Estimation of standardized reference evapotranspiration on the Canadian Prairies using simple models with limited weather data

Transcription

1 stimation of standardized reference evapotranspiration on the Canadian Prairies using simple models with limited weather data C. Maulé 1 *, W. Helgason, S. McGinn 3 and H. Cutforth 4 1 epartment of Agricultural and Bioresource ngineering, 57 Campus rive, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5A9, Canada; Centre for Hydrology, 117 Science Place, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C8, Canada; 3 Agriculture and AgriFood Canada/Agriculture et Agroalimentaire Canada, Avenue South, Lethbridge, Alberta T1J 4B1, Canada; and 4 Agriculture and AgriFood Canada/Agriculture et Agroalimentaire Canada, Semiarid Prairie Agricultural Research Centre, P.O. Box 13, Swift Current, Saskatchewan S9H 3X, Canada. *mail: charles.maule@usask.ca Maulé, C., Helgalson, W., McGinn, S. and Cutforth, H. 6. stimation of standardized reference evapotranspiration on the Canadian Prairies using simple models with limited weather data. Canadian Biosystems ngineering/le génie des biosystèmes au Canada 48: Potential evapotranspiration (PT) can be accurately calculated with a PenmanMonteith model, however this model requires inputs that are not all measured at most weather stations. The agricultural region of the Canadian Prairies is a large geographic region of dry continental weather (cold semiarid to subhumid) and could benefit from simple, yet accurate empirical models for determination of evapotranspiration (T). The purpose of our study was to develop simple (limited data) T models to estimate standardized reference evapotranspiration. We used daily weather data from and from ten stations across the agricultural region of the prairies to develop temperature, temperaturerelative humidity, and temperaturerelative humiditywind speed models. Our models were developed by regression using the ASC (5) standardized reference model for a wellwatered short crop surface (T os ) as the 'observed' variable. We compared our developed models to other published simple models by BaierRobertson, Hargreaves, and Linacre. To verify the accuracy of the models (relative to T os ), we considered averages, standard errors, regression parameters (r, slope, and intercept), as well as the coefficient of efficiency. Of the temperature based models, our model and Hargreave s model were the most accurate. Our temperaturerelative humidity model improved the estimate of evapotranspiration compared to temperature based models. The Linacre and the BaierRobertson temperature and temperaturerelative humidity models were not accurate and are not recommended for estimating evapotranspiration in the Canadian Prairies. Incorporation of temperature, relative humidity, and wind speed into our statistically developed model resulted in the most accurate and precise estimation of standardized reference evapotranspiration. Keywords: potential evapotranspiration, Canadian Prairies, temperature, relative humidity, models. Bien que le modèle de PenmanMonteith permette un calcul précis de l évapotranspiration potentielle (TP), ce dernier requiert des données qui ne sont pas mesurées par la plupart des stations météorologiques. La zone agricole des Prairies canadiennes est une vaste région géographique au climat continental sec (froid semiaride à subhumide) et celleci bénéficierait grandement de modèles empiriques pour la détermination de l évapotranspiration qui soient à la fois simples et précis. Le but de notre étude était donc de développer des modèles T simples et ne requérant que des données limitées pour estimer une évapotranspiration de référence standardisée. Nous avons utilisé les données météorologiques journalières de et provenant de dix stations à travers la région agricole des Prairies pour développer des modèles de température, température humidité relative et, température humidité relative vent. Nos modèles ont été développés par régression en utilisant le modèle standardisé de référence ASC (5) avec comme variable observée une culture de surface courte et bien arrosée (T os ). Nous avons comparé les modèles ainsi développés avec d autres modèles simples publiés par Baier Robertson, Hargreaves et Linacre. Pour vérifier l exactitude de ces modèles (comparativement à T os ), nous avons considéré les moyennes, les erreurs standards, les paramètres de régression (r, pente et ordonnée à l origine), de même que le coefficient d efficacité. e tous les modèles basés sur la température, notre modèle de même que le modèle de Hargreaves se sont révélés les plus précis. Notre modèle de température humidité a permis d améliorer les estimations de l évapotranspiration comparativement aux modèles basés sur la température. Les modèles de température et de température humidité de Linacre et de BaierRobertson n étaient pas précis et ne sont donc pas recommandés pour estimer l évapotranspiration dans les Prairies canadiennes. L incorporation de la température, de l humidité et de la vitesse du vent dans notre modèle statistique nous a permis d obtenir l estimation la plus juste et précise de l évapotranspiration de référence standardisée. Mots clés: évapotranspiration potentielle, Prairies canadiennes, température, humidité relative, modèles. INTROUCTION Potential evapotranspiration (PT) is a required parameter for hydrological and agricultural projects. Although PT is related to freewater evaporation and may be estimated from measurements using evaporation pans or atmometers (Thom et al. 1981), it is more commonly calculated from climatic parameters (e.g., temperature, relative humidity) and related to readily available soil water transpired through a specified vegetated surface (ASC 5). arly work by Thornthwaite (1948) proposed the concept of evapotranspiration (T), which was based upon the idea that radiation is a common forcing factor for longterm air temperature and evaporation, and therefore temperature is a predictor of PT. Thornthwaite (1948) used air temperature and daylength to characterize seasonal change in water balance and then delineated climate zones based on this soil water balance. For applications where T is needed for short durations of a few days or hours, temperature alone proved to be inadequate to predict T (Pelton et al. 196). Thornthwaite recognized that his simple approach Volume 48 6 CAIAN BIOSYSTMS NGINRING 1.1

2 lacked mathematical elegance in that it was not understood why the relationship to radiation was spatially variable. Further development of the T concept recognized the underlying factors needed to better predict T. In the same year, Penman (1948) reported on an approach that recognized not only the radiative forcing parameter but also the aerodynamic restrictions to evaporation. Penman simplified this aerodynamic term using a wind speed function. Since the work of Thornthwaite and Penman, there have been many T models developed. The one model that is the most widely accepted is the PenmanMonteith (PM) model (Shuttleworth 1993) which provides sufficient accuracy for use in general hydrological and crop irrigation applications. A disadvantage of this physically based model is the large number of parameters needed to calculate T. The minimum requirements for the PM model are daily measurements of solar radiation, relative humidity, air temperature, and wind speed at the m height. Although electronic instrumentation and automatic data recording have increased the availability and ease of obtaining the parameters needed to drive the PM model, it still requires resources to train personnel to install and maintain the equipment. Historical data for a given location are frequently limited to just temperature or temperature and relative humidity requiring T estimation using models with fewer data requirements than the PM model. There are different procedures for the calculation of T via the PenmanMonteith method. Currently the standardized reference evapotranspiration equation has been recommended for use by the American Society of Civil ngineers (ASC 5). This method is a variation of the PM method and attempts to standardize the use of one method amongst many users. The equation provides a recommended determination of reference T for a wellwatered short (T os ) or tall grass surface. It needs to be recognized that there is a difference between that of 'potential evapotranspiration' and that of 'reference evapotranspiration'. Potential T is that considered from a wet surface that is nonspecific as to crop type. Reference T refers to the T from a reference grass surface of specific characteristics and that is well watered (Allen et al. 1998). Although there are a number of models for calculating daily T using temperature or temperature and relative humidity (RH) along with extraterrestrial solar radiation (R a ) (e.g., Baier and Robertson 1965; Linacre 1977; Hargreaves and Samani 1985), the performance of many of these models has not been compared to T os across the whole of the Canadian Prairies. Grace and Quick (1988) compared several models for calculating PT in the semiarid climate surrounding Lethbridge, Alberta. The models performed similarly under low wind speed and moderate humidity. However, model estimates differed widely under dry, windy conditions conditions typical of much of the semiarid climatic region within the Canadian Prairie. For the semiarid climate of southern Alberta, they recommended estimating PT with models using wind and especially relative humidity as well as temperature and radiation data. roogers and Allen () found that including a rainfall term with a modified monthly Hargreaves method (Hargreaves and Samani 1985) significantly improved its estimation of the FAO56 PenmanMonteith method for global arid regions. Given the great amount of historical data for the Canadian Prairies, and the number of current weather stations that do not measure solar radiation, wind speed, or relative humidity, there continues to be a need for simple yet representative daily T models. The purpose of our paper is to develop simple daily T models that will represent standardized reference T for short crop surfaces (T os, as calculated by the ASC method) for the agricultural region of the prairies. Therefore, our objectives are to: 1. Compare the performance of the following published models for estimating daily T: (a) BaierRobertson temperature T (T BR1 ); (b) BaierRobertson temperature and relative humidity T (T BR ); (c) Linacre temperature (T L1 ); (d) Linacre temperature and relative humidity (T L ); and (e) Hargreaves temperature (T H ).. evelop and compare the performance of simple models for estimating daily T by using the following combinations of parameters: (a) Temperature and extraterrestrial radiation; (b) Temperature, relative humidity, and extraterrestrial radiation; and (c) Temperature, relative humidity, extraterrestrial radiation, and wind speed. 3. Recommend the empirical models that best estimate T os for the agricultural region of the prairies. We assumed our empirical equations would apply across the Canadian Prairies because of fairly similar climate across this broad region. This region has a subhumid to semiarid climate that is characterized by colddry winters and warm summers within which the majority of precipitation occurs. MTHOOLOGY All models, published and developed, were compared against the standardized reference evapotranspiration equation for a short crop (T os, ASC 5). The models were developed and tested using daily data from 15 weather stations across the agricultural region of the prairies (Table 1). With the exception of another six stations in southern Alberta, these 15 weather stations represent all the accessible stations within the agricultural region of the prairies. There are likely other private stations (e.g., within the irrigation districts of Manitoba) or other individual research stations, however in our search we either could not locate or could not access others. Although there are more than one hundred stations available through nvironment Canada, most record only temperature and precipitation and do not measure all the parameters necessary to calculate T os. The data from each of the weather stations used in our study were reviewed for erroneous values and missing information. To accomplish objective, a subset of data (ten stations, years and ) was used to develop a set of regression based models with T os as the predicted variable. Another subset of data (five stations, various years) was used to compare the performance of the models and to help recommend the most suitable model for estimating T os. All the data necessary to calculate daily standardized reference T for a short crop (T os, ASC 5) were recorded at these selected stations. 1. L GÉNI S BIOSYSTÈMS AU CAA MAULÉ et al.

3 Table 1. Weather station locations and identification. Station Province Latitude ( N) Longitude ( W) levation (m) WMO I Climate I Years* Affiliation** evelopment Beaverlodge Lacombe Onefour Stavely Vauxhall lstow field Perdue field Scott Swift Current Morden MB () 4 (31) 4 (3) 4 (6) 4 (1) 4 (8) 4 (8) 4 () 4 () 4 (43) Research Research valuation ston field Lethbridge Strathmore Kernen farm Outlook (55) 4 () (4) 1999 () (8) Research IMCIN IMCIN U of S IMCIN * Numbers in parentheses are days of missing data. ** Agriculture and AgriFood Canada; IMCIN Irrigation Management Climate Information Network; U of S University of Saskatchewan; Research weather stations for authors research xisting evapotranspiration models We used four published models to calculate PT for a wellwatered short crop surface that varied between.1 and.15 m in height. Standardized reference evapotranspiration: T os (ASC 5): T os. 48 = C n ( Rn G) + γ u ( es ea ) T γ ( 1+ Cd u ) T os = standardized reference T for short surfaces of.1 m, R n = calculated net radiation at crop surface (MJ m d 1 ), G = soil heat flux density at soil surface (MJ m d 1 ), T = mean daily air temperature at 1.5 to.5m height, (T max + T min )/ ( C), T max = daily maximum air temperature (ºC), T min = daily minimum air temperature (ºC), u = mean daily or hourly wind speed at m height (m/s), e s = saturation vapor pressure at 1.5 to.5m height as average of saturation vapor pressure at maximum and minimum air temperatures (kpa), e a = mean actual vapor pressure at 1.5 to.5m height (kpa), = slope of saturation vapor pressuretemperature curve at T (kpa/ C), given by: 17. 7T 54 exp T = 37 3 ( T +. ) (1) γ = psychrometric constant =.665P (kpa/ C), P = atmospheric pressure (kpa), C n = numerator constant that changes with crop reference type (9 for short and 16 for tall crop surfaces), and C d = denominator constant that changes with crop reference type (.34 for short and.38 for tall crop surfaces). Standardized reference T is defined as the T rate from a uniform surface of dense, actively growing vegetation that is not short of water and represents an expanse of at least 1 m (ASC 5). Hargreaves: T H (Hargreaves and Samani 1985; Hargreaves et al. 1985):. 5 ( ) ( ) TH =. 94 Tmax Tmin T Ra () T H = reference T for wellwatered short crop, R a = extraterrestrial radiation (MJ m d 1 ) as described in ASC (5). BaierRobertson: T BR1, T BR (Baier and Robertson 1965; Baier 1971): ( ) ( ) ( es ea ) TBR1 = 157. Tmax Tmax Tmin Ra TBR =. 39Tmax Tmax Tmin Ra (4) T BR1, T BR (3) = PT calibrated to Penman s formula for a crop with an albedo of.5 and a crop coefficient of 1. throughout the growing season (Baier 1971). Volume 48 6 CAIAN BIOSYSTMS NGINRING 1.3

4 Linacre: T L1, T L (Linacre 1977): T L 5Tm L = 8 T ( T T ) T L = grass reference T calculated using measured dew point temperature, T m = temperature adjusted for elevation, T m = T +.6h ( C) h = elevation (m), T d = dew point temperature ( C), and L = latitude ( ). Where dew point temperature is not available, q. 6 may be used to substitute into q. 5 to to calculate T L1. T T =. 3h +. 37T T +. 35T 1. 9 (6) d rd ra T rd = mean daily range of temperature ( C) and T ra = difference between the mean temperatures of the warmest and coldest months of the year ( C). To use either form of the Linacre equation, the station must have at least 5 mm of precipitation per month and the mean dew point depression (T T d ) must be at least 4 C. The current study area satisfies these limitations. As most of the above models (qs. to 5) were developed for a short crop surface (as opposed to a tall crop), this was the standard used within our study. Procedure Weather stations from the agricultural region of the three prairie provinces representing three soil climatic zones (Brown, ark Brown, and Black) were used in this study. Recorded at each station were the data necessary for the calculation of daily T os (q. 1) (Table 1). ata from the first group of stations listed in Table 1 were used to calculate T using qs. 1 to 6 and to develop models involving temperature, relative humidity, wind, and extraterrestrial solar radiation. ata from the second group of stations (Table 1) were used to compare the relative accuracy with which our developed models and the published simple models could represent T os. Although we desired a representative distribution of weather stations across the agricultural potion of the Prairies, the majority of the stations with suitable data were located in western Saskatchewan and Alberta. There were a lack of suitable stations within eastern Saskatchewan and Manitoba; the ones used were the only accessible stations with full data sets. aily weather data from April 1 to October 31 for two years, and, and from 1 weather stations (Table 1) were used to develop the following models: 1. T t as a function of air temperature and extra terrestrial solar radiation (R a );. T Ht as a function of air temperature and R a, using a modified Hargreaves equation; and 3. T tr as a function of temperature, humidity, and R a 4. T tru as a function of temperature, humidity, wind speed, and R a. uring model development, various parameters (e.g., T max, T, RH max,, e a ) and various transformations (e.g., conversion of d (5) temperature or relative humidity to vapour pressures, multiplication of terms together, such as that done by the T os and Hargreaves models) were investigated for improvement of fit. Because about twothirds of the daily rainfall totals were zero, we assumed the contribution of daily rainfall to the regression estimate of daily T was minimal and therefore rainfall was not included in model development. The following statistical coefficients of comparison were used to both select the best parameters during model development and to evaluate them, relative to q. 1: 1. r, the correlation coefficient for the linear regression equation of predicted vs observed (T os ); the closer to 1. the better the fit;. m, the slope of the linear regression equation; the closer to 1. the more representative the prediction of T os ; 3. b, the yintercept from the linear regression equation; the closer to. the more representative the T estimate; 4. S, the standardized error; and 5., coefficient of efficiency (q. 7). ata from the first group of weather stations in Table 1 were used to develop the models, while the second group of weather stations was used to evaluate the developed models. Legates and McCabe (1999) suggested using the coefficient of efficiency (q. 7) to overcome limitations when using r for evaluating the goodnessoffit with hydroclimatic and hydrologic data sets. The coefficient of efficiency,, is defined as: = 1. n i = 1 n i= 1 ( Oi Pi ) ( Oi O ) O, P = observed and predicted values, respectively. ranges from minus infinity to 1. with larger values indicating better agreement. A value of for indicates that the observed mean Æ is as good a predictor as the model, while negative values indicate that the observed mean is a better predictor than the model. The is similar to the efficiency of a model by Nash and Sutcliffe (197) that is also used for hydrological investigations. ata quality and missing data The following procedures were used to ensure that the climatic data sets were of good quality and as representative as possible: C Only climatic data from April 1 to October 31 were used. These months have average monthly air temperatures greater than C. C If any single data parameter (e.g. maximum daily temperature) was missing for a day then that day was not used for either development or for evaluation. We preferred using actual rather than estimated data for developing and evaluating models. C Temperatures were checked for unexplainable outliers. C RH max values were checked for values greater than 1%. C Wind speeds were checked for consistently higher or lower velocities (systematic error) over a period of time. (7) 1.4 L GÉNI S BIOSYSTÈMS AU CAA MAULÉ et al.

5 C solar radiation (R s ) was checked by plotting daily values against calculated clear sky radiation (R o ) using procedures and equations described in Appendix of ASC (5). The higher values of R s should be representative of clear sky conditions and should be within 3 to 5% of the computed value, R o. If these R s values were consistently higher or lower than the corresponding R o values by more than 5%, then it could have meant that the instrument measuring R s had not been calibrated properly, had not been properly leveled, or had become contaminated with dust. In that case, R s was adjusted by multiplying R s by the average value of R o /R s on clear days (ASC 5). No unexplainable outliers for temperature were found for any of the stations. Most stations had some RH max values at or slightly less than 1% but not exceeding; however four stations (Morden, Outlook, Onefour, and Vauxhall) had numerous occurrences where RH max was greater than 1% (13 to 11%). Because of the lack of any other correction information, we assumed that the error would be greater for higher values of RH and zero at the lowest value. Thus q. 8, that provided a greater correction weight to high values, was applied: RH c = RH uc ( RH 1)( RH RH ) s max uc s min RH s max RH s min RH c = corrected RH value (%), RH uc = uncorrected RH value (%), RH smax RH smin (8) = highest uncorrected maximum RH value that occurred for that station in the entire measurement set (%), and = lowest uncorrected minimum RH value that occurred for that station in the entire measurement set (%). The wind speeds at Scott, between January 1 and June 3,, were much higher (by an average factor of 1.96) than the rest of the data set after June 3, or for similar dates in. Thus the daily wind speed during this period was corrected by dividing it by All wind speeds at Agriculture and AgriFood Canada () Research stations were recorded at 1 m; those at University Research stations at 3 m; and those at Lethbridge and Strathmore IMCIN stations at m. All stations were corrected to m height using the procedure described in ASC (5). The following stations required correction of their R s readings so that a match was obtained for days of maximum R s (assumed clearsky days) against calculated clear sky radiation, R o : Scott (correction multiplication coefficient of 1.1), Lethbridge (1.5 for summer and 1.8 for summer ), Strathmore (1.5), and Outlook (.9). According to the procedure of ASC (5), e a was calculated using the RH that occurred at the same time as T max (approximately RH min ) and the same time as T min (approximately RH max ). However, for data obtained from, RH min and RH max were measured at 8:h and 16: or 17:h, respectively regardless of when T max and T min occurred. Whether this would constitute a large misrepresentation in the calculation of T os was explored using hourly data sets from the station located at ston. Using RH measured at 8:h and 16:h, RH values, as opposed to RH min and RH max values, resulted in the average T os differing by only. mm/d. This difference was deemed not large and so either method for obtaining RH min and RH max was utilized. RSULTS and ISCUSSION Station climate summary On average, T os during the warm season (April to October) of was.6 mm/d greater than (Table ). This was due to the higher temperature, slightly greater wind speed, lower relzative humidity, and greater solar radiation of. The longterm temperature average for (Canadian Institute for Climate Studies 1) for the same approximate longitude and latitude as these 1 stations (Table ) is 11.3 C confirming that was warmer than average and cooler than average. The warmest and coldest stations (not including Morden or Perdue due to their large number of missing data points) were Onefour and Beaverlodge, respectively, although for, lstow, Lacombe, and Scott had the same average temperature as Beaverlodge. Similarly, Onefour had the highest T os values (of the complete data sets) for both years and Beaverlodge and Lacombe the lowest T os values. This difference between Onefour and Beaverlodge is in part due to the extreme differences in latitude (Table 1), although Onefour is located in the driest part of the prairies in terms of low relative humidity and high wind speed. The highest average relative humidity occurred at Scott and Swift Current in. eveloped T models For temperature based T, the following parameters provided statistical models with the best fit: T or T max or e smax (saturated vapor pressure calculated at T max ), T max T min or e d (saturated vapour deficit calculated from T max and T min that is e smax e smin ), and R a. There was little difference between any of these combinations: T max or e smax had the greatest effect of the parameters (T max regressed alone against T os resulted in an r of.7, whereas using e smax resulted in an r of.71). Multiplying R a by improved the fit (for q. 9 from an r of.71 to.78). From these parameters the following temperature based model was chosen: ( ) T = 134. T T +. 19T R. 669 t max min r =. 78, S =. 9 Use of T max or e smax in place of T resulted in similar r and S values, however we wished to keep similar parameters for all our developed models and the parameter T' provided the best fit for the temperature and humidity model (q. 11). A modified Hargreaves model was developed by altering the coefficients within the published version (.3 and 17.8 of q. ) until T Ht as regressed against T os had a slope of 1. and an intercept of :. 5 ( max min ) ( ) T =. 816 T T T R Ht r =. 77, S =. 9 a a (9) (1) For the temperature and relative humidity based model, the following humidity parameters provided the developed model (along with R a ) with the best fit; RH, RH min, and e s e a. The vapor deficit (e s e a ) had the greatest role in representing T os Volume 48 6 CAIAN BIOSYSTMS NGINRING 1.5

6 Table. Climatic averages (April 1 to October 31) during and at weather stations used to develop T models. Station Year T ( C) RH (%) u (m/s) R s (MJ m d 1 ) T os Missing days* Beaverlodge Lacombe Onefour Stavely Vauxhall lstow field Perdue field Scott Swift Current Morden Beaverlodge Lacombe Onefour Stavely Vauxhall lstow field Perdue field Scott Swift Current Morden Average** Average** * Missing days days in which T was not calculated due to missing data. ** Averages do not include both data years for Lacombe, Morden, and Perdue due to their large number of missing data days. and if considered alone resulted in an r of.8. quation 11 was chosen as the statistical temperaturerelative humidity model that provided the best linear fit, while still retaining the same structure as q. 9: ( ) T =. 51 T T T R 318. e tr max min a a r =. 91, S = 56. (11) Removal of from R a resulted in the r decreasing to.86 and the S increasing to.7. If temperature, wind, and relative humidity are available, but radiation is not measured, then q. 1 provides the best fit to T os. ( ) T =. 77 T T T R. 77e tru max min a a +. 69u r =. 94, S =. 46 (1) valuation of published and developed T models The second data set (Table 1) was used to evaluate the fit (relative to T os ) of the models. Of all the temperaturebased equations, T t, T Ht, and T H had the best fit (greatest r and, lowest S, slope nearest 1, intercept nearest ) and T BR1 and T L1 the poorest fit (Table 3). The intercept of the Hargreaves model (T H ) was not zero which resulted in a slightly lower average T estimate (between. and.3 mm/d) than for our temperature based model (T t ) (Table 3). Visually it appears that the Hargreaves model has a slightly better estimate of T os at low values ( to 1 mm/d) than the T t method which provides some negative values in this range. However, for values >1 mm, T H tended to overestimate T os more than the T t method (Fig. 1). The BaierRobertson model underestimated T os by.5 mm/d and the Linacre model overestimated T os by 1.7 mm/d. At Lacombe, T L1 consistently overestimated daily T os by about mm/d; T BR1 tended to overestimate T os whereas, overall, T t and T H followed more closely the daily variations of T os (Fig. ). The Linacre model (T L1 ) uses a mean annual difference in daily temperature and the mean monthly difference in temperature (q. 6); for the prairie stations these differences are about 1 and 5 C, respectively. If both of these were reduced to 5 C, then the T L1 line would shift downwards resulting in a fit similar to the other models (Fig. ). The coefficient of efficiency () showed more clearly than the r value the poor fit of T BR1 and T L1. Of the temperature and humidity based equations, our statistical model, T tr (q. 11) provided the best fit (Table 3). The Linacre model (T L ) provided the poorest fit, overestimating T by.8 mm/d. The BaierRobertson model (T BR ) also overestimated T by.7 mm/d and although its r was only slightly less than T tr, its S was larger and its coefficient of efficiency much smaller. Consideration of how these T models compare on a daily basis is illustrated in Fig. 3 for data from Kernen farm. The BaierRobertson model, T BR, provided the lowest T os estimates and T tr the most reasonable; however T L also provided generally reasonable values of T os at Kernen farm. The period of high T os, May 5 to May 9, 1.6 L GÉNI S BIOSYSTÈMS AU CAA MAULÉ et al.

7 Table 3. Regression parameters used to compare model estimates to the standard, T os, for data sets used to develop () and to evaluate () the models. Model q. Number ata set Average r * S Intercept Slope ** (q. 8) Temperature based T os T t T Ht T H T BR1 T L Temperature and relative humidity based T tr T BR T L Temperature, relative humidity, and wind speed based T tru * Regression parameters (r, S, Intercept, and Slope) are from comparison of each model to T os. ** coefficient of efficiency. to May 9, 1999 was the least well represented by any of the temperaturerelative humidity models. uring this period some higher than average wind speeds occurred. Adding wind speed to the temperaturerelative humidity model further improved the fit while decreasing S to.46 from.56 for T tr (qs. 11 and 1). emonstration of the ability of our developed models (qs. 9, 11, and 1) to estimate T os is shown in Fig. 1, where daily estimates from all weather stations used to develop and compare the performance of the models are displayed. Our developed models, T t, T tr, and T tru, are slightly curvilinear at low T values and develop negative T values as they approach zero (Fig. 1). This may have been avoided if we excluded days with T max values less than C (11 days in the data set used to develop the models). As more parameters were added to the models, the cloud of points became more compact about the linear regression line (i.e., precision relative to T os was increased). With the exception of the model that included windspeed (T tru ), the spread of points about the regression line increased as T increased. The precision of the T tru model is noticeably superior to the other models, especially at higher T rates. When these models are compared for a six week continuous period for the Lethbridge weather station (Fig. 4), they all provide a reasonable fit (most daytoday differences relative to T os of less than 1 mm) with T tr providing the best overall fit. Comparison to individual weather stations The models, T t, T Ht, T tr, and T tru, were evaluated using stations independent of those used to develop the models (Fig. 1 and Table 4). For the stations used to evaluate the models, the average absolute difference between T estimated by the models compared to T os was.16 mm/d for T t and.18 mm/d for T tr. For the data set used to develop the models, the average absolute difference was.9 mm/d for T t and.11 mm/d for T tr. With regards to r, S, intercept, slope, and coefficient of efficiency, there were larger differences between individual weather stations than between the data sets used to develop or evaluate the models. For example, Stavely had the largest average difference between T t and T os (T t underestimated T os by.7 mm/d); whereas for Kernen farm 1999, T tr underestimated T os by the largest absolute amount,.4 mm/d. Stations used to develop or evaluate the models were equally represented by the models. Further, Fig. 1 shows weather stations not used to develop the models fell within the boundary of the stations used to develop the models. Reference T as determined from non ideal sites T os represents the evaporation from a hypothetical grass crop that is not short of water. When these equations are applied to nonideal surfaces such as a weather stations located in a rainfed agricultural region, errors may occur due to temperature and relative humidity differences caused by the aridity of the site. As Volume 48 6 CAIAN BIOSYSTMS NGINRING 1.7

8 T os T os T t T tr 1:1 1:1 T os T os T H T tru Fig. 1. Comparison of temperature (T t ), Hargreaves (T H ), temperaturerelative humidity (T tr ), and temperaturerelative humiditywind (T tru ) models against T os using weather stations with which the models were developed ( ) and evaluated (") (Table 1). 1:1 1:1 the soil dries, a greater proportion of incoming radiation is used to increase air temperatures rather than to evaporate water. As a result, the parameters driving the T os equations may result in an overestimation of reference evaporation. Overestimations in reference T have been found to be as high as 5% in very arid regions (Temesgen et al. 1999). The effect of the o ver estimatio n in the agricultural region of the Canadian prairies is yet undetermined as few of the rainfed stations exist where a close neighbouring station is irrigated. T he models developed in this paper r epresent a range o f conditions from semiarid to subhumid. Accordingly, the effect of aridity of the site will range from minimal at the subhumid sites to potentially more significant in the semiarid southern regions. Ultimately, some care in applying the models in arid regions or for applications requiring absolute accuracy should be applied. 1 8 T os T t T BR1 T H T L1 av S T 6 4 7// 7/7/ 8/3/ 8/1/ 8/17/ 8/4/ 8/31/ Fig.. aily T calculated using T os and temperature based models for Lacombe for July August 31,. 1.8 L GÉNI S BIOSYSTÈMS AU CAA MAULÉ et al.

9 1 8 T os T t T BR T tr T L av S T 6 4 5/1/1999 5/8/1999 5/15/1999 5//1999 5/9/1999 6/5/1999 6/1/1999 Fig. 3. aily T calculated using T os and temperaturerelative humidity based models for Kernen farm for May 1 June 11, T T os T t T tr T tru T H av S // 7/7/ 8/3/ 8/1/ 8/17/ 8/4/ 8/31/ Fig. 4. aily T calculated using T os and developed models of T t, T tr, and T tru for Lethbridge for July August 3,. SUMMARY and CONCLUSIONS Using daily weather data from 1 weather stations within the Canadian Prairies, empirical models were developed to estimate T calculated by T os a standardized reference equation used to calculate T from a full complement of weather data and based on the PenmanMonteith equation. Using daily weather data from stations independent of those used to develop the models, our models were evaluated with regards to how well they estimated T os. In addition, our models were compared to other published simple models: BaierRobertson, Hargreaves, and Linacre. All models used T os as the comparison standard. T models were compared to the standard (T os ) using average T, r, S,, and regression equation parameters of intercept and slope. Models based upon temperature (along with extraterrestrial radiation calculated from latitude) are listed from most accurate to least: T T T > T > T t Ht H BR1 L1 There was very little difference between our statistically developed model, T t, and the Hargreaves model, T H. The regression against the Hargreaves model did not have an intercept of zero (Table 3), but if the coefficients within the Hargreaves model were slightly modified as with T Ht (q. 1) then the intercept was zero. Of the temperature based models, T t, T H, or T Ht would be suitable to represent T os under prairie climatic conditions. BaierRobertson (T BR1, q. 3) and Linacre (T L1, q. 6) temperature based models are not recommended for estimating T os for prairie conditions as they can result in a 3 to 5% error. Temperaturehumidity models improved the estimate of T os compared to temperature based models. Listing these models from most accurate to least: T > T T tr BR L Volume 48 6 CAIAN BIOSYSTMS NGINRING 1.9

10 Table 4. Comparison of model estimates of T for two models versus T os for individual stations by year. T t T tr Station Year AV* r ** S Int Slope AV r S Int Slope evelopment Beaverlodge Beaverlodge Stavely Stavely Swift Current Swift Current valuate ston field ston field ston field Kernen farm Lethbridge Lethbridge Outlook Strathmore * AV = T from model minus T os ** r regression coefficient; S standard error of regression; Int intercept; coefficient of variation T tr is recommended for estimating T os on the prairies. Linacre (T L, q. 5) and BaierRobertson (T BR, q. 4) models are not recommended for estimating T os (Table 3). Incorporation of measured values of temperature, relative humidity and wind speed into a model, T tru (q. 1) resulted in the most precise estimation of T os (Fig. 1, Table 3). In summary, the developed models of T t and T tr provided increased representation of T os as compared to the models of Baier and Robertson (1965) and Linacre (1977) and are recommended for use within agricultural regions of the prairie provinces where daily weather data is limited to just temperature or temperature and relative humidity. Of course, the model of choice will depend upon the daily weather data collected. For greater accuracy and precision, choose the model that uses the full complement of available data. The most accurate and precise model was T tru, which used temperature, relative humidity and wind speed. However, we recognize that few weather recording sites measure wind speed and/or relative humidity (dew point temperature). Our study was limited to the agricultural region of the prairies. Future studies could consider whether or not the information found in this study could be extended to other regions in Canada. Of particular interest is how applicable is the Hargreaves equation, or slightly modified versions of it, to other Canadian regions. ACKNOWLGMNTS For data sources we thank the IMCIN (Irrigation Management Climate Information Network) of Alberta Agriculture Food and Rural evelopment, Agriculture and AgriFood Canada, and research climatic sites funded through Saskatchewan Agriculture evelopment Fund. Topic concept originated while working on research funded through Saskatchewan Agriculture evelopment Fund. RFRNCS Allen, R.G., L.S. Pereira,. Raes and M. Smith Crop vapotranspiration Guidelines for Computing Crop Water Requirements. FAO Irrigation and rainage Paper 56. Rome, Italy: FAO. x49e.htm (6/3/5). ASC. 5. The ASC Standardized Reference vapotranspiration quation. dited by R. G. Allen, I.A. Walter, R. lliott, T. Howell,. Itenfisu, and M. Jensen. New York, NY: American Society of Civil ngineers. Baier, W valuation of latent evaporation estimates and their conversion to potential evaporation. Canadian Journal of Plant Sciences 51: Baier, W. and G.W. Robertson stimation of latent evaporation from simple weather observations. Canadian Journal of Plant Sciences 45: Canadian Institute for Climate Studies. 1. Canadian Gridded Climate. (5/3/9). roogers, P. and R.G. Allen.. stimating reference evapotranspiration under inaccurate data conditions. Irrigation and rainage Systems 16: Grace, B. and B. Quick A comparison of methods for the calculation of potential evapotranspiration under the windy semiarid conditions of southern Alberta. Canadian Water Resources Journal 13:919. Hargreaves, G.H. and Z.A. Samani Reference crop evapotranspiration from temperature. Applied ngineering in Agriculture 1(): Hargreaves, G.L., G.H. Hargreaves and J.P. Riley Agricultural benefits for Senegal River Basin. Journal of Irrigation and rainage ngineering 111: L GÉNI S BIOSYSTÈMS AU CAA MAULÉ et al.

11 Legates,.R. and G.J. McCabe, Jr valuating the use of goodnessoffit measures in hydrologic and hydroclimatic model validation. Water Resources Research 35:3341. Linacre,.T A simple formula for estimating evaporation rates in various climates, using temperature data alone. Agricultural Meteorology 18: Nash, J.. and J.V. Sutcliffe River flow forecasting through conceptual models. Part I A discussion of principles. Journal of Hydrology 1: 89. Pelton, W.L., K.M. King and C.B. Tanner An evaluation of the Thornthwaite method for determining potential evapotranspiration. Journal of Agronomy 5: Penman, H.L Natural evaporation from open water, bare soil and grass. Proceedings Royal Society (London), Series A 193: Shuttleworth, W.J vaporation. In Handbook of Hydrology, ed..r. Maidment, New York, NY: McGrawHill Inc. Temesgen, B., R.G. Allen and.t. Jensen Adjusting temperature parameters to reflect wellwatered conditions. Journal of Irrigation and rainage ngineering 15: 633. Thom, A.S., J.L. Thony and M. Vauchlin On the proper employment of evaporation pans and atmometers in estimating potential transpiration. Quarterly Journal Royal Meteorological Society 17: Thornthwaite, C.W An approach toward a rational classification of climate. Geography Review 38:5594. C d C n e a e d e s e smax e smin T BR1 T BR NOMNCLATUR denominator constant that changes with crop reference type (.34 for short and.38 for tall crop surfaces) numerator constant that changes with crop reference type (9 for short and 16 for tall crop surfaces) coefficient of efficiency mean actual vapor pressure at 1.5 to.5m height (kpa) saturated vapor pressure deficit = e a e s saturation vapor pressure at 1.5 to.5m height as average of saturation vapor pressure at maximum and minimum air temperatures (kpa) saturated vapor pressure calculated at T max (kpa) saturated vapor pressure calculated at T min (kpa) PT calibrated, using temperature only, to Penman s formula for a crop with an albedo of.5 and a crop coefficient of 1. throughout the growing season PT calibrated, using temperature and relative humidity, to Penman s formula for a crop with an albedo of.5 and a crop coefficient of 1. throughout the growing season T H Hargreaves reference T for wellwatered short crop T Ht modified Hargreaves reference T for wellwatered short crop T L1 grass reference T calculated using temperature T L grass reference T calculated using measured dew point temperature T os standardized reference T for short surfaces,.1 m T t temperature and extraterrestrial radiation based model for T T tr temperature, extraterrestrial radiation, and relative humidity based model for T T tru temperature, extraterrestrial radiation, relative humidity, and wind speed based model for T h elevation (m) G soil heat flux density at the soil surface (MJ m d 1 ) O i observed values Æ observed mean P i predicted values P atmospheric pressure (kpa) R a extraterrestrial radiation (MJ m d 1 ) as described in ASC (5) R n calculated net radiation at crop surface (MJ m d 1 ) R s solar radiation (MJ m d 1 ) R calculated clear sky radiation (MJ m d 1 ) RH c corrected RH value (%) RH max daily maximum RH (%) RH min daily minimum RH (%) RH uc uncorrected RH value (%) RH smax highest uncorrected maximum RH value that occurred for that station in the entire measurement set (%) RH smin lowest uncorrected minimum RH value that occurred for that station in the entire measurement set (%) T mean daily air temperature at 1.5 to.5m height, (T max + T min )/ ( C) T d dew point temperature ( C) T m temperature adjusted for elevation, T m = T +.6h T max daily maximum air temperature (ºC) T min daily minimum air temperature (ºC) L latitude ( ) T ra difference between the mean temperatures of the warmest and coldest months of the year ( C) mean daily range of temperature ( C) T rd u γ mean daily or hourly wind speed at m height (m/s) slope of saturation vapor pressuretemperature curve at T (kpa/ C), given by: 17. 7T 54 exp T = 37 3 ( T +. ) psychrometric constant =.665P (kpa/ C) Volume 48 6 CAIAN BIOSYSTMS NGINRING 1.11