In Search of the Standard Day

By Dr Fabio Capezzuoli

Recent posts and discussions on WUWT regarding air temperature sampling frequencies and their influence on the daily average – propagating to monthly and yearly trends – demonstrated that the classic sampling method of Tmax and Tmin is not adequate to correctly represent daily averages (Tav); to produce a representative value at least 24 samples (hourly readings) should be used.

From the discussions also an idea emerged, that it could be possible to produce a “Standard Day” temperature curve and use it to correct older data sampled by Tmax and Tmin only, in order to obtain a more representative value of Tav.

Because I’d like to give a contribution to knowledge, and also because I want to hone my Python coding skills, I decided to process some data and see if it can help going towards the goal of a “Standard Day”.

The series I used for my study are hourly air temperature measurements:

PRM – Parma-Urban, PR, Italy, weather station (44.808 N, 10.330 E, Elev. 79 m), covering 2015-2016. Despite its latitude, Parma’s climate is classified as Humid Subtropical (Koppen: Cfa).

EVG – Everglades City 5 NE CRN Station – 92826 (25.90 N, 81.32 W, Elev. NA), Florida, USA, covering 2015-2016. The climate of Everglades City is classified as Tropical Savannah (Koppen: Aw).

Parma station location:

Everglades City station location:

Data were downloaded from the access systems provided by the station’s managing organization (ARPAE-ER, Italy and NOAA, US) and not preprocessed in any way except for removal of empty and invalid records.

I chose these stations as representative of the temperate latitudes situation (Parma), and of the tropical situation (Everglades City); my choice of tropical stations was limited, and in the end only the CRN produces data with the necessary frequency and quality.

Before diving head first into curve-fitting, I decided to do some grouping and visualization, so that I can get an idea of the parameters of a typical day. What I chose are:

– H(Tmin), H(Tmax): Hour of the day (local time) at which min and max temperatures are recorded.

– DTR: (Tmax – Tmix) – Diurnal Temperature Range

– Delta-H: (H(Tmax) – H(Tmin)) – Time interval (in hours) between Tmax and Tmin

Using a Python code, I calculated the parameters defined above for each day of the temperature series.

The aggregate parameters’ values over the whole time period (2015-2016) are shown in Fig.1a for Parma and Fig.1b for Everglades City.



For Parma (Fig.1a), the aggregate data show that – over the study period – Tmax and Tmin occur usually 9 – 11 hours apart; DTR has a very non-normal distribution spanning 0 – 15 °C but with higher count around 10 °C; finally Tmin is recorded most frequently around 07:00 and Tmax around 16:00 (all times are local).

For Everglades City (Fig1b), Delta-H is most frequently 8 hours; the DTR distribution is more bell-shaped and centered around 10 °C, while Tmin is most frequently recorded around 23:00 and 03:00 and Tmax around 12:00.

Then, I also plotted the same parameters month by month for the whole study period. The first quantity is Delta-H, for both locations (Fig.2).

clip_image006clip_image006Delta-H distributin for Parma (Fig.2a) is narrower and shifted towards longer timespan in the summer; wider and shifted towards shorter timespan in winter: this is consistent with the varying length of day in the temperate region.

clip_image008clip_image008Delta-H distribution at Everglades City (Fig.2b) is rather uniform throughout the year.

Then, DTR for both locations (Fig.3)

clip_image010clip_image010Parma shows DTR distributions (Fig.3a) that are wide all over the year, but with larger mean DTR in summer months than winter months.

For Everglades City, DTR distribution (Fig.3b) is somewhat narrower and shifted to smaller values in the summer months, becoming wider and shifting to larger values in winter.


Fig.4 shows H(Tmin, Tmax).


clip_image016clip_image016In Parma (Fig.4a), Tmin is recorded most often between 05:00 and 10:00 while Tmax is recorded most often between 15:00 and 20:00, with a shift towards later hours in summer (this could be a consequence of the station being in an urban environment rich with heatsinks); the separation between Tmin and Tmax distributions is clear in summer but less so in winter.

In Everglades City (Fig.4b), Tmin occurs mostly at night (20:00 – 05:00) and Tmax around noontime (10:00 – 15:00); the distributions are wider and show an appreciable level of superimposition throughout the year.

I computed also another parameter, which can be seen as a synthetic indicator for DTR and Delta-H together: the daily gradient, or Dgrad.

It is defined at (Tmax-Tmin)/Delta-H; it is by definition positive and gives a measure of how fast temperature changes over the course of one day. I also decided to visualize Dgrad to show its monthly variation over the whole study period, in Fig.5.



Dgrad for both stations varies in a rather narrow interval, but while for Everglades City it appears to reach a maximum in spring months and a minimum in summer, Parma shows a slowly rising trend from the winter minimum to September, followed by an abrupt fall in October / November.

Both series are also highly noisy and present a number of outliers. Curiously, the highest outliers occur in Sept-15 and Aug-16 for both stations.


I never imagined this study would bring dramatic revelations, and this is in fact the case.

There still are, however, some conclusions that can be drawn even from a dataset limited in space and time:

– As far as defining a “standard day” can be desired, it should be limited to month-by-month and station-by-station. The variation of daily parameters in time and space is, at a first look, too large to warrant wider generalizations.

– The long-term trend of the daily parameters can be investigated in order to gain more information about variation of climate than just daily min, max and average temperatures.

– The long-term trend of daily gradient, can give information about whether climate is becoming more unstable and extreme phenomena are on the increase.


Datasets and source code (Python 3) are available upon request.

Constructive criticism and observations are welcome. Please cite the words you are responding to, as to avoid confusion and misunderstandings.

via Watts Up With That?

February 16, 2019 at 04:04AM

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