How Latitude and Date Change Your ET0

Latitude and ET0 are linked through Ra, the extraterrestrial radiation that reaches the top of the atmosphere. When latitude or date changes, Ra changes, and ET0 changes with it. At a fixed example temperature pair, ET0 at 50 N rises from 1.21 mm per day on 15 January to 5.47 mm per day on 15 July, while ET0 at the equator stays between 4.61 and 5.09 mm per day across the same four dates.

How Latitude and ET0 Are Linked Through Ra

Ra is the solar energy at the top of the atmosphere. The evapotranspiration calculator uses Ra from latitude and day of year, following FAO 56. Latitude sets sun angle and day length through the year, and both set the energy available for evaporation.

Hold temperature fixed and change only latitude or date, and any change in ET0 comes from Ra. The formula is ET0 equals 0.0023 times Ra times Tmean plus 17.8 times the square root of Tmax minus Tmin. Tmean is the mean of the daily maximum and minimum temperature. Ra must be in mm per day equivalent. The FAO 56 table gives Ra in MJ per m2 per day, so divide by 2.45 to get mm per day. Missing that division makes ET0 about 2.45 times too high.

Ra by Latitude and Date

The table below uses FAO 56 Annex 2 Table 2.6. Every value is for the 15th day of the month named. The table gives one value per month, for the 15th day only. It does not give a value for 1 July, or for any other single day.

Latitude	15 January	15 April	15 July	15 October
30 N	21.1 MJ, 8.61 mm	36.8 MJ, 15.02 mm	40.6 MJ, 16.57 mm	27.6 MJ, 11.27 mm
40 N	15.0 MJ, 6.12 mm	34.7 MJ, 14.16 mm	40.8 MJ, 16.65 mm	22.5 MJ, 9.18 mm
50 N	8.9 MJ, 3.63 mm	31.5 MJ, 12.86 mm	40.2 MJ, 16.41 mm	16.9 MJ, 6.90 mm
Equator	36.2 MJ, 14.78 mm	36.8 MJ, 15.02 mm	33.9 MJ, 13.84 mm	37.4 MJ, 15.27 mm
30 S	43.1 MJ, 17.59 mm	27.2 MJ, 11.10 mm	19.6 MJ, 8.00 mm	37.5 MJ, 15.31 mm

Read the table down a column first, then across a row. On 15 January, Ra rises from 3.63 mm per day at 50 N to 17.59 mm per day at 30 S. On 15 July, the order reverses, with Ra highest in the north at 16.65 mm per day at 40 N and lowest in the south at 8.00 mm per day at 30 S. Across a row, at 50 N Ra rises from 3.63 mm per day in January to 16.41 in July. At 30 S, it runs the other way, from 17.59 in January down to 8.00 in July. At the equator, the row is almost flat, moving only from 13.84 to 15.27 mm per day.

ET0 From Those Ra Values at One Fixed Temperature Pair

Every ET0 value below uses the same example input, a high of 30 degrees C and a low of 18 degrees C. That pair is an example input only, not observed weather. Holding it fixed is the point. When temperature is fixed, only Ra can change ET0 in the table.

The arithmetic is the same in every cell. Tmean is 24 degrees C, Tmean plus 17.8 is 41.8, the range is 12, and the square root of 12 is 3.464. Multiply 0.0023 by 41.8 by 3.464 and you get 0.3330, so ET0 is Ra in mm per day times 0.3330. Check one cell. At 40 N on 15 July, Ra is 40.8 MJ per m2 per day. Divide by 2.45 to get 16.65 mm per day. Multiply by 0.3330 to get 5.55 mm per day. That is the 15 July table value, not the 1 July worked example of about 5.7 mm per day. On exact 1 July, Ra at 40 N is 41.66 MJ per m2 per day, 17.00 mm per day, and ET0 is 5.66 mm per day, about 5.7.

Latitude	15 January	15 April	15 July	15 October
30 N	2.87 mm per day	5.00 mm per day	5.52 mm per day	3.75 mm per day
40 N	2.04 mm per day	4.72 mm per day	5.55 mm per day	3.06 mm per day
50 N	1.21 mm per day	4.28 mm per day	5.47 mm per day	2.30 mm per day
Equator	4.92 mm per day	5.00 mm per day	4.61 mm per day	5.09 mm per day
30 S	5.86 mm per day	3.70 mm per day	2.66 mm per day	5.10 mm per day

The highest ET0 in the table is 5.86 mm per day at 30 S on 15 January. The lowest is 1.21 mm per day at 50 N on 15 January. The July values at 30 N, 40 N, and 50 N sit inside the page FAQ summer range of about 4 to 7 mm a day. The January values sit well below it.

Northern Hemisphere Versus Southern Hemisphere

July is high season in the north and low season in the south. January is the mirror image. At 30 S, ET0 is 5.86 mm per day on 15 January and 2.66 mm per day on 15 July. At 40 N, ET0 is 2.04 mm per day on 15 January and 5.55 mm per day on 15 July.

A guide that calls July the peak month is a northern hemisphere guide. In the southern hemisphere, July is a low ET0 month, and January is the peak. Enter latitude as a negative number south of the equator, for example minus 30 for 30 S. A positive latitude for a southern garden gives a northern season.

The Equator and the Small Seasonal Swing

At the equator, ET0 is 4.92 mm per day on 15 January, 5.00 on 15 April, 4.61 on 15 July, and 5.09 on 15 October. The difference between the highest and lowest is only 0.48 mm per day, against 4.26 mm per day at 50 N.

The reason is day length. Near the equator, day length stays close to 12 hours all year, and the sun stays high. Ra therefore stays high all year, between 13.84 and 15.27 mm per day.

The Large Swing at 50 N

At 50 N, the swing is the largest in this table. ET0 is 1.21 mm per day on 15 January, 4.28 on 15 April, 5.47 on 15 July, and 2.30 on 15 October. The January to July difference is 4.26 mm per day. July ET0 is about 4.5 times January ET0. At 40 N, the ratio is about 2.7 times. At 30 N, it is about 1.9 times. At the equator, it is only about 1.1 times.

Latitude	Highest ET0 in table	Lowest ET0 in table	Difference
30 N	5.52 mm per day, 15 July	2.87 mm per day, 15 January	2.65 mm per day
40 N	5.55 mm per day, 15 July	2.04 mm per day, 15 January	3.51 mm per day
50 N	5.47 mm per day, 15 July	1.21 mm per day, 15 January	4.26 mm per day
Equator	5.09 mm per day, 15 October	4.61 mm per day, 15 July	0.48 mm per day
30 S	5.86 mm per day, 15 January	2.66 mm per day, 15 July	3.20 mm per day

In winter at 50 N, days are short and the sun angle is low, so Ra falls to 3.63 mm per day on 15 January. In July, days are long and the sun is high, so Ra rises to 16.41 mm per day. A single annual ET0 figure is a poor guide at high latitude. That gap matters in practice, because a watering plan built on a single annual figure would overwater in winter and underwater in summer at high latitude.

How to Use the Calculator for Your Latitude and Date

Open the evapotranspiration calculator and enter your latitude first, using a negative number south of the equator. Then enter the date, or the month you are planning for. Then enter the daily maximum and minimum temperature, or the monthly average maximum and minimum if you are planning rather than scheduling. The calculator returns daily ET0 in mm per day or inches per day. To get crop water use, multiply ET0 by a crop coefficient in the crop water requirement calculator. This blog gives no Kc values.

For planning, run the calculator once per month with monthly average temperatures. For scheduling on a given day, run it with that day maximum and minimum. To turn a daily ET0 into a weekly figure, multiply by 7. At 40 N on 15 July, 5.55 mm per day times 7 is 38.8 mm per week. At 50 N on 15 January, 1.21 mm per day times 7 is 8.5 mm per week. Those weekly figures are ET0 only. To plan watering frequency from ET0, use the garden watering schedule calculator or the irrigation scheduling calculator.

Common Mistakes

Using the 15th day Ra as the Ra for the 1st of the month is the first mistake. The FAO 56 table gives Ra for the 15th day only. At 40 N, 15 July gives ET0 of 5.55 mm per day, while exact 1 July gives 5.66 mm per day.

Forgetting to divide Ra by 2.45 is the second mistake. Table 2.6 gives Ra in MJ per m2 per day, while the formula needs Ra in mm per day equivalent. Put 40.8 straight into the formula, and ET0 comes out about 2.45 times too high.

Entering a southern latitude as a positive number is the third mistake. A positive 30 for a garden at 30 S gives northern seasons, with July high and January low.

Using a summer ET0 all year is the fourth mistake. The page FAQ gives about 4 to 7 mm a day as a typical summer range. That range does not apply in winter at 40 N or 50 N, where ET0 falls to 2.04 and 1.21 mm per day in January.

Treating the fixed example temperatures as real weather is the fifth mistake. A high of 30 degrees C and a low of 18 degrees C is an example input used here to isolate Ra. Real January weather at 50 N is colder, so real ET0 there would be lower still.

FAQs

Q: Does latitude change ET0 even if temperature stays the same?
A: Yes. Latitude and date set Ra, and Ra sets ET0. At the fixed example temperatures, ET0 on 15 January is 1.21 mm per day at 50 N and 5.86 mm per day at 30 S.

Q: Why is ET0 highest in July in the north and in January in the south?
A: Because Ra follows the sun. In July the sun is over the northern hemisphere. In January the pattern reverses.

Q: Why does ET0 change so little at the equator?
A: Because day length near the equator stays close to 12 hours all year and the sun stays high. Ra stays between 13.84 and 15.27 mm per day, so ET0 stays between 4.61 and 5.09 mm per day.

Q: What Ra value should I use for 1 July?
A: Use the exact 1 July Ra from FAO 56 Equation 21, or use the 15 July table value and label it as 15 July. At 40 N, exact 1 July Ra is 41.66 MJ per m2 per day, giving ET0 of 5.66 mm per day. The 15 July value gives 5.55 mm per day.

Q: Is a low winter ET0 a sign that the calculator is wrong?
A: No, in most cases it is a sign that Ra is low. At 50 N on 15 January, Ra is only 3.63 mm per day, so ET0 is only 1.21 mm per day.

Q: How do I turn ET0 into a watering amount for my crop?
A: Multiply ET0 by a crop coefficient in the crop water requirement calculator. ET0 is for a reference grass surface, not for a specific crop.