> For the complete documentation index, see [llms.txt](https://swatplus.gitbook.io/io-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://swatplus.gitbook.io/io-docs/theoretical-documentation/section-1-climate/untitled/1-1.3-temperature/1-1.3.2-hourly-air-temperature.md).

# 1:1.3.2 Hourly Air Temperature

Air temperature data are usually provided in the form of daily maximum and minimum temperature. A reasonable approximation for converting these to hourly temperatures is to assume a sinusoidal interpolation function between the minimum and maximum daily temperatures. The maximum daily temperature is assumed to occur at 1500 hours and the minimum daily temperature at 300 hours (Campbell, 1985). The temperature for the hour is then calculated with the equation:

$$T\_{hr} = \overline T\_{av} + \frac{T\_{mx}-T\_{mn}}2  cos(0.2618 (hr-15))$$                                                                                               1:1.3.1

where $$T\_{hr}$$ is the air temperature during hour $$hr$$ of the day ($$\degree C$$), $$\overline T\_{av}$$ is the average temperature on the day ($$\degree C$$), $$T\_{mx}$$ is the daily maximum temperature ($$\degree C$$), and $$T\_{mn}$$ is the daily minimum temperature ($$\degree C$$). 

Table 1:1-6: SWAT+ input variables that pertain to hourly air temperature.

| Definition                                             | Source Name | Input Name | Input File                                                                    |
| ------------------------------------------------------ | ----------- | ---------- | ----------------------------------------------------------------------------- |
| $$T\_{mx}$$: Daily maximum temperature ($$\degree C$$) | max temp    | tmpmax     | [.tmp](/io-docs/introduction-1/climate/tmp.cli-and-temperature-data-files.md) |
| $$T\_{mn}$$: Daily minimum temperature ($$\degree C$$) | min temp    | tmpmin     | [.tmp](/io-docs/introduction-1/climate/tmp.cli-and-temperature-data-files.md) |