canopy cover as low as 10% (Jacobs et al. 1996) or as high as 100%, depending on the trellising. Consequently, using crop coefficients and reference evapotranspiration to estimate crop evapotranspiration is not as straightforward as for other crops (Williams and Ayars 2005). Large lysimeters, which are capable of accurately measuring evapotranspiration on an hourly basis, are extremely expensive (Scott et al. 2005), so it is hard to justify their use by farmers.
A large variation in seasonal water use of mature grapevines has been reported, and it is unknown how much of the variability results from production practices or the measurement method (Williams et al. 2003a). Paraphrasing Williams et al. (2003b), the main limitations to determining evapotranspiration from vineyards are that “(1) soil and water balance techniques require difficult assessments of various soil and/or water parameters, (2) reliability of sap flow sensors is questionable; especially on large vines, and (3) micrometeorological techniques require expensive instrumentation and large areas of uniform fetch, which are uncommon in many grape production areas.” Because the surface renewal (SR) method may operate close to the canopy (Paw U et al. 1995, 2005), fetch requirements may be minimized, which makes it a useful micrometeorological method for small grape vineyards where fetch requirements limit the application of other methods. Spano et al. (2000), Castellví et al. (2002), and Castellví (2004) have used the SR method to estimate sensible heat flux H over grape vineyards. The methodology used in Spano et al. (2000) included high-frequency temperature measurements at several heights within the canopy. In their method, thermocouple damage was a possible limitation. The Castellví et al. (2002) and Castellví (2004) methods require temperature measurements only at a single level. The main difference between methods is that Castellví (2004) is a half-order closure model (i.e., scalar flux depends on the square root of the eddy diffusivity), whereas Castellví et al. (2002) is a semiempiric first-order closure model. The Castellví (2004) procedure gave a better match to sonic anemometer H data than Castellví et al. (2002). When measurements are taken within the roughness sublayer, however, the Castellví (2004) method requires (z* − d) as an input, where z* is the roughness sublayer depth and d is the zero-plane displacement.
This paper reports on a new SR procedure based on Castellví (2004) that is used to estimate sensible heat flux over a mature vineyard. An experiment was conducted during the summer of 2007 at the University of California in the Kearney Agricultural Research and Extension Center (KAC) near Parlier, California. The local climate is characterized by light winds and regional advection of sensible heat flux. The new procedure overcomes limitations derived from 1) fetch requirement restrictions, because it operates close to the canopy, 2) potential thermocouple damage and data acquisition system limitations, because required measurements are taken at a single level, and 3) the need to measure the zero-plane displacement, the roughness length for momentum, the plant area index (PAI), etc. It is indirectly shown that it is difficult to a priori guess realistic z* and d values based on observed weather conditions.
In grape vineyards, negligible heat storage may be assumed in the canopy. Based on Wilson et al. (2002), storage was considered insignificant for woody canopies with height less than 8 m. In Meyers and Hollinger (2004) storage in maize and soybean was less than 5% of the net radiation when the canopy was fully developed. Eddy covariance (EC) measurements of sensible and latent heat fluxes over pear and mango orchards with PAIs that are considerable greater than those of grapevines showed a lack of energy balance closure of 10%–12% (Conceição et al. 2008; Teixeira et al. 2008). Therefore, the lack of closure observed was similar to that of other canopies with negligible storage, such as grasses (Twine et al. 2000; Wilson et al. 2002; Castellví et al. 2008). For irrigation assessment and routinely hydrological applications, it is generally assumed that the simplified surface energy balance equation applies and closure is forced (Brutsaert 1988). At sites influenced by regional advection of sensible heat flux, however, closure forced via the Bowen ratio using similarity theory should be discarded (Motha et al. 1979; Todd et al. 2000; Lee et al. 2004). To use robust, easy to maintain, and affordable instrumentation in regional advection conditions, forcing closure to estimate latent heat flux as the residual of the simplified surface energy balance equation is an alternative if reasonable sensible heat flux estimates can be determined. In this paper, it is shown that the inputs required for estimating the sensible heat flux and the work of the expansion of air parcel under constant pressure can be provided by a two-dimensional sonic anemometer.
2. Theory
a. Surface renewal analysis for estimating sensible heat flux densities
b. Determination of the roughness sublayer depth
3. Materials and methods
a. The field experiment
The campaign was carried out from 28 August 2007 [1400 Pacific standard time (PST)] through 18 October 2007 (1300 PST). The drip-irrigated vineyard (Thompson Seedless Grapes) was about 1.4 ha (168 × 82 m2), and was mainly surrounded by annual and perennial crops and some bare soil. The space between vine trunks in a row was 2.15 m and across the rows it was 3.5 m. The canopy height was 2.3 m; the foliage extended from 0.4- to 2.3-m height above the ground, and there was about 2.5 m of clear space between foliage from one row to the next. The terrain was flat, the rows were aligned east–west, and the prevailing wind direction was from the north-northwest. The measurement tower was set up near the midpoint of the plantation with approximately 84 m in the prevailing wind direction. No half-hourly samples with wind direction parallel to the row alignment were observed.
The three wind speed components and the sonic temperature were recorded at 10 Hz at a height of 2.8 m above the ground using a 3D sonic [31000RE, R. M. Young, EXW (EX Works) Traverse City, Michigan]. The raw data were stored in binary format using a CR1000 logger (Campbell Scientific, Inc., Logan, Utah). Postprocessing consisted of conversion of the half-hourly data files to ASCII and processing the data using the protocol from Mauder et al. (2007) to determine means, variances, and covariances. The 3D classic coordinate rotation method was used instead of the planar rotation method.
No rainfall, calm winds, and high-amplitude daily temperatures were observed during the experiment. Table 1 shows the maximum, minimum, mean, and standard deviations observed for the wind speed, air temperature, friction velocity, sensible heat flux for unstable and stable atmospheric surface layer conditions, and the number of samples collected under stable and unstable conditions. Regional advection was common, and the atmospheric surface boundary layer typically became neutral around 1430 PST. Regional advection results from air movement from large nonirrigated areas, which surround the San Joaquin Valley, over the irrigated cropped areas on the valley floor.
b. Sensible heat flux determination
Ramp dimensions, friction velocity, roughness sublayer depth, the zero-plane displacement, and the stability parameter are required as input to estimate the sensible heat flux iterating Eqs. (1)–(5).
1) Ramp dimensions
Determination of coherent structures assuming a sequence of ideal ramps combined with the use of structure functions of different order (Van Atta 1977; Chen et al. 1997a) is an objective technique to estimate ramp dimensions (Paw U et al. 2005) which is desirable to provide an independent method to estimate scalar surface fluxes. Scheme 1 (Fig. 1b) was used. It requires a lower frequency than scheme 2 (the microfront time is on the order of few seconds). Once the ramp amplitude was determined, several time lags r were used to linearize the relationship, which holds for r ≪ Lr, A3 = −{[S3(r)]/r}τ, where S3(r) is the third-order structure function for solving the ramp period. According to Chen et al. (1997a), the shortest time lag to be used for linearization (r1G) is that which produces the first global maximum of S3(r)/r. To estimate the maximum time lag (rend) to be used for linearization so that r ≪ Lr, the second global maximum of S3(r)/r was determined. Based on a ramp model shown in scheme 2, the second global maximum for scheme 1 occurs at a time lag r2G, giving r2G ≈ ¾τ. According to Qiu et al. (1995), Lq ≈ 0.25τ and, therefore, r2G ≈ Lr. The last time lag used for linearization was determined as 1% of r2G or rend ≈ 0.01Lr to ensure that rend ≪ Lr. Therefore, the structure functions were evaluated within a range of time lags that provides a close ramp amplitude (Chen et al. 1997a) and total period (Chen et al. 1997b) to ramp model in scheme 2.
2) Friction velocity
3) Roughness sublayer depth, zero-plane displacement, and sensible heat flux estimation
If one selects samples at near-neutral conditions, (z*N − d) can be determined by rearranging terms in Eq. (5) by setting the appropriate
Some scientists found that d depends on the wind speed and stability conditions (Rosenberg 1974; Brutsaert 1988; Raupach 1994; Verhoef et al. 1997; Gao et al. 2003; Harman and Finnigan 2007), but others have not found this dependency, which suggests that d likely depends on the canopy architecture (Munro and Oke 1973; Adrie and Van Boxel 1988). Expressions for estimating d that depends exclusively on h, such as d ≈ ch, where c is a constant in the 0.5–0.95 range, were reported for uniform canopies and plants in rows when the wind direction was not aligned with the rows (Stanhill 1969; Kondo 1971; Brutsaert 1988; Wieringa 1993; Verhoef et al. 1997; Oue 2001; Takagi et al. 2003). We note that most studies to determine d are based on fitting the wind log law by measuring the wind speed at different heights using cup anemometers. To ensure high-quality measurements, samples were typically not used when u < 2 m s−1. Consequently, under light wind conditions over a heterogeneous surface, it is difficult to assign a priori a value for coefficient c for the scale d ≈ ch.
A procedure based on two steps is proposed to solve H. The procedure avoids d determination or subjective estimation and assumes that it remains constant. The appropriate expression for ϕh(ζ) [Eq. (4)] is known after determining the ramp dimensions for temperature. The two steps are described below.
(i) Step 1
Equation (1), with a constant α parameter, is used to estimate H for near-neutral cases. The
(ii) Step 2
Assuming d ≈ ch and coefficient c is known regardless of the wind direction (i.e., flow direction variability did not sense drastic roughness changes), Eqs. (1)–(4) can be iterated to solve for H. Starting with ζ = 0 and (z* − d), the first approximations for α, H, and L are found for the actual atmospheric surface layer. Using L, the first approximation for ζ is determined. Then, the process is iterated until convergence is achieved for ζ. Coefficient c is solved by trial and error to match H from steps 1 and 2; H estimates from step 1 are taken as a reference. Thus, coefficient c is estimated for near-neutral conditions by forcing agreement between Eqs. (2) and (5) through Eq. (4) via ζ. A method based on simulating annealing (SA) was used to solve for c. SA is a global optimization method that distinguishes between different local optima. By giving the different boundaries for the unknown coefficients involved in the function to be optimized, starting from an initial point, the algorithm takes a random step and the function is evaluated. After minimizing (or maximizing) the function, any downhill step is accepted; however, some uphill steps may also be accepted. Acceptability implies that the initial process starts. The uphill decision is made by the Metropolis criteria (Metropolis et al. 1953). As the optimization process proceeds, the length of the steps decline until it closes in a global optimum. SA is recommended as a local optimizer for difficult functions because it has proven superior to multiple restarts and conventional optimization routines for difficult problems. SA is even capable of providing solutions out of initial boundaries for very complicated functions, but it requires a powerful computer. Because boundaries for coefficient c can clearly be restricted between 0 and 1, a standard computer can accomplish the SA calculations (Goffe et al. 1994). The root-mean-square error (rmse) was the target function to be minimized.
c. Performance evaluation
Linear regression analysis (slope and intercept), coefficient of determination R2, and the rmse were used to compare the SR sensible heat flux HSR against the EC method HEC. The coefficient D = ∑y/∑x with x the estimate and y the reference value was also computed as an evaluation parameter (Marth 1988). The coefficient D is used to determine the percentage (p) being over- or underestimated as p = 100(1 − D), which provides an integrated evaluation of the bias on daily, weekly, and monthly time scales by averaging out random errors in the half-hourly estimates. The bias is (D − 1) times the mean value determined from the observations.
4. Results
a. Estimating (z*N − d)
According to vineyard architecture, the degree of heterogeneity was considered moderate, and thus according to the appendix
b. Estimating the zero-plane displacement and sensible heat flux
The optimum SA downhill gave the scale d = 0.62h. The H estimates comparing step 2 HSR2 and step 1 HSR1 are shown in Fig. 2. The linear fit had the following: slope = 1.00, intercept = 1.0 W m−2, and R2 = 0.98. Figure 3 shows HSR2 versus HEC for all of the data. The performance was generally excellent, with some spurious samples observed for a few stable cases when the sign of the ramp did not match the sign of HEC, or when HSR2 was close to zero. The worst estimates corresponded to samples gathered around 1500 (early September) to 1700 (October) PST during the transition from unstable to stable atmospheric conditions and during the night under calm conditions. However, the total number of spurious data was small, regardless of the stability case. Table 2 shows slope, intercept R2, rmse, and D obtained for HSR2 versus HEC for the unstable and stable cases and for all data. No bias was observed, and the rmse was small.
For all data, Eq. (6) provided reliable friction velocity estimates with linear fitting u* = 0.38σu and R2 = 0.91. In Eq. (5), the mean value found for (z*N − d) seemed small in comparison with other studies. Cellier and Brunet (1992) reported that the scale (z*N − d)/δ, where δ is the mean clear distance between rows aligned across the flow, fell between 3.0 and 4.0 over a 2.35-m-tall maize canopy, with δ = 0.8 m. For trees (savannah), Garrat (1980) found (z*N − d) ≈ 3δ, where δ is the mean horizontal spacing between trees. Fazu and Schwerdtfeger (1989) reported a factor of 4.6 and Wenzel et al. (1997) found a factor of 8.0 for a coniferous forest. Figure 4 shows the actual α [i.e., by rearranging terms in Eq. (1) and using HEC as the actual H] versus L for all of the data. When turbulence was mainly mechanically driven, the actual α values tended to fall within the interval (0.4, 0.6), so an
1) Analysis of sensitivity
If trial and error was directly applied to adjust (z*N − d) and d by minimizing the rmse between HSR2 and HEC for all the data, the results (Table 2) would be obtained for different pairs of (z*N − d) and d/h. For example, the local downhill providing the pair (3.5, 0.95) gave the following: slope = 1.0, intercept = −5.0 W m−2, R2 = 0.96, rmse = 15.0 W m−2, and D = 1.01. If LR denotes the rmse corresponding to a local downhill and GR corresponds to the global downhill (i.e., the optimum) rmse, then the total of 46 local downhills gave LR − GR ≤ 5 W m−2. This implies that the two-step process is useful for reliable H estimates, but the best estimates for (z*N − d) and d will remain unknown.
Table 2 shows the HSR2 performance for the other two pairs. The pair (2.58, 0.4) corresponding to
Based on Physick and Garratt (1995), it is questionable to consider (z*N − d) a constant. The authors suggested that (z* − d) linearly decays to about 37% of (z*N − d) when (z*N − d)/L ≥ 0.2, whereas (z* − d) remains fairly close to (z*N − d) for unstable cases. The same stability correction was implemented in the iteration procedure. For stable cases, HSR2 underestimated HEC by about 6% (D = 0.94). The intercept and rmse were the same as that shown in Table 2, but the regression statistics were slightly worse, with slope = 0.78 and R2 = 0.77. In essence, it was found that the H estimates captured a higher portion of the HEC variability when (z*N − d) was assumed constant. A variable (z* − d) stability correction could provide better estimates in other experiments. The actual z* and d was unavailable.
Because Eq. (4) is based on similarity theory, the procedure is only recommended for flat terrain. Castellví et al. (2008), however, showed that SR analysis, operating in the inertial sublayer, performed well for sensible heat, latent heat, and carbon dioxide fluxes over moderately sloping grassland located in the foothills of the Sierra Nevada Mountains near Ione, California, where similarity did not hold.
In the SR analysis, fetch requirements require further research (i.e., according to the authors’ knowledge; there is no publication on this topic). Therefore, it is difficult to address how the different footprints sensed by SR analysis and the EC method might alter the results shown in Table 2.
It is of interest to remark that the site showed little change in surface roughness with wind direction. Thus, the observed performance shown in Table 2 corresponds only to flows across rows. For wind direction that is parallel to the rows, a new pair [(z*N − d), d] might be needed.
5. Summary and concluding remarks
A new procedure to iterate H in SR analysis was presented. The results were close to H from the EC method. Only a few spurious H estimates were obtained, and they mainly corresponded to periods where ramps were not well formed. Because Eq. (6) is a key part of the estimation procedure, reliable measures of σu are crucial. Therefore, use of an affordable, two-dimensional sonic anemometer is recommended to ensure accurate inputs at low wind speeds of the wind direction and standard deviation. The work of expansion of air parcels under constant pressure needs to be included for closure of the surface energy balance. Using the sonic “near virtual” temperature addresses this problem (Paw U et al. 2000).
To conclude, a two-dimensional sonic anemometer operating close to the canopy can provide all of the inputs required to estimate half-hourly H and the work of expansion of air parcels under constant pressure in the new SR method. The combination of the SR procedure and the simplified surface energy balance equation appears to be an affordable alternative to be considered for estimating water use at sites influenced by regional advection of sensible heat flux.
Acknowledgments
The authors acknowledge the review task made by the three reviewers. Neil Rambo and Steve Ewert (Dept. of Water Resources, San Joaquin District, Fresno, California), Alfonso Russo (University of Catania, Catania, Italy), Tom Shapland and Frank Anderson (University of California, Davis, Davis, California), Larry E. Williams (University of California, Kearney Agricultural Center, Parlier, California), James Ayars (USDA ARS, Fresno, California) for helping with data collection and providing the research site, and Asun, Carla, and Tània for their help in using various facilities at the University of Lleida. This work was supported by a grant (4600004549) from the California Department of Water Resources (Sacramento, California), the TRANSCLA project (CGL 2006-12474-C01), and the Ministerio de Ciencia y Innovación (Spain).
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APPENDIX
The Parameter α: A Qualitative Analysis for Neutral Cases
(a) Sonic temperature vs time for a short interval on 15 Sep. (left) The unstable case with a 40-s ramp period and 2.5°C amplitude within a sample from 1030 to 1100 PST. (right) A ramp period of 42 s and amplitude of −0.5°C within a sample from 1500 to 1530 PST. Straight lines following the main trends were included to show the ramp-like pattern in time series. (b) Air parcel diagram of the renewal process. The time course of the scalar concentration for the positions shown in the diagram are idealized in two air temperature ramp models. Scheme 1 assumes a quiescent period and a sharp instantaneous drop in temperature. Scheme 2 neglects the quiescent period and assumes a finite microfront. Parameters Lr, Lq and Lf denote the warming, quiescent and microfront periods, respectively; A is the ramp amplitude and τ is the total ramp duration.
Citation: Journal of Hydrometeorology 11, 2; 10.1175/2009JHM1151.1
HSR2 corresponding to pair (3.0, 0.62) vs HEC.
Citation: Journal of Hydrometeorology 11, 2; 10.1175/2009JHM1151.1
Iterated α values corresponding to the pair (3.0, 0.62) vs (a) the pair (2.58, 0.40), and (b) the actual.
Citation: Journal of Hydrometeorology 11, 2; 10.1175/2009JHM1151.1
Maximum, minimum, mean, and standard deviation, observed for the wind speed, air temperature, friction velocity, and buoyant sensible heat flux for unstable and stable cases (N; number of half-hourly samples).
HSR2 corresponding to three distinct [(z*N − d), d/h] pairs vs HEC for unstable (Unst) and stable (Stab) cases, and for all data (All). Linear regression analysis: slope a, and intercept b (W m−2); R2, Rmse (W m−2), and D are defined in the text.
Table A1. Determined αN(z=h), from (A11), corresponding to different surfaces reported in the literature (Graefe 2004; Table 1). The following notation is used: D, mean distance between roughness elements; λ, frontal area index; PAI, plant area index; z0, roughness length for momentum; WT, wind tunnel experiment; and N/a, not available. Remaining terms are defined in the text.