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Help Of SD GCM
Statistical Downscaling General Circulation Models

Statistical downscaling methods which used in SD GCM V1.0 Tool

There are three methods of statistical downscaling in SD GCM tool, namely Delta method, QM (Quantile Mapping) method, and EQM (Empirical Quantile Mapping) method. All of them are explained in the following:

Delta statistical downscaling method (Dessu and Melesse, 2013):

As presented in Eq. 1 and Eq. 2 the precipitation and temperature of GCM data are downscaled

Statistical downscaling- Delta

where, P(SD,Delta) and T(SD,Delta) are downscaled data of precipitation and temperature, respectively. P(Obs) refers the average observed and P(GCMhist) represents to GCM mean simulation historical data of precipitation. Subscript GCMrcp represents the GCM's RCP outputs over the future period and subscript Obs represents the observation values. In Eq. 2 all the subscripts are the same as Eq. 1 for temperature.

Quantile Mapping (QM) statistical downscaling method

As Panofsky and Brier (1968) revealed, QM is a statistical downscaling method that has been used in different field of studies. In the equation of QM, the modelled probabilistic distribution to observed probabilistic distribution is calculated. This concept is computed as Eq. 3 for precipitation data. SD GCM uses Eq 3-1 for evaluation and Eq 3-2 for future downscaling.

Statistical downscaling- QM

In the presented equation (Eq. 3), CDF is the cumulative distribution function of the observation and GCM data, over considering period.

Empirical Quantile Mapping (EQM) statistical downscaling method

Wetterhall and his colleagues (2012), have published a complete paper for statistical downscaling methods, as EQM. The EQM employs the empirical cumulative distribution function (ECDF) as Eq. 4, and all the items are the same as Eq.1. SD GCM uses Eq 4-1 for evaluation and Eq 4-2 for future downscaling.

Statistical downscaling- EQM

Statistical downscaling- main

Fig. 1 Three statistical downscaling method in SD GCM tool

How can we run SD GCM V1.0 Tool?

The main screen of SD GCM tool (Statistical Downscaling GCM) is presented in Fig. 2. In this screen, we have 4 tabs, namely “Input Data”, “Evaluation”, “Downscale”, and “Registration”.

Statistical downscaling- main

Fig. 2 The main screen of SD GCM tool, with 4 tabs

Step 1. Input Station and GCM Data

In this step, three kinds of data would be loaded, namely observation data, GCM historical data, and Prediction GCM data under RCPs scenarios. First of all, in the “Delimiter“ icon, if the input data file would be a text or csv file, then the user should write the used delimiter on that file, in the blank space, as Fig. 3 No. 1. If the input file is an excel file, the user don’t need to write delimiter. Then by clicking on the “Browse File” (Fig. 3 No. 2), the user can select the weather data of selected station. In the open window, the user browses and selects the aimed file (observation data/in-situ). As Fig. 3 No. 3, finally the user clicks on the Open button. The station data should be in daily scale.

Statistical downscaling-observation

Fig. 3 Select and browse station (observation) data file

When the input file was selected, then the user needs to set some of attributes of the station data. As you see the Fig. 4 No. 1, in this phase the user needs to select the aimed sheet. By selecting the desirable input sheet, then the user should write the “Station Name” (Fig. 4 No. 2), “Latitude” (Fig. 4 No. 3), “Unit” (Fig. 4 No. 4), and “Longitude” (Fig. 4 No. 5), as following.

Statistical downscaling-excel sheet

Fig. 4 Select the desirable sheet, type the station name and other characteristics

If the input data file has header in the first row, so the user should check the “First row is header” check box (Fig. 5 No.1), if not, don’t check it. For the type of the input data’s time, the user needs to determine it, as the Fig. 5 No. 2.

Statistical downscaling-Date format

Fig. 5 Consider the header of input file (No. 1) and Select the format of date (No. 2)

About the input data, in this phase, we need to assign the type of data, the user can assign all the kind of input columns or just select the date and for example precipitation. In this sample, here, we select the “Date” as the first column (Fig. 6), and the precipitation (rain) as the fourth column (Fig. 7 No. 1). Finally, in this step the user can would select the “Load Data” button (Fig. 7 No. 2).

Statistical downscaling-column

Fig. 6 Select the content of each column

Statistical downscaling-load data

Fig. 7 Select the input variable, and finally click the load data button

When the data (input station file) was loaded, then the user can see a message box with content of “Data Loaded”, click the OK button (Fig. 8 No. 1), and then we can go to the rightest box with header of “GCMs” (Fig. 8 No. 2). In Fig. 9.1 No. 1, the user can type the name of selected variable, such as “pr” as precipitation in this sample. If you write a wrong name or make a mistake in typing the word in this field, you would face to error. So, be careful for typing the name in the blank field of Fig. 8 No. 2. Usually, in CMIP5 data models the precipitation is written as ‘pr’, and temperature as ‘tas’. As well, the CMIP5 models should be in daily time scale and nc format file (NetCDF).

Statistical downscaling-gcms

Fig. 8 Click on the message box, and the GCMs column in the right hand of the figure

Statistical downscaling- gcm

Fig. 9.1. Type the selected variable of the GCMs file

When the user wants to browse the selected model of the GCM’s files by clicking on the “Browse All Files” button (Fig. 9.2 No. 1), he/she can do it. But, in this step, the user should consider an important tip. As you see in the presented example in Fig. 9.2 No. 2, when you load the data, the period is historical data, then you load all the data of it, you should load RCP data. Since the historical data were loaded, so in RCP data you face with a message that asked you about overwrite the years or no? For better clarification, see the example of Fig. 9.2 No. 2. The historical file of MIROC5 and the RCP45 of MIROC5 have a common period, which is the period of 2006 up to 2009 - in the separate files -, as well you see the 2010 up to 2012 (three years) are same with historical data. So, the simplest way is unselect the common year in RCP data (2006-2009) as Fig. 9.2 No. 2, and for the rest of common years, we can ignore the message that it mentions “Do you want overwrite?” (Fig. 9.3), so we should select “No”. Overall, it is depend on your selected CMIP5 model, and the common base of data, and it would be changed with different models.

Statistical downscaling- cmip5

Fig. 9.2. Browse the desirable CMIP5 model during historical and RCPs projections

Statistical downscaling- cmip5

Fig. 9.3. Click on the No button to ignore overwrite the common year

- Step 2. Evaluation Of Statistical Downscaling Methods

The second main tab in the Statistical Downscaling GCM (SD GCM) tool is “Evaluation” tab. In this tab we can assess the performance of statistical downscaling methods during the common period. According to the Fig. 10 No.1, in the “Evaluation Downscaling” panel, we should set three different periods of time, namely “Station Period”, “Historical Period”, and “Predicted Period”. Be careful to filling the times and selecting the proper year from the combo box. In Fig. 10 No.2, you can see them. For the “Station Period”, it is exactly the first file of the case study station that you have browsed it in the “Input Data” tab, and the start and end time of it, are equal to the observation time. In this sample, start time of the station data is started 1979 and the end is equal to 2017. For the “Historical Period”, it refers to historical GCM data. As we know the start and the end of this data are depend on the used model of GCM. For example some of the models have a period of 1950-2010, or 1950-2012, or may be another one. So, in SD GCM you can select a common base according to the same period of station and historical data. In this sample, we have selected the 2012 as the end year for the evaluation period, see Fig. 10 No. 2 and Fig. 11. As well, for the “Predicted Period” (Fig. 12 No.1), we have selected 2012 for the end year in the predicted period. In the panel of “Downscaling Method”, as you can see there are 4 methods of statistical downscaling that three of them are active, and the user can apply them, namely Delta, QM, and EQM methods. The equations and all of the details for these methods are presented in the “Overview” file. For the first example as you see in Fig. 12 No. 2, the Delta method is selected for statistical downscaling method. When the periods and the statistical downscaling method is selected, then by clicking “Downscale” button, the statistical method would performed on the data, during selected period by user (Fig. 12 No. 3).

Statistical downscaling- evaluate

Fig. 10 The Evaluation tab and other panels it

Statistical downscaling- evaluate

Fig. 11 The downscaling period for evaluation process

Statistical downscaling- evaluate

Fig. 12 Set the predicted period foe evaluation process

When the data was downscaled correctly you can see a message box, as Fig. 13 No. 3, by clicking the OK message, then your data were downscaled. If you clicking on the “View Data”, you can see your evaluation data and save them as an excel file. In Fig. 14 No. 1, by clicking on the “Send for Compare” button, you can observe the result of efficiency criteria’s. In the “Comparison of Evaluations” panel (Fig. 14 No. 2), the user can achieve 5 methods of efficiency criteria’s, between observation and historical data for knowing that does GCM model has generated proper data in compare to observation data? By considering the result of efficiency criteria’s, the user can make a decision.

Statistical downscaling- evaluate

Fig. 13 When the data were downscaled correctly you can see the message box

Statistical downscaling- compare

Fig. 14 The data send for comparing during evaluation period

In Fig. 15 No. 1, the user can see the whole period of common base for evaluation process in the top of efficiency criteria table. In Fig. 15 No. 2, the user can check on the box which is asked about plotting the observation period on the table or no. There is a legend box on the graph (Fig. 15 No. 3), which is represent the used signs for Delta (historical period) and observation data as Obs.

Statistical downscaling- gcm

Fig. 15 Draw the Obs vs. GCM downscaled data during common base

3. Statistical Downscaling Tab

In the third step, the user can start downscaling method for future data under selected RCPs scenarios. In this phase, similar to the evaluation step, the user needs to assign three periods of time, namely station, historical and predicted data. According to the Fig. 16 and Fig. 17 No. 1, the user can select the desired year manually, for downscaling future data. As Fig. 17 No. 2 shows, the user can select one of the statistical downscaling method in this panel. Since, in the evaluation period, the Delta method was selected, so it is reasonable to select Delta method in this step.

Statistical downscaling

Fig. 16 The Downscale tab and statistical downscaling over future period

Statistical downscaling

Fig. 17 Selecting the prediction data under selected RCP scenarios

By clicking the “Downscale” button (Fig. 17 No. 1), the user faces to a message box (Fig. 18 No. 2), which is showed downscaling process was done. In the “Future plot” panel, by checking the “Plot Observation Data” box (Fig. 19), the user can observe the time series of observation data in the graph. The graph which is located in the bellow of Fig. 19, is the final graph of the future data. Fig. 20 shows the results of EQM statistical downscaling method.

Statistical downscaling- future

Fig. 18 Downscaling future data and plot the future data

Statistical downscaling- precipitation

Fig. 19 Plot the precipitation values during 1980-2059

Statistical downscaling- eqm

Fig. 20 Select EQM statistical downscaling method

Pay Attention Please:

1- The SD GCM version 1.0 tool cannot downscale all the CMIP5 models, such as HadGEM, since this model was developed according to calendar with the 360-days, if a customer wants to use such models, he/she can make a request to Agrimetsoft, and then Agrimetsoft can do it for him/her.

2- All the input files for GCM models should be in daily scale, as well the station data of the case study has daily scale.

3- The format of CMIP5 models are in nc (NetCDF) format file.