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Impact of Alternative Data on the Penman-Monteith Method Considering Windy Conditions in the Semi-Arid Area

Homayoon Ganji*, Takamitsu Kajisa

Graduate School of Bioresources, Mie University, 514-8507 Kurimamachiya-Cho 1577, Tsu, Japan

Abstract: When real data are unavailable, the standard Penman-Monteith method for estimating reference evapotranspiration can be calculated using alternative input data: wind speed from a nearby station, the default global average wind speed, solar radiation based on temperature and vapour pressure based on the minimum temperature. These alternative data are recommended in FAO paper 56. In this study, we assessed the accuracy achieved when using these alternative data for reference evapotranspiration estimation in a semi-arid region characterised by a strong persistent wind speed. Western Afghanistan was selected as the study site, as it is exposed to strong winds over the 120-day period from June to September. Significant differences were found in the estimates produced using full data and those obtained using wind speed data from a nearby station, the default global average wind speed, and vapour pressure based on the minimum temperature. Root Mean Square Error (RMSE) was found 1.51 mm d⁻¹, 1.27 mm d⁻¹ and 1.07 mm d⁻¹, respectively. Errors were especially significant on days with strong wind. The smallest RMSE of 0.36 mm d⁻¹ was found when basing solar radiation on temperature. The assumption that the dew point temperature will be close to the minimum temperature was shown to be unreliable on days of strong wind.

Keywords: reference evapotranspiration, Penman-Monteith, alternative data, strong wind, semi-arid

Received October 01, 2018; Revised November 20, 2018; Accepted December 12, 2018

Citation: Homayoon Ganji, Takamitsu Kajisa, Impact of Alternative Data on the Penman-Monteith Method Considering Windy Conditions in the Semi-Arid Area. American Journal of Water Resources, 6 (6). 217-223. January 2018. doi:10.12691/ajwr-6-6-2

1. Introduction

A number of methods for estimating reference evapotranspiration () have been reported in the literature [1,2]. Empirical equations are one of the simpler methods and are used worldwide.

The empirical methods have mainly been based on climatological data, because of the difficulty of making direct measurements of . These methods can be divided into four groups, based on their requirements. One of the most accurate methods currently available is the Penman-Monteith method, which has been widely accepted by the international scientific community [3,4].

The Penman-Monteith equation is recommended by the United Nations Food and Agriculture Organisation (FAO) as the only method offering high accuracy. However, to estimate using the Penman-Monteith equation, complete input data are required [5]. The Penman-Monteith method was found to be the most accurate of the six well-known methods used to estimate in the western region of Afghanistan [6].

The Penman-Monteith method requires data on the maximum and minimum temperature ( and ), relative humidity () and/or dew point temperature () for estimating actual vapor pressure () net radiation (),and wind speed () measured at a height of two metres above ground level [5].

Few weather stations in the world are equipped to supply this complete set of weather variables [7]. This places a severe restriction on the application of the Penman-Monteith method [8]. FAO paper 56 supplies alternative workarounds that allow the missing , and solar radiation () to be estimated.

When and/or data are unavailable, actual vapor pressure based on temperature can be estimated using Equation 14 from Table 1, on the assumption that is close to . This is true in humid areas, where the difference between and is small. In arid areas, however, there is often a large difference between and [9].

When is missing, Hargreaves' radiation formula as a function of and is recommended for the calculation of solar radiation based on temperature This is shown as Equation 15 in Table 1. Hargreaves' radiation formula assumes that the difference between and is governed by the daily solar radiation at the given location.

When data are lacking, two alternative approaches are recommended, one in which the default world average value of as 2 m s⁻¹ is used, and one in which data from a nearby station are used, if such data are available [5]. In this study, the data of wind speed from airport was used as it was the only available data. The wind speed data from the airport , adjusted at 2 meters height, using Equation 8 from Table 1.

All the proposed methods have been tested at a variety of sites worldwide. It has been shown that the results are different in different climate regimes.

Popova et al. [8] found the procedures proposed by FAO to be accurate when applied in Southern Bulgaria. In a study conducted in Southern Ecuador, Cordova et al. [10] found that the use of alternative data has no significant effect on the calculation of , but that when the data were missing, the calculations became erroneous. A study in Southern Ontario, Canada reported similar results [11]When and were missing, the FAO Penman-Monteith method still provided very good estimates of .

Although these procedures are suboptimal, when working in areas where the required data are lacking or of questionable quality, their use is recommended [5].

The aim of the present study was to contribute to irrigation planning by evaluating the performance of the Penman-Monteith method both when complete input data () are available, and when some are missing. The study was conducted in Herat, Afghanistan. No previous studies have quantified the effect of applying these alternative procedures in climates with strong winds and semi-arid conditions, in Afghanistan or in any other region.

2. Methods

2.1. Site and Data Collection

The study site was selected for their semi-arid climate and exposure to strong winds over a continuous 120-day period from June to September.

Two locations in the west of Afghanistan were selected for data collection: Urdo Khan agricultural farm and Herat airport, in Herat province. The locations of the two sites are shown in Figure 1.

Urdu Khan research farm is located approximately 11 kilometres from Herat airport. The climate is semi-arid, with warm, windy and low humidity conditions in the summer. Annual average precipitation is low, and mainly limited to the winter and spring seasons. The lowest ratio of cloud cover occurs in the summer season, and the highest ratio in the winter season.

A significant factor at the study site is what is known locally as the ‘120-day winds’. This strong winds persist from June to September, with speeds exceeding 450 km d⁻¹. Such winds have been shown to be the most significant factor in the estimation.

Herat Airport is located 11 km to the north of the Urdo Khan Farm at an elevation of 973 m above sea level. The height of the wind speed measurement was 10 m above the ground level, therefore, it was converted in 2 m for Herat Airport. The weather conditions are very similar to those at Urdo Khan, characterised by strong winds that blow continually from May to September, with a daily average peak exceeding14 m s⁻¹ in 2016.

Figure 1. Locations of Urdu Khan Farm and Herat Airport, Afghanistan

2.2. Estimation and Analyzing

The Penman-Monteith equation was used to estimate both with complete and incomplete input data, as shown in Table 1.

When complete input data were available, recorded at the Urdo Khan site, the calculation was done using , which is mainly associated with , and measured at Urdo Khan Farm (Eq. 1).

When the data were missing, the calculations were done using and which are associated with and , respectively (Eqs. 2-3).

When were missing, the calculation was done using , associated with (Eq. 9).

Finally, when data were missing, was calculated using (Eq. 11).

Regression analysis was used to assess the validity of the results given by the estimation. The regression slope was used as the measure of accuracy, and the coefficient of determination was used as the measure of exactness. The values and suggest perfect results. The root mean square error () and mean bias error () were also calculated to evaluate the impact of the proposed methods on the results. A smaller and value would mean a better result. This allows the impact of applying the alternative procedures on estimation to be quantified.

Table 1. Model’s equations

3. Results and Discussion

3.1. Daily Average Weather Variables

The mean air temperature , , , and hours of sunshine (n) were measured from January 24th to December 28th in 2016. was measured and adjusted at 2 meter height at both locations, whereas the other data were measured at Urdo Khan only.

The period from May to September was warm, with greater than 20°C. The hottest days were recorded in June, with a greater than 30°C. The cold period lasted from November to February, with less than 10°C. The lowest temperature was recorded in early November, with a below 0°C (Figure 2).

Over the course of the year, ranged from 0 m s⁻¹ to above 14 m s⁻¹ at both study sites though the daily average was higher at the airport site. The daily average was approximately 2 m s⁻¹ in the period July to August, with an average daily maximum of almost 6 m s⁻¹. The daily average fell below 2 m s⁻¹ in the period from September to May, with a range between 6 and 2 m s⁻¹ at Urdo Khan station. The maximum reading at the airport exceeded 10 m s⁻¹, recorded in June (Figure 3).

ranged from approximately 10% to above 80%, over the course of the year. The period May to August were drier. The driest air was recorded in August, at which time the dropped below 20% (Figure 4).

The estimation of is related to the length of the day over the course of the year. The highest value of above 25 MJ m⁻² d⁻¹, was recorded in the period May to July, while in the lowest value was recorded in November. A difference between and was only found in the period May to August; in the other months, their rates were identical (Figure 5).

The Application of produced results that were different from those estimated using . The difference was particularly pronounced in the period from April to September. Over the full year, produced a lower estimate than (Figure 6). These large differences reflected the difference between and , especially between April and September. This difference was greater than 10°C (Figure 7).

3.2. Daily Average Estimation of ET₀

The rate of ranged from 0 mm d⁻¹ to above 10 mm d⁻¹ over the course of the year. The highest rate was recorded in the period from June to August, with a peak of above 10 mm d⁻¹ in June.

When only the daily average data were missing, two alternatives were used. First, the default world average value of was used to estimate . The result was close to that produced by . Over the course of the year, produced a small overestimate, though in the period May to August it produced a lower rate than (Figure 8a).

Figure 2. Daily average temperature, 2016

Figure 3. Daily average of wind speed, 2016

Figure 4. Daily average of relative humidity, 2016

Figure 5. Daily average of solar radiation, 2016

Figure 6. Daily average of actual vapor pressure, 2016

Figure 7. Daily average of and , 2016

This is because the value of is lower than the daily average wind rate at Urdo Khan Farm between June and August. The annual average value of at this location was 1.84 m s⁻¹, however, in the period June to August exceeded 3 m s⁻¹.

The data from the airport near Urdo Khan were then used in the calculation. The result is shown in Figure 8b. It can be seen that was greater than 6 mm d⁻¹ from May to September, with a peak in June of almost 15 mm d⁻¹. For the period from May to October, the use of produced a higher estimation than . The difference was largest in the period from June to August. This difference arose because the rate was higher than that at the nearby station. The impact of the wind speed on the results was therefore relatively large, especially on days that were dry and windy.

The ‘120-day winds’ was found a very important factor in this region, especially when estimating . The wind speed may vary, even over short distances. Although, the two study locations were within 11 km of each other, the wind speeds was not identical, and the wind speed had a significant impact on the estimation of .

Figure 8. From (a) to (d) daily average estimation of given by and when input data are missing. Herat, 2016

A higher rate of was produced on days of strong wind, so that there was a positive correlation between wind speed and .

When only was missing, data were used to estimate . The results produced by and were similar over the course of the full year, however, relatively large differences were found in the period from June to September, produced a lower rate than (Figure 8c).

This suggested that is not a good substitute for when deriving on days when the wind is strong.

When only the data was missing, data were used in their place, producing satisfactory results, as the and rates were identical over the course of the year (Figure 8d). This method of estimating when the data are missing appears to produce good results.

3.3. Relationship between Actual and Alternative Weather Variables

Relationship between the from Urdo Khan and was weak and ). The data were widely dispersed, particularly on windy days (Figure 9-(a)). The significant differences in wind speed between the two sites were attributed to the site elevation and surrounding terrain. The airport station is bounded by desert on all four sides and is 33 metres higher than the Urdo Khan site. The Urdo Khan site is surrounded by agricultural land, gaining protection from trees, walls, and fences. This might explain the lower wind speed.

No significant relationship was found between the estimates of and . Figure 9-(b) shows the relatively weak relationship between the two datasets and ). This reflects differences between and over the course of the year, and especially on windy days.

The relationship between and is shown in Figure 9-(c), where and , suggesting a weak relationship. The assumption that will be close to was not supported, and was shown to be especially unreliable on days of strong wind at the research sites. The relationship between and is shown in Figure 9-(d). Here with and , indicating a significant correlation. The use of was confirmed to be applicable for calculation when data are missing.

3.4. Regression Analysis and Error Estimation

The relationship between and cases where alternative data used (), was shown by statistical indices given in Table 2.

When the data of was missing, which was measured 11 km from the site was used in the calculation. The value of confirms a significant correlation between and , however, the value of shows a low accuracy of the estimation. On the other hand, yielded the largest of 1.51 mm d⁻¹, and showed an overestimation of 1.07 mm d⁻¹ (Table 2). This was due to the higher rate of . It was confirmed that the rate was different at the two locations, particularly on days when the wind was strong. This suggested that the distance between two locations is important when collecting data in the semi-arid areas characterised by strong winds, such as the West region of Afghanistan.

Figure 9. Relationship between; (a) at the two stations; (b) and ; (c) and ; (d) and

For the condition in which was used in the calculation, the result produced by had the third largest of 1.07 mm d⁻¹ and an of -0.02 mm d⁻¹, indicating an underestimation (Table 2).

When data were missing, was used in the calculation. Considering the value of a signaficant agreement was found between and , however, the value of 0.70 indicates low accuracy between the estimates. On the other hand, The associated error (mm d⁻¹) was high in compression with the results reported by Jabloun and Sahli (2008) in the semi-arid conditions of Tunisia. The value of mm d⁻¹ confirmed an underestimation estimates (Table 2).

When only was missing, the results yielded by produced values of and , confirming that the estimation of using data is applicable when data are unavailable. The yielded an of below 0.36 mm d⁻¹, the smallest value, and an of -0.15 mm d⁻¹, representing an underestimate (Table 2). The results yielded by was almost in line with the result reported by Jabloun and Sahli (2008) in the semi-arid conditions of Tunisia.

Table 2. Determination Coefficient, Slope of Regression, and for Daily Average Given by the Penman-Monteith method with Complete and Incomplete Data

4. Conclusions

The unavailability of complete weather data in most locations in Afghanistan means that the data obtained through alternative procedure can be used to estimate via Penman-Monteith method.

Alternative procedures set out in FAO paper 56 allow estimates to be made when real data are lacking. In this study, we quantified the estimates obtained when using these alternative data in a semi-arid region characterised by strong winds.

The evaluations compared the performance of the Penman-Monteith method when using complete and incomplete data for estimating . The study was carried out in the west of Afghanistan, where is exposed to strong winds over the 120-day period.

The results demonstrated that the largest error (an overestimate of 1.51 mm d⁻¹) arose when using data. This reflected the large difference in at the two sites, even though they were separated by only 11 km. This suggests that data from a nearby location should not be used if an accurate estimate of is expected. When using the default average m s⁻¹ in the estimation, an underestimate of 1.07 mm d⁻¹ was produced.

When was used instead of , the Penman-Monteith method performed poorly over the period May to September, when there were many strongly windy days. A divergence between and was noted only on windy days. In the period when winds were light, from September to May, the results were good. We do not, therefore, recommend the use of as a substitute for missing when estimating on windy days.

The lack of was shown to be of least importance, as significant estimates were achieved using instead.

References

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