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Seasonal and climatic variation of weighted VPD for transpiration estimation
European Journal of Agronomy 113 (2020) 125966
Contents lists available at ScienceDirect
European Journal of Agronomy journal homepage: www.elsevier.com/locate/eja
Seasonal and climatic variation of weighted VPD for transpiration estimation
T
Michel Edmond Ghanema, Zakaria Kehelb, Hélène Marrouc, Thomas R. Sinclaird,* a
Mohammed VI Polytechnic University, AgroBioSciences (AgBS), Lot 660 Hay Moulay Rachid, 43150, Ben Guerir, Morocco International Center for Agricultural Research in the Dry Areas (ICARDA), Rabat, Morocco c SYSTEM, Montpellier SupAgro, INRA, CIRAD, IAMM, Univ Montpellier, Montpellier, France d Crop and Soil Sciences Department, North Carolina State University, Raleigh, NC 27695-7620, USA b
A R T I C LE I N FO
A B S T R A C T
Keywords: Daily vapor pressure deficit France Seasonal vapor pressure deficit Weighted vapor pressure deficit
Vapor pressure deficit (VPD) is one of the critical variables that drives evapotranspiration, and is of fundamental importance in crop physiology and modeling in the face of climate change. Unfortunately, direct records of atmospheric moisture are rarely available at short temporal scales, e.g. hourly, and country or regional scales. Most models use approximations to estimate daily transpiration-weighted VPD. Tanner and Sinclair (1983) suggested an approach to calculate weighted daily VPD as a fraction (0.75) of the difference between daily maximum and minimum vapor pressure based on estimates calculated from daily maximum and minimum temperatures, respectively. A test of the Tanner-Sinclair suggestion is reported by obtaining daily weighted VPD from hourly measurements of humidity and temperature. The objective of this study was to assess the fractional value to obtained daily weighted VPD estimations. This study was based on ten years of hourly weather data collected at thirty five stations across the wide diversity of environments that exist in France.
1. Introduction Water deficits are the major limitation to increasing crop yields in many regions of the world. The driving force of transpiration rate is the gradient in vapor pressure between the comparatively dry atmosphere and the wet interior of leaves, commonly referred to as the vapor pressure deficit (VPD). A surrogate for this vapor pressure gradient is VPD of the air since leaf temperature does not often differ greatly from air temperature. Therefore, air VPD is calculated as the difference between the saturated water vapor pressure at air temperature (es) and the actual water vapor pressure of the air (ea). That is, VPD = es- ea, where es (kPa) and ea (kPa) are saturation vapor pressure and actual vapor pressure, respectively. Clearly, VPD is temporally dynamic through the daily weather cycle usually with minimum values in the morning and maximum values in the mid-afternoon. The importance of VPD in the determination of transpiration rate was originally identified by Penman (1948) in his “sink strength” model. More recently, Tanner and Sinclair (1983) and Sinclair et al. (1984) presented a theoretical derivation describing transpiration rate based on plant characteristics and VPD. Their derivation can be arranged to define integrated transpiration (Tr) as an explicit function of integrated plant growth (G).
⁎
ʃ Tr dt = ʃ (G *
VPD ) dt kd
(1)
Where kd a transpiration efficiency coefficient (Pa), which is essentially constant within a species because it is dependent on the explicitly defined, stable physiological terms of conversion coefficient of hexose to plant mass and of the biochemical pathway for CO2 assimilation (i.e., C3 vs. C4) (Tanner and Sinclair, 1983). While both Penman’s sink strength model and Eq. (1) can be readily applied to determining integral Tr for short-time periods of minutes, it becomes more problematic for longer-time periods of hours and days because of the likely variability of VPD over these longer-time periods. Since in many practical approaches it is desired to estimate daily Tr, the critical question is what is the appropriate value of VPD in the calculation of daily Tr. Somewhat surprisingly, estimation of daily weighted VPD is yet to be fully explored. Tanner and Sinclair (1983) originally described a method to estimate weighted daily VPD from daily maximum temperature (Tmax) to calculate daily maximum vapor pressure (VPmax), and from daily minimum temperature (Tmin) to calculate daily minimum vapor pressure (VPmin). The value of VPmin was calculated assuming Tmin approximated dew point temperature for the day, reflecting a more-or-less stable value for the atmospheric vapor pressure
Corresponding author. E-mail address: [email protected] (T.R. Sinclair).
https://doi.org/10.1016/j.eja.2019.125966 Received 29 December 2018; Received in revised form 13 September 2019; Accepted 25 October 2019 1161-0301/ © 2019 Elsevier B.V. All rights reserved.
European Journal of Agronomy 113 (2020) 125966
M.E. Ghanem, et al.
Fig. 1. Meteorological stations distribution accross France.
Fig. 2. Changes of daily VPD fraction (Fracd) in Gif-sur-Yvette (A) variation of the daily Fraction. (B) moving mean of Frac based on the daily Frac values for two weeks before and after each date.
Meinke et al. (1997) found that a Frac value of 0.75 worked well for a study in Queensland, Australia. The most extensive study in approximating VPDw was subsequently done in Argentina where Abbate et al. (2004) examined the appropriateness of Eq. (2) for environments in Argentina. Their analysis was based on weather data collected at five weather stations during the wheat production season. They found a slightly lower coefficient than suggested by Tanner and Sinclair (1983) of 0.72 as the appropriate Frac in estimating VPDw. These previous studies indicating a fairly constant value for Frac offer a very limited basis for such a conclusion. The current study was undertaken to explore the possibility that the value of Frac may be more variable than previously recognized. Therefore, the objective of this study was to examine values of Frac over a range of divergent environments. France offers such a wide range of climates and an extensive hourly historical weather record to undertake such an analysis. Across the country, climates range from the influence of oceanic and semi-oceanic flows in the west to continental and mountain impacts in the east. In addition, the south coast of France is subjected to a Mediterranean climate, which is generally drier than the rest of France, and without the cold winters of the other climate zones (Joly et al., 2010). Therefore, it is anticipated that this range of environments across France offers a broad test for possible variability in the value of Frac.
through the day. Using our notation, Tanner and Sinclair (1983) suggested the weighted daily vapor pressure deficit be approximated as “three-quarters the distance between VPmin and VPmax; this is reasonable for locations with a diurnal temperature range of 20°C and low Tmin, assuming the daily vapor pressure should be integrated from about 0900 h to evening, when net radiation becomes negative.” This conclusion was based on measurements made at Madison, WI, USA. Tanner and Sinclair (1983) went on to suggest that at locations where Tmin is high such as Yuma, Ariz, the daily vapor pressure deficit was “about two-thirds” of the distance between VPmin and VPmax. Therefore, the generalized equation to express daily weighted VPD (VPDw) based on the suggestion of Tanner and Sinclair (1983) is
VPDw = Frac *(VPmax − VPmin)
(2)
where the vapor pressures are calculated from measurements of daily maximum and minimum temperature. That is,
17.269 * Tmax ) 237.3 + Tmax
(3)
17.269 * Tmin ) 237.3 + Tmin
(4)
VPmax (kPa) = 0.61078 *exp(
VPmin (kPa) = 0.61078 *exp(
Frac is a fraction, which based on the suggestions of Tanner and Sinclair (1983) would have values in the range of 0.75 to 0.66. 2
European Journal of Agronomy 113 (2020) 125966
M.E. Ghanem, et al.
Fig. 3. Distribution of monthly VPD fraction (Fracm) in the Alenya, Salon de Provence, Orléans, Gif-sur-Yvette, Thonon and Creysse stations.
2. Material and methods
assumption of this approach is that the contribution of transpiration rate at each hour to the daily transpiration was proportional to the radiation received at each hour (Sh) consistent with Eq. (1). Hence,
Weather data were obtained for ten years at each of thirty-five meteorological stations in France, which were selected to cover the wide diversity of environments in France. Fig. 1 shows the location of the selected meteorological stations in continental France, Corsica and Guadeloupe. Hourly air temperature (T, °C), relative humidity (RH, %), and solar radiation (S, Joule cm−²) were obtained from INRA France CLIMATIK platform (https://intranet.inra.fr/climatikv2/) for each of the meteorological stations. Hourly measurements were used to compute hourly VPD (VPDh) based on reported RHh measurements using the following equation:
VPDwd =
n i=0
((7))
Daily estimates of the fraction Fracd were obtained by rearranging Eq. (2) such that
Fracd = VPDwd /(VPmax − VPmin )
(8)
2.1. Data analyses
RH VPDh = (1 − ⎛ h ⎞ )* SVPh ⎝ 100 ⎠
(5)
2.1.1. Fraction estimation using linear mixed models A linear mixed model was fitted to the daily calculated fraction (Fracd) from all stations. The data from stations were unbalanced as climatic records were not available for all stations in all months/years. Station, month, and year and all interactions with station effects were considered as random. This was useful to partition the total variance into different effects influencing the estimation of the daily calculated Frac and a separate residual for each station/month/year. Outliers were
Where SVPh (kPa) is hourly saturation vapor pressure calculated from hourly temperature as:
SVPh (kPa) = 0.61078 *exp(
n
∑i =0 (VPDh * S h) / ∑ Sh
17.269 * T ) 237.3 + T
(6)
A daily weighted vapor pressure deficit (VPDwd) was obtained by scaling the hourly VPDh based on solar radiation values. The 3
European Journal of Agronomy 113 (2020) 125966
M.E. Ghanem, et al.
Fig. 4. Distribution of monthly VPD fraction (Fracm) across France A for December, May, June, and September.
Frac were considered as the station fraction (Fracs). Mixed model analysis was run using AsReml (Gilmour et al., 1995; Butler et al., 2010) package in (R Development Core Team, 2008). 2.1.2. Spatial analysis Spatial autocorrelation (SAU) was used to assess whether Fracs for each station is clustered, dispersed, or random over space. Moran’s I was used to calculate spatial autocorrelation and its significance (Cliff and Ord, 1973, 1981). To determine how data were clustered, we used methods developed by Getis and Ord (1992, 1996) not only to allow hypothesis testing to determine whether clustering has occurred within the data, but also to provide information on the extent to which aboveand below-average values cluster and to identify local concentrations of clustering (Laffan, 2006; Mueller-Warrant et al., 2008). This is done by computing local spatial autocorrelation by means of G statistics. Zscores and their related p-values were then extracted. The Z-score is highly positive (negative) and significant at 1, 5, or 10%, which shows that high (low) values of the data are clustered spatially together and that there is a less than 1, 5, or 10% likelihood that this high-clustered (low-clustered) pattern could be the result of a random process. The spatial analyses were done using spdep (Bivand and Wong, 2018) package in R (R Development Core Team, 2008).
Fig. 5. Distribution of Station VPD fraction (Fracs) (average over 12 months of monthly fraction Fracm) across France. Red colors indicate higher Fracs values. Green color indicates lower Fracs values. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
3. Results 3.1. Seasonal differences in daily and monthly fraction Daily Fracd was not constant over the full range of tested conditions and it varied from 0 to 4.12 across the tested environments. Fig. 2a shows an example of variation of the daily Fracd at the Gif-sur-Yvettes station. These results indicate that calculations of individual daily transpiration rates based on a constant Frac may not be uniformly reliable as a result of the day-to-day variation in Frac. On the other hand, long-term transpiration rates relying on a stable Frac were found to be satisfactory for many locations. The results in Fig. 2b are the moving mean of Frac based on the daily Frac values for two weeks before and after each date. In this example, Frac is fairly stable with a mean value of 0.75 ± 0.33.
Fig. 6. A) Local G statistics (clusters of high values in red) of yearly (average over months Fracm) VPD fraction across France. B) corresponding p-value (blue are significant local high clusters at 5%). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
identified as data points with studentized residuals superior to 3.5 and were removed from data and were defined as missing. Monthly fractions (Fracm) per station across years were then estimated using best linear unbiased predictors (Blups). The average of monthly values of 4
European Journal of Agronomy 113 (2020) 125966
M.E. Ghanem, et al.
Fig. 7. Scatter plots comparing the weighted VPD to VPD0 calculated with a fraction of a) 0.75 and b) 0.98 for the Mediterranean stations.
Fig. 8. Correlation between daily dewpoint temperature (Tdew) and minimum temperatures (Tmin) in two different stations: Orléans, and Salon de Provence.
continental and semi-oceanic climates. However, in the Mediterranean region, and in the eastern parts of France and in Brittany the value of Fracm was in the range of 0.8 to 0.9. During September, Fracm was greater than 0.9 along the Mediterranean Coast (Fig. 4). Clustering analyses showed that southern French meteorological stations (corresponding to the Mediterranean stations) always clustered together and that the Fracm in these stations were always higher than the remaining stations in France across the year (Figs. 5 and 6). Spatial analysis revealed a significant spatial autocorrelation with a value of Moran’I = 0.4 showing that meteorological stations that are geographically close have similar Frac. In addition, Z-scores values of five Mediterranean stations (Avignon, Salon de Provence, Roujan,
Mean monthly values of Fracm were calculated for each of the 35 locations. These results highlighted both seasonal and regional differences. As shown in Fig. 3 for six locations, minimum values of Frac occurred during the summer and high values occurred during the winter. The minimum Fracm value calculated for the summer months varied somewhat among locations. 3.2. Regional differences in Frac estimation The results presented in Fig. 4 for the three growing-season months (May, June, and September) showed the appropriate Fracm was in the range of 0.7 to 0.8 for large areas of France. This narrow range of Fracm previously predicted was prevalent in the areas generally experiencing 5
European Journal of Agronomy 113 (2020) 125966
M.E. Ghanem, et al.
annual water loss since during the cold winter months transpiration is very low due to the fact that there is either no crop growth or growth is extremely small. That is, the calculated transpiration rates will be very low regardless of the error in the value of Frac. The second situation where Frac was found to deviate from the 0.7 to 0.8 range was in those regions and times of year where it was likely winds came off of the neighboring seas (Fig. 4). This situation appears to be another case where the minimum temperature does not reach the dew point. Air moving from the seas at night is likely to have been warmed so the minimum temperature did not decrease to the dew point temperature. Hence, the high minimum temperature resulted in an over-estimated high VPDmin and a low VPDd (Fig. 8). Consequently, estimation of Frac in the coastal Mediterranean region needs special attention in the Fall and Winter months were Fracm was calculated to be in the range of 0.9 to 1.0 for a large area in these sea-influenced regions.
Alenya and Bellegarde) were significantly higher than the other stations in France (Fig. 6A). The results for Frac in December (Fig. 4) showed elevated values of greater than 0.8 in virtually all areas of France. The central area running southwest to northeast had Frac in the range of 0.80 to 0.90. For the southern and eastern areas and Brittany, the estimates of Frac were in the range of 0.90–1.0 for December. To illustrate the impact of Frac on calculated VPDwd, values of VPDwd for the five Mediterranean stations with the extreme Frac of 0.98 were calculated (Fig. 7). These results were compared with the estimates based on a Frac value of 0.75. VPD calculated using both fractions explained 93% of the weighted VPD. However, the results with Frac equal to 0.98 matched much better the 1:1 correspondence line than the results obtained using the 0.75 value. 4. Discussion
References Estimates of daily canopy transpiration require a weighted VPD to reflect the temporally dynamic atmospheric conditions under which transpiration is occurring. A mean daylight VPD, for example, fails to properly weight VPD for the fact that much of the transpiration occurs during the midday when the VPD is the highest. Tanner and Sinclair (1983) suggested that an appropriately weighted VPD could be approximated as a fraction of maximum daily VPD based on minimum and maximum temperature, which we have labeled as Frac. They suggested a value for Frac of 0.75. In this study of the diverse climates of France, it was found that during the summer and fall months, when crop transpiration accounts for much of the annual evaporated water, the derived values of Frac were, in fact, in the range of 0.7 to 0.8 (Figs. 3,4). This range for Frac was consistent with the suggestion of Tanner and Sinclair (1983) and the observations of Meinke et al. (1997) and Abbate et al. (2004). However, this study indicated two situations where a value of Frac of about 0.75 cannot be assumed. The results of the environmental analysis of this study showed the appropriate Frac value being greater than 0.8 (Figs. 3,4) under special circumstances. For example, the impact of assuming a Frac equal to 0.75 for the Mediterranean area in contrast to 0.98 (Fig. 7) results in an inappropriately small value of VPDw and an underestimation of canopy water loss in most models. To more accurately reflect VPD conditions at some times of the year and locations, it may be necessary to account for environmental variation in VPDw. One specific situation requiring a larger Frac than 0.75 in calculating the VPDw is during the winter months. The value of Frac to calculate transpiration during the winter months was found to be 0.8 or greater for most of France. These high values for Frac seem likely to be a result of daily minimum temperature often not decreasing to the dew point temperature, which would be very low as a result of the cold, dry atmosphere during the winter months. This is illustrated in Fig. 8 of a plot in December for Orléans of dewpoint temperature vs. minimum temperature on many days. Of course, this winter deviation in Frac to estimate transpiration is likely to result in only a small error in total
Abbate, P.E., Dardanielli, J.L., Cantarero, M.G., Maturano, M., Melchiori, R.J.M., Suero, E.E., 2004. Climatic and water availability effects on water-use efficiency in wheat. Crop Sci. 44, 474–483. Bivand, R.S., Wong, D.W.S., 2018. Comparing implementations of global and local indicators of spatial association. TEST 27 (3), 716–748. https://doi.org/10.1007/ s11749-018-0599-x. Butler, D.G., Cullis, B.R., Gilmour, A.R., Gogel, B.J., 2010. Analysis of Mixed Models for S Language Environments: ASReml-R Reference Manual. DPI Publications, Brisbane. Cliff, A.D., Ord, J.K., 1973. Spatial Autocorrelation (London: Pion). Cliff, A.D., Ord, J.K., 1981. Spatial Processes: Models and Applications (London: Pion). Getis, A., Ord, J.K., 1992. The analysis of spatial association by use of distance statistics. Geogr. Anal. 24, 3. Getis, A., Ord, J.K., 1996. Local spatial statistics: an overview. In: Longley, P., Batty, M. (Eds.), Spatial Analysis: Modelling in a GIS Environment. GeoInformation International, Cambridge, pp. 261–277. Gilmour, A.R., Thompson, R., Cullis, B.R., 1995. Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models. Biometrics 51, 1440–1450. Joly, D., Brossard, T., Cardot, H., Cavailhes, J., Hilal, M., Wavresky, P., 2010. Les Types de climats en France, une construction spatiale, Cybergeo: European Journal of Geography [online], Cartographie, Imagerie, SIG, document 501, Published online on 18 June 2010, Consulted on 10 September 2019. URL:. https://doi.org/10.4000/ cybergeo.23155. http://journals.openedition.org/cybergeo/23155. Laffan, S.W., 2006. Assessing regional scale weed distributions, with an Australian example using Nassella trichotoma. Weed Res. 46, 194–206. Meinke, H., Hammer, G., van Keulen, H., Rabbinge, R., Keating, B.A., 1997. Improving wheat simulation capabilities in Australia from a cropping systems perspective: water and nitrogen effects on spring wheat in a semi-arid environment. Eur. J. Agron. 7, 75–88. Mueller-Warrant, G.W., Whittaker, G.W., Young, W.C., 2008. GIS analysis of spatial clustering and temporal change in weeds of grass seed crops. Weed Sci. 56 (5), 647–669. Penman, H.L., 1948. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. Lond. A193, 120–146. R Development Core Team, 2008. R: A Language and Environment for Statistical Computing. ISBN 3-900051-07-0, URL. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org. Sinclair, T.R., Tanner, C.B., Bennett, J.M., 1984. Water-use efficiency in crop production. BioScience 34, 36–40. Tanner, C.B., Sinclair, T.R., 1983. Efficient water use in crop production: research or research? In: Taylor, H.M., Jordan, W.R., Sinclair, T.R. (Eds.), Limitations to Efficient Water Use in Crop Production. ASA CSSA and SSSA, Madison. WI, pp. 1–27.
6
Contents lists available at ScienceDirect
European Journal of Agronomy journal homepage: www.elsevier.com/locate/eja
Seasonal and climatic variation of weighted VPD for transpiration estimation
T
Michel Edmond Ghanema, Zakaria Kehelb, Hélène Marrouc, Thomas R. Sinclaird,* a
Mohammed VI Polytechnic University, AgroBioSciences (AgBS), Lot 660 Hay Moulay Rachid, 43150, Ben Guerir, Morocco International Center for Agricultural Research in the Dry Areas (ICARDA), Rabat, Morocco c SYSTEM, Montpellier SupAgro, INRA, CIRAD, IAMM, Univ Montpellier, Montpellier, France d Crop and Soil Sciences Department, North Carolina State University, Raleigh, NC 27695-7620, USA b
A R T I C LE I N FO
A B S T R A C T
Keywords: Daily vapor pressure deficit France Seasonal vapor pressure deficit Weighted vapor pressure deficit
Vapor pressure deficit (VPD) is one of the critical variables that drives evapotranspiration, and is of fundamental importance in crop physiology and modeling in the face of climate change. Unfortunately, direct records of atmospheric moisture are rarely available at short temporal scales, e.g. hourly, and country or regional scales. Most models use approximations to estimate daily transpiration-weighted VPD. Tanner and Sinclair (1983) suggested an approach to calculate weighted daily VPD as a fraction (0.75) of the difference between daily maximum and minimum vapor pressure based on estimates calculated from daily maximum and minimum temperatures, respectively. A test of the Tanner-Sinclair suggestion is reported by obtaining daily weighted VPD from hourly measurements of humidity and temperature. The objective of this study was to assess the fractional value to obtained daily weighted VPD estimations. This study was based on ten years of hourly weather data collected at thirty five stations across the wide diversity of environments that exist in France.
1. Introduction Water deficits are the major limitation to increasing crop yields in many regions of the world. The driving force of transpiration rate is the gradient in vapor pressure between the comparatively dry atmosphere and the wet interior of leaves, commonly referred to as the vapor pressure deficit (VPD). A surrogate for this vapor pressure gradient is VPD of the air since leaf temperature does not often differ greatly from air temperature. Therefore, air VPD is calculated as the difference between the saturated water vapor pressure at air temperature (es) and the actual water vapor pressure of the air (ea). That is, VPD = es- ea, where es (kPa) and ea (kPa) are saturation vapor pressure and actual vapor pressure, respectively. Clearly, VPD is temporally dynamic through the daily weather cycle usually with minimum values in the morning and maximum values in the mid-afternoon. The importance of VPD in the determination of transpiration rate was originally identified by Penman (1948) in his “sink strength” model. More recently, Tanner and Sinclair (1983) and Sinclair et al. (1984) presented a theoretical derivation describing transpiration rate based on plant characteristics and VPD. Their derivation can be arranged to define integrated transpiration (Tr) as an explicit function of integrated plant growth (G).
⁎
ʃ Tr dt = ʃ (G *
VPD ) dt kd
(1)
Where kd a transpiration efficiency coefficient (Pa), which is essentially constant within a species because it is dependent on the explicitly defined, stable physiological terms of conversion coefficient of hexose to plant mass and of the biochemical pathway for CO2 assimilation (i.e., C3 vs. C4) (Tanner and Sinclair, 1983). While both Penman’s sink strength model and Eq. (1) can be readily applied to determining integral Tr for short-time periods of minutes, it becomes more problematic for longer-time periods of hours and days because of the likely variability of VPD over these longer-time periods. Since in many practical approaches it is desired to estimate daily Tr, the critical question is what is the appropriate value of VPD in the calculation of daily Tr. Somewhat surprisingly, estimation of daily weighted VPD is yet to be fully explored. Tanner and Sinclair (1983) originally described a method to estimate weighted daily VPD from daily maximum temperature (Tmax) to calculate daily maximum vapor pressure (VPmax), and from daily minimum temperature (Tmin) to calculate daily minimum vapor pressure (VPmin). The value of VPmin was calculated assuming Tmin approximated dew point temperature for the day, reflecting a more-or-less stable value for the atmospheric vapor pressure
Corresponding author. E-mail address: [email protected] (T.R. Sinclair).
https://doi.org/10.1016/j.eja.2019.125966 Received 29 December 2018; Received in revised form 13 September 2019; Accepted 25 October 2019 1161-0301/ © 2019 Elsevier B.V. All rights reserved.
European Journal of Agronomy 113 (2020) 125966
M.E. Ghanem, et al.
Fig. 1. Meteorological stations distribution accross France.
Fig. 2. Changes of daily VPD fraction (Fracd) in Gif-sur-Yvette (A) variation of the daily Fraction. (B) moving mean of Frac based on the daily Frac values for two weeks before and after each date.
Meinke et al. (1997) found that a Frac value of 0.75 worked well for a study in Queensland, Australia. The most extensive study in approximating VPDw was subsequently done in Argentina where Abbate et al. (2004) examined the appropriateness of Eq. (2) for environments in Argentina. Their analysis was based on weather data collected at five weather stations during the wheat production season. They found a slightly lower coefficient than suggested by Tanner and Sinclair (1983) of 0.72 as the appropriate Frac in estimating VPDw. These previous studies indicating a fairly constant value for Frac offer a very limited basis for such a conclusion. The current study was undertaken to explore the possibility that the value of Frac may be more variable than previously recognized. Therefore, the objective of this study was to examine values of Frac over a range of divergent environments. France offers such a wide range of climates and an extensive hourly historical weather record to undertake such an analysis. Across the country, climates range from the influence of oceanic and semi-oceanic flows in the west to continental and mountain impacts in the east. In addition, the south coast of France is subjected to a Mediterranean climate, which is generally drier than the rest of France, and without the cold winters of the other climate zones (Joly et al., 2010). Therefore, it is anticipated that this range of environments across France offers a broad test for possible variability in the value of Frac.
through the day. Using our notation, Tanner and Sinclair (1983) suggested the weighted daily vapor pressure deficit be approximated as “three-quarters the distance between VPmin and VPmax; this is reasonable for locations with a diurnal temperature range of 20°C and low Tmin, assuming the daily vapor pressure should be integrated from about 0900 h to evening, when net radiation becomes negative.” This conclusion was based on measurements made at Madison, WI, USA. Tanner and Sinclair (1983) went on to suggest that at locations where Tmin is high such as Yuma, Ariz, the daily vapor pressure deficit was “about two-thirds” of the distance between VPmin and VPmax. Therefore, the generalized equation to express daily weighted VPD (VPDw) based on the suggestion of Tanner and Sinclair (1983) is
VPDw = Frac *(VPmax − VPmin)
(2)
where the vapor pressures are calculated from measurements of daily maximum and minimum temperature. That is,
17.269 * Tmax ) 237.3 + Tmax
(3)
17.269 * Tmin ) 237.3 + Tmin
(4)
VPmax (kPa) = 0.61078 *exp(
VPmin (kPa) = 0.61078 *exp(
Frac is a fraction, which based on the suggestions of Tanner and Sinclair (1983) would have values in the range of 0.75 to 0.66. 2
European Journal of Agronomy 113 (2020) 125966
M.E. Ghanem, et al.
Fig. 3. Distribution of monthly VPD fraction (Fracm) in the Alenya, Salon de Provence, Orléans, Gif-sur-Yvette, Thonon and Creysse stations.
2. Material and methods
assumption of this approach is that the contribution of transpiration rate at each hour to the daily transpiration was proportional to the radiation received at each hour (Sh) consistent with Eq. (1). Hence,
Weather data were obtained for ten years at each of thirty-five meteorological stations in France, which were selected to cover the wide diversity of environments in France. Fig. 1 shows the location of the selected meteorological stations in continental France, Corsica and Guadeloupe. Hourly air temperature (T, °C), relative humidity (RH, %), and solar radiation (S, Joule cm−²) were obtained from INRA France CLIMATIK platform (https://intranet.inra.fr/climatikv2/) for each of the meteorological stations. Hourly measurements were used to compute hourly VPD (VPDh) based on reported RHh measurements using the following equation:
VPDwd =
n i=0
((7))
Daily estimates of the fraction Fracd were obtained by rearranging Eq. (2) such that
Fracd = VPDwd /(VPmax − VPmin )
(8)
2.1. Data analyses
RH VPDh = (1 − ⎛ h ⎞ )* SVPh ⎝ 100 ⎠
(5)
2.1.1. Fraction estimation using linear mixed models A linear mixed model was fitted to the daily calculated fraction (Fracd) from all stations. The data from stations were unbalanced as climatic records were not available for all stations in all months/years. Station, month, and year and all interactions with station effects were considered as random. This was useful to partition the total variance into different effects influencing the estimation of the daily calculated Frac and a separate residual for each station/month/year. Outliers were
Where SVPh (kPa) is hourly saturation vapor pressure calculated from hourly temperature as:
SVPh (kPa) = 0.61078 *exp(
n
∑i =0 (VPDh * S h) / ∑ Sh
17.269 * T ) 237.3 + T
(6)
A daily weighted vapor pressure deficit (VPDwd) was obtained by scaling the hourly VPDh based on solar radiation values. The 3
European Journal of Agronomy 113 (2020) 125966
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Fig. 4. Distribution of monthly VPD fraction (Fracm) across France A for December, May, June, and September.
Frac were considered as the station fraction (Fracs). Mixed model analysis was run using AsReml (Gilmour et al., 1995; Butler et al., 2010) package in (R Development Core Team, 2008). 2.1.2. Spatial analysis Spatial autocorrelation (SAU) was used to assess whether Fracs for each station is clustered, dispersed, or random over space. Moran’s I was used to calculate spatial autocorrelation and its significance (Cliff and Ord, 1973, 1981). To determine how data were clustered, we used methods developed by Getis and Ord (1992, 1996) not only to allow hypothesis testing to determine whether clustering has occurred within the data, but also to provide information on the extent to which aboveand below-average values cluster and to identify local concentrations of clustering (Laffan, 2006; Mueller-Warrant et al., 2008). This is done by computing local spatial autocorrelation by means of G statistics. Zscores and their related p-values were then extracted. The Z-score is highly positive (negative) and significant at 1, 5, or 10%, which shows that high (low) values of the data are clustered spatially together and that there is a less than 1, 5, or 10% likelihood that this high-clustered (low-clustered) pattern could be the result of a random process. The spatial analyses were done using spdep (Bivand and Wong, 2018) package in R (R Development Core Team, 2008).
Fig. 5. Distribution of Station VPD fraction (Fracs) (average over 12 months of monthly fraction Fracm) across France. Red colors indicate higher Fracs values. Green color indicates lower Fracs values. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
3. Results 3.1. Seasonal differences in daily and monthly fraction Daily Fracd was not constant over the full range of tested conditions and it varied from 0 to 4.12 across the tested environments. Fig. 2a shows an example of variation of the daily Fracd at the Gif-sur-Yvettes station. These results indicate that calculations of individual daily transpiration rates based on a constant Frac may not be uniformly reliable as a result of the day-to-day variation in Frac. On the other hand, long-term transpiration rates relying on a stable Frac were found to be satisfactory for many locations. The results in Fig. 2b are the moving mean of Frac based on the daily Frac values for two weeks before and after each date. In this example, Frac is fairly stable with a mean value of 0.75 ± 0.33.
Fig. 6. A) Local G statistics (clusters of high values in red) of yearly (average over months Fracm) VPD fraction across France. B) corresponding p-value (blue are significant local high clusters at 5%). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
identified as data points with studentized residuals superior to 3.5 and were removed from data and were defined as missing. Monthly fractions (Fracm) per station across years were then estimated using best linear unbiased predictors (Blups). The average of monthly values of 4
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Fig. 7. Scatter plots comparing the weighted VPD to VPD0 calculated with a fraction of a) 0.75 and b) 0.98 for the Mediterranean stations.
Fig. 8. Correlation between daily dewpoint temperature (Tdew) and minimum temperatures (Tmin) in two different stations: Orléans, and Salon de Provence.
continental and semi-oceanic climates. However, in the Mediterranean region, and in the eastern parts of France and in Brittany the value of Fracm was in the range of 0.8 to 0.9. During September, Fracm was greater than 0.9 along the Mediterranean Coast (Fig. 4). Clustering analyses showed that southern French meteorological stations (corresponding to the Mediterranean stations) always clustered together and that the Fracm in these stations were always higher than the remaining stations in France across the year (Figs. 5 and 6). Spatial analysis revealed a significant spatial autocorrelation with a value of Moran’I = 0.4 showing that meteorological stations that are geographically close have similar Frac. In addition, Z-scores values of five Mediterranean stations (Avignon, Salon de Provence, Roujan,
Mean monthly values of Fracm were calculated for each of the 35 locations. These results highlighted both seasonal and regional differences. As shown in Fig. 3 for six locations, minimum values of Frac occurred during the summer and high values occurred during the winter. The minimum Fracm value calculated for the summer months varied somewhat among locations. 3.2. Regional differences in Frac estimation The results presented in Fig. 4 for the three growing-season months (May, June, and September) showed the appropriate Fracm was in the range of 0.7 to 0.8 for large areas of France. This narrow range of Fracm previously predicted was prevalent in the areas generally experiencing 5
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annual water loss since during the cold winter months transpiration is very low due to the fact that there is either no crop growth or growth is extremely small. That is, the calculated transpiration rates will be very low regardless of the error in the value of Frac. The second situation where Frac was found to deviate from the 0.7 to 0.8 range was in those regions and times of year where it was likely winds came off of the neighboring seas (Fig. 4). This situation appears to be another case where the minimum temperature does not reach the dew point. Air moving from the seas at night is likely to have been warmed so the minimum temperature did not decrease to the dew point temperature. Hence, the high minimum temperature resulted in an over-estimated high VPDmin and a low VPDd (Fig. 8). Consequently, estimation of Frac in the coastal Mediterranean region needs special attention in the Fall and Winter months were Fracm was calculated to be in the range of 0.9 to 1.0 for a large area in these sea-influenced regions.
Alenya and Bellegarde) were significantly higher than the other stations in France (Fig. 6A). The results for Frac in December (Fig. 4) showed elevated values of greater than 0.8 in virtually all areas of France. The central area running southwest to northeast had Frac in the range of 0.80 to 0.90. For the southern and eastern areas and Brittany, the estimates of Frac were in the range of 0.90–1.0 for December. To illustrate the impact of Frac on calculated VPDwd, values of VPDwd for the five Mediterranean stations with the extreme Frac of 0.98 were calculated (Fig. 7). These results were compared with the estimates based on a Frac value of 0.75. VPD calculated using both fractions explained 93% of the weighted VPD. However, the results with Frac equal to 0.98 matched much better the 1:1 correspondence line than the results obtained using the 0.75 value. 4. Discussion
References Estimates of daily canopy transpiration require a weighted VPD to reflect the temporally dynamic atmospheric conditions under which transpiration is occurring. A mean daylight VPD, for example, fails to properly weight VPD for the fact that much of the transpiration occurs during the midday when the VPD is the highest. Tanner and Sinclair (1983) suggested that an appropriately weighted VPD could be approximated as a fraction of maximum daily VPD based on minimum and maximum temperature, which we have labeled as Frac. They suggested a value for Frac of 0.75. In this study of the diverse climates of France, it was found that during the summer and fall months, when crop transpiration accounts for much of the annual evaporated water, the derived values of Frac were, in fact, in the range of 0.7 to 0.8 (Figs. 3,4). This range for Frac was consistent with the suggestion of Tanner and Sinclair (1983) and the observations of Meinke et al. (1997) and Abbate et al. (2004). However, this study indicated two situations where a value of Frac of about 0.75 cannot be assumed. The results of the environmental analysis of this study showed the appropriate Frac value being greater than 0.8 (Figs. 3,4) under special circumstances. For example, the impact of assuming a Frac equal to 0.75 for the Mediterranean area in contrast to 0.98 (Fig. 7) results in an inappropriately small value of VPDw and an underestimation of canopy water loss in most models. To more accurately reflect VPD conditions at some times of the year and locations, it may be necessary to account for environmental variation in VPDw. One specific situation requiring a larger Frac than 0.75 in calculating the VPDw is during the winter months. The value of Frac to calculate transpiration during the winter months was found to be 0.8 or greater for most of France. These high values for Frac seem likely to be a result of daily minimum temperature often not decreasing to the dew point temperature, which would be very low as a result of the cold, dry atmosphere during the winter months. This is illustrated in Fig. 8 of a plot in December for Orléans of dewpoint temperature vs. minimum temperature on many days. Of course, this winter deviation in Frac to estimate transpiration is likely to result in only a small error in total
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