## Calculating Number of Days Over a Threshold - Perturbation Method (site browser)

This technique outlined below explains how to generate a timeseries of temperature projections to query for number of days on average over a temperature threshold per year.

- Question on the method and reply from CLIMsystems

The purpose of including this is to give context to how the tool projects future climate using timeseries of observed data.

OK: Each time I perturb the historical data, using the same parameters (ensemble, emissions, year etc), will the results be the same? i.e. hypothetically: 1/4/1980 has max of 25.2 degrees, the ensemble median gives 2 degrees of warming for 2030 so the perturbed value of that date becomes 27.2 degrees? Or does each perturbation (holding the parameters the same) generate slightly different results?

CLIMsystems: A perturbation always generates the SAME result for the same selected parameters. Note that the perturbation uses the monthly normalized values (also with the ensemble) thus the perturbation value is different for different months (this can cause shifts as to which month has the highest temperature)

An idea was to perturb the historical max temp data in the data browser for the site “Observatory Hill” (the only site in the council area with historical max temp data) for the four time steps using the 40 GCM ensemble (10%, median, 90% intervals)

Then

- Set the viewing period 1980 to 2010 (30 year baseline) to keep consistent with the 1995 baseline as used in other analyses.
- Export the data to excel.
- Then count the number of occurrences of temperatures over those thresholds and divide by 30 (number of years in the baseline) to get the average number of days per year.
- Is this a sound approach?
- If not, is there another way to do this?

This is the correct approach. Additionally you can sort the data from small to large (either in SimCLIM or in Excel), get the data in Excel and use the Percentile (returns the temperature for a given percentile) and PercentRank(gives the percentile for the given temperature), to get the values you are after (instead of doing the count). Percent to days is done by multiplying by 365 (not 30 or 30x365) as the percent applies to the chosen timeframe, in your case number of days per year.

#### Generating the data

Site browser

#### Calculating the number of days over a threshold

Proposed method reviewed by CLIMsystems (Using percentile or percentrank in excel)

The following method of analysis has been provided by CLIMsystems.

Extreme weather events can be expressed in multiple ways, i.e. through a chosen return period (i.e. 20 year) and then listing the extreme event (i.e 37.3°C), or vice versa, selecting an extreme event (i.e. 37°C) and then listing the return period (16.6 years). SimCLIM directly supports these types of calculations through its extreme event analyser. It can also show the effect of climate change on the values.

A different way is to select an extreme event (i.e. 37°C) and then list the average number of days this value is exceeded (i.e. 10 days). A statement like this takes results from the PDF (probability density function) of the climate variable (temperature). SimCLIM can produce this information as well. This Technical Note describes how this is done.

The desired output (exceedance days) can be created through the Data Browser ( ):

Select the station (i.e. Proserpine Airport in Australia).

Sort the climate variable of interest ( i.e. temperature), accepting the default order (small to big).

Plot the variable:

This is the probability distribution function of the variable (TMax), with the values on the y-axis and the sequence number on the x-axis (this does not start at 0, as it counts the missing values). Because the grid-division (vertical lines) shows for every 1/10, these correspond to the 10% intervals. Thus the high 10% value (corresponding to 36.5 days) is about 33°C. The 10-day value is about 35°C.

To generate the climate changed results, the scenario option of the databrowser is used ():

Clicking OK will perturb the climate variable values with the specified climate change scenario. This can take some time.

The table needs to be sorted again and then the variable can be plotted:

\

The 10% value has shifted to about 35°C. As this was the former 10-day value, this shows that this now has become 36.5 days.

More precise information can be generated and displayed by using Excel (using the export to Excel function in the data browser by right clicking the table) and the percentile function:

percentile |
baseline |
2040 |

1 |
36.5 |
38.1 |

2 |
35.6 |
37.1 |

3 |
35.0 |
36.6 |

4 |
34.6 |
36.2 |

5 |
34.2 |
35.8 |

6 |
34.0 |
35.6 |

7 |
33.7 |
35.3 |

8 |
33.4 |
35.0 |

9 |
33.1 |
34.8 |

10 |
33.0 |
34.7 |

(thus on average, 5% of the year the daily maximum temperatures are currently at or above 34.2°C, which will have changed to 35.8°C by 2040 - RCP8.5-high, 40-GCM ensemble)

days |
baseline |
2040 |

5 |
36.0 |
37.7 |

10 |
35.1 |
36.7 |

15 |
34.x |
36.1 |

20 |
34.0 |
35.7 |

25 |
33.7 |
35.4 |

30 |
33.3 |
34.9 |

35 |
33.0 |
34.7 |

(thus on average, 10 days per year have daily maximum temperatures at or above 35.1°C, which will have changed to 36.7°C by 2040 - RCP8.5-high, 40-GCM ensemble)

Note that the axes have been reversed from the SimCLIM 4.0 for Desktop output.

#### Probability of magnitude of exceedance over threshold

This is an output that was never fully developed. The text below outlines the thinking behind this type of analysis.

OK: So the other request in the brief was how for the days every year that exceed 35 degrees, how much higher than 35 degrees will the temperature reach.

My idea here was to somehow plot a frequency distribution for the baseline and 2020, 2030 and 2040 for temperatures 35 degrees and above to give a graphical indication of the likelihood of the how far past 35 degrees the max temp would be on average. As temperatures vary every year, this should be enough for the client to make a decision about which HVAC system etc to install on the trams.

Unfortunately I don’t know how to do this in excel. Do you? (even if you just give me the name of the chart type or function I can look up how to use it in office help)

CLIMsystems: If you want to use the perturbed datasets (the same ones as you used for calculating the days over 35 and 42), graphing the sorted (low to high) data (temperature on Y-axis), gives a cumulative distribution function. You could scale the x-axis from 0-100 (as percentage) (or 0-365 as number of days), possibly through creating "dummy" x-values (row/count(x), maybe times 365) (use scatter-plot).

If you want to do this through the extreme event analysis, you would export the tables (right click) to Excel, possibly after first defining a larger default return-period set (under tools, options, graphing) and then create a chart. You could put the return period on the x-axis (possibly as a log-scale), the max temp values on the y-axis (use scatter-plot).

Modelling Assumptions and Limitations

### Limitations of temperature modelling for HVAC systems

OK: It occurred to me that the cooling load on in the carriages could vary significantly depending on whether it is sitting in the shade at 35 degrees or in the sun at 35 degrees. Have you ever factored this in to any analyses you have done before?

CLIMsystems: This requires much more complicated modelling (thermo-physics), and would include all kinds of things like albedo, angle of attack, wind, properties of the surrounding (reflections, absorption, local heating). We would not want to go there!