Exercise 2 - Sourcing rainfall & flow data
Introduction
The previous exercise focused on estimating rainfall and runoff at catchment scales during a single (daily) storm event. This focused on catchment scale rainfall and processes. In this exercise we will learn how to access rain and flow data, and examine the nature of rainfall data and use some simple statistics in Excel to describe these data. This will help you prepare for the Assignment 1A where you will examine at how rainfall may be changing over time, how it varies over space across Western Australia, and how it correlates with flow.
Objective
By the end of this activity, you should:
- Be able to source rainfall and flow data, understand the nature of that data and describe it using simple statistics in Excel.
Getting Rainfall Data
- Start by downloading the daily rainfall data for a chosen BOM site from the Bureau of Meteorology web site. Choose a site of interest in Western Australia. Use the site ID to get the data as below. Download and extract the zipped file to get a CSV file that can be opened in Excel.
Statistical Properties of Rainfall Data
Before moving forward with our analysis lets open the dataset and make sure the site has a suitable period of data.
Now, let’s plot the time series of DAILY rainfall. Clean up the plot as required and add to your activity sheet. Describe the main features of this data set. Consider: what is the most appropriate type of graph for rainfall data (bar, scatter, line)?
Calculate the annual SUM of rainfall. But note, we want to ensure that there are only whole years to calculate the sums or else the incomplete years will be in error (the sum will be artificially low due to missing data). Delete the rows of data for the last partial year (e.g., 2021) and any partial years at the start (the first and last year measured may change depending on the site you selected). To explore each year’s data we will use a PIVOT table. Select the required data across multiple columns (year C to rainfall amount F). Then insert PIVOT table (select “Create a new tab”). Select Year and Rainfall amount as the FIELDS. Drag the Year FIELD into the ROWS box. Left click on the “Sum of Year” in the VALUES box and remove it. Plot the annual sums as a timeseries. You can also select “COUNT” to see how many entries are given for each. Years with more than 10% of days missing (e.g <300 days counted), are unreliable to include in our analysis so see if your station has any incomplete years. Clean up the plot with the sum of rainfall as required and add to your activity sheet. What are the main features of this annual data set? What variability can you see?
Now we have a “clean” dataset, we want to explore some statistics. Use the Data Analysis add-in to calculate descriptive statistics (mean annual rainfall, max annual rainfall, min annual rainfall, Standard deviation of annual rainfall, Skewness) for the whole data (you can install by going to Tools->Add-ins->Analysis ToolPack). Copy the results here and complete Table 4 for your site (and others when they are done). Describe the values you got and what they mean. How “useful” are these statistics for your understanding of the system? What if any assumptions are there about these statistics?
Next, let’s look at the distribution of the rainfall data. Do this by plotting a histogram of the rainfall data (you will need to decide on a reasonable bin size) and plotting the cumulative probability distribution (you can ask Excel to generate this automatically when it makes the histogram, or generate it manually – each data point represents a probability of 1/#data points). What do these plots tell you about the rainfall data? Are the data normally distributed?
Plot the seasonal (monthly average) rainfall. Use a PIVOT table again. Insert PIVOT table (select OK to create a new tab). Select Month and Rainfall amount as the FIELDS; drag the Month FIELD into the ROWS box. Left click on the “Sum of Month” in the VALUES box and remove it. Plot the annual sums as a timeseries. Clean up the plot as required and submit on your answer sheet. How would you describe the seasonal pattern of rainfall (hint look at the climate type)? What factors may influence it (hint, think about earth orbit)?
| Station | Station ID | Years | Mean | SD | Min / Max |
|---|---|---|---|---|---|
| Swanbourne | 9215 | ||||
| Perth | 9225 | ||||
| Perth Airport | 9021 | ||||
| Bickley | 9240 | ||||
| Mundaring | 9030 | ||||
| Chidlow | 9007 | ||||
| Northam | 10111 | ||||
| Kellerberrin | 10073 | ||||
| Merredin | 10092 | ||||
| Kalgoorlie-Boulder | 12038 | ||||
| Leonora | 12241 | ||||
| Cape Leeuwin | 9518 | ||||
| Busselton | 9515 | ||||
| Geraldton Town | 8050 | ||||
| Carnarvon | 6011 | ||||
| Exmouth Gulf | 5004 | ||||
| Broome | 3003 | ||||
| Wyndham | 1006 | ||||
| Bridgetown Comparison | 9510 | ||||
| Wagin | 10647 | ||||
| Hyden | 10568 | ||||
| Albany | 9500 | ||||
| Esperance Downs | 9631 | ||||
| Manjimup | 9573 | ||||
| Narrogin | 10614 |
Part A - Rainfall and streamflow data analysis
In this assessment we will explore the nature of rainfall and runoff data. Rainfall is influenced by a number of processes that operate on different space and time scales (see Figure 5). We first examine these during this exercise and then we explore how different modes of climate variability affect patterns in annual rainfall. Lastly, we look to see if we can find a relationship between rainfall and streamflow (assumed equal to runoff). To achieve this, we use a large number of weather stations across WA to quantify the variability of rainfall in space and time.
In this assignment you will work to explore data from an individual site. You will then share with class members the results from your site so we can build a more complete picture. We will be sharing our data using an online spreadsheet. Please make sure that you upload your data as soon as possible so that others can include it in their analysis.
.](images/assessment2A/image1.png)
Figure 5: A guide to the timescales applicable to weather, climate variability and climate change Pacific Climate Futures.
Objectives
By the end of this assignment, you should:
- Understand how and why rainfall may be changing over time and use statistics and regression to test this hypothesis.
- Know how different modes of climate variability such as IOD and ENSO can affect annual rainfall.
- Be able to elucidate the nature of the relationship between rainfall and streamflow.
Temporal trends in rainfall
Prior to starting this work, make sure you have completed the Exercise 2 activity.
For your chosen site, calculate the trend in rainfall for the last 5 years. Either copy and paste the annual totals from the PIVOT table (include the year and amount columns) or calculate the manually. Select the last 5 years of data and in DATA ANALYSIS start a REGRESSION. Input the data range for x (the independant variable) and y (the dependant variable). Select “Line Fit Plots”. What did you find and what were you expecting? Is this long enough for a reliable trend? Is the relationship really linear – discuss? (You can do this same analysis by adding a trend-line to the data, as described in 2. below).
Now, calculate the trend in rainfall for all years available at the site. You can calculate that annual total rainfall using a PIVOT table (include the year and amount columns) or by calculating them manually using SUM. Select the all years of data and INSERT a SCATTER plot. Add a linear trend line and “display the equation” on the chart. The slope of the equation of the line tells you the trend. Add the Pearson correlation coefficient (r2) value as well to see how well the line fits the data (1 is a perfect fit, 0 is no fit). Add the information for your site into Table 5 and the online spreadsheet).
| Station | Station ID | Years of data | Sign of trend | Trend rate (mm/decade) | T-value | Significance (p value) |
|---|---|---|---|---|---|---|
| Swanbourne | 9215 | |||||
| Perth | 9225 | |||||
| Perth Airport | 9021 | |||||
| Bickley | 9240 | |||||
| Mundaring | 9030 | |||||
| Chidlow | 9007 | |||||
| Northam | 10111 | |||||
| Kellerberrin | 10073 | |||||
| Merredin | 10092 | |||||
| Kalgoorlie-Boulder | 12038 | |||||
| Leonora | 12241 | |||||
| Cape Leeuwin | 9518 | |||||
| Busselton | 9515 | |||||
| Geraldton Town | 8050 | |||||
| Carnarvon | 6011 | |||||
| Exmouth Gulf | 5004 | |||||
| Broome | 3003 | |||||
| Wyndham | 1006 | |||||
| Bridgetown Comparison | 9510 | |||||
| Wagin | 10647 | |||||
| Hyden | 10568 | |||||
| Albany | 9500 | |||||
| Esperance Downs | 9631 | |||||
| Manjimup | 9573 | |||||
| Narrogin | 10614 |
Looking at the plot of rainfall over time at your site, what hypothesis can we make about changes in rainfall amount over time? Using the full temporal dataset (all years), perform a REGRESSION analysis like you did in the first question. These results will inclue a t-statistic (t Stat) and P-value, enter them also into Table 5. The null hypothesis is the the rainfall did NOT change over time. If the P-value is smaller than alpha = 0.05 then we can REJECT the null hypothesis (which means that the rainfall amount has changed significantly over time). You can also reject the null hypothesis if the t-statistic is less than -2.101 or greater than 2.101 (based on a normal distribution). Describe the results and conclusions of this analysis.
Inspect the results of everyone’s analysis for Table 5 Google Sheets version. Which station(s) have a statistically significant slope. Are there statistically significant changes in rainfall? Are they consistent across WA? What may be causing the changes?
Spatial patterns in rainfall
- Take the information in Table 5 (Google Sheets version) and record the values onto a map of Western Australia. Now think about the spatial patterns rather than the temporal ones (i.e climate modes). What spatial patterns might you expect and what do you notice? What may be causing these spatial patterns?
Interannual variability in rainfall
Here we determine how rainfall correlates with known modes of climate variability (i.e. Indian Ocean Dipole (IOD) and El Nino Southern Oscillation (ENSO).
Other indicators of temporal variability (look for cyclic patterns). Does rainfall correlate with known modes of climate variability (i.e. IOD and ENSO using the Southern Oscillation Index (SOI). SOI is calculated as follows.
where:
- \(P_{\text{diff}}\) = (average Tahiti MSLP for the month) - (average Darwin MSLP for the month)
- \(P_{\text{diffav}}\) = long term average of \(P_{\text{diff}}\) for the month in question, and
- \(SD(P_{\text{diff}})\) = long term standard deciation of \(P_{\text{diff}}\) for the month in question.
IOD is calculated by anomalous Sea Surface Temperature gradient between the western equatorial Indian Ocean (50E-70E and 10S-10N) and the south eastern equatorial Indian Ocean (90E-110E and 10S-0N) in units of degrees Kelvin.
We will use the extremely useful Climate Explorer for the next section. First you will need to register so you can save data series. Access the rainfall from the previous site that you used in the previous section. Click on “Monthly Station Data” (right hand menu), select “precipitation” from the “GHCN-M (all)” column, search for your station (e.g. type BROOME in the “Select stations” section), and then press “Get stations”. If the selection works you will see relevant stations listed, and then click “get data”. You will then see graphs and options for further integrating the data. Make a name to save the data (the default should be fine). Click “Add to list”.
Now get the first climate index for the IOD called the DMI. Go to “Monthly climate indices” and then select DMI. Note any trend and variability in the index.
To correlate the index and rainfall select “Correlate with other time series”. And tick your previously saved rainfall timeseries and then press “Correlate” and copy the results into Table 6 and the appropriate tab in the online spreadsheet.
| Month | DMI Corr | DMI p-value | SOI Corr | SOI p-value |
|---|---|---|---|---|
| Jan | ||||
| Feb | ||||
| Mar | ||||
| Apr | ||||
| May | ||||
| Jun | ||||
| Jul | ||||
| Aug | ||||
| Sep | ||||
| Oct | ||||
| Nov | ||||
| Dec |
- Highlight any months that have a significant p-value (<0.05). What relationships do you see between rainfall and climate mode and why? Do they correlate in specific seasons? How strong are these correlations really? How are they consistent or different across WA?
We can do the same exercise except using gridded data (climate data divided into say 0.5 degree spacing using reanalysis information) to investigate the whole of Australia. Click on “Monthly observations” and go to Precipitation CRU TS 0.5.
We then want to correlate each grid cell on the earth with our climate index (SOI and DMI) to see how the correlations very spatially. Click on “Correlate with a time series” and choose either SOI or DMI. Then click correlate at the bottom and wait (the calculations are being done online and the graph returned for viewing). Do the same for both SOI and DMI.
- For DMI which month had the highest (negative) correlation (copy that plot to your results). What areas of Australia have significant correlations and what time of year? For SOI which month had the highest (positive) correlation (copy that plot to your results). What areas of Australia have significant correlations and what time of year? Does this match with your own rainfall station correlations?