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Converting rainfall timeseries in mm(depth) to mm/day (?)

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  • Converting rainfall timeseries in mm(depth) to mm/day (?)

    I need to convert a rainfall timeseries in 10 minute intervals from mm (depth) to mm/day.

    (a) I understand the measurement logic for depth in mm; as represented in mm/10 min intervals and in mm per day interval. What does the unit 'mm/day' in 10 minute intervals represent. Rate? Accumulation? Why use mm/day in 10 min intervals when depth (mm) seems more straightforward?

    (b) What is the formula or algebra to convert a rainfall timeseries between mm (depth) and mm/day (??) in 10 min intervals.

    Thanks for any help.

    I have a mental block from using mm/day as one depth value for the whole day and cannot understand the logic of the unit mm/day in 10 min time intervals. So cannot comprehend the the conversion logic.

  • #2
    Originally posted by rary2013 View Post
    I need to convert a rainfall timeseries in 10 minute intervals from mm (depth) to mm/day.

    (a) I understand the measurement logic for depth in mm; as represented in mm/10 min intervals and in mm per day interval. What does the unit 'mm/day' in 10 minute intervals represent. Rate? Accumulation? Why use mm/day in 10 min intervals when depth (mm) seems more straightforward?

    (b) What is the formula or algebra to convert a rainfall timeseries between mm (depth) and mm/day (??) in 10 min intervals.

    Thanks for any help.

    I have a mental block from using mm/day as one depth value for the whole day and cannot understand the logic of the unit mm/day in 10 min time intervals. So cannot comprehend the the conversion logic.
    A 10 min interval is 1/6 of an hour or 1/144 day. The rain does not fall evenly, continuously. If you have the 144 element time series for the day, simply sum them to get the total for the day.

    If you are missing any data, and feel the rainfall was relatively even through the missing periods, you might interpolate, but it invites error. The most straightforward procedure is to sum the data

    Comment


    • #3
      Thanks for replying John.

      Yes, you are correct: mm per day is simply the sum of all 144 values for the unit mm per 10 minutes.

      This provides me with the daily rainfall depth derived from 10 minute rainfall intervals.


      However I am looking to convert to a different rainfall unit: "mm per day per 10 minutes" ("mm/day/10min" ??)

      Is this called rainfall rate? or something else?


      Comment


      • #4
        From what I have read online, it seems that the unit is rainfall intensity:

        "Rainfall intensity is defined as the ratio of the total amount of rain (rainfall depth) falling during a given period to the duration of the period.
        It is expressed in depth units per unit time, usually as mm per hour (mm/h)."
        source: FAO, http://www.fao.org/3/r4082e/r4082e05.htm

        Does anyone have an excel formula to convert between rainfall depth (mm) in sub-hourly intervals to rainfall intensity (mm/day) in sub-hourly intervals?

        Comment


        • #5
          Let's assume it rains 1 mm in 10 minutes. That is a date of 0.1 mm per minute (0.1 mm/min). Multiply by 1440 min/day and you get 144 mm/day. This only has real meaning if the rain rate stays constant, but that is the unit conversion.

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          • #6
            Hi John

            I have attached an example time series for three days.
            I have several years of rainfall data to convert from depth to rainfall intensity.
            The rain events are intermittent and not constant.

            Is there a formula to use in such intermittent rainfall cases to convert from depth to intensity?

            Thanks for looking,
            Tim

            Comment


            • #7
              It seems that attaching files doesn't work.

              I created a table below; there is no rainfall after 02:50 AM in the morning.
              The days are Julian days.

              I am assuming that the rainfall intensity column should sum to total mm for the day. That is, it should equal the total amount of rain per day - 7.6 mm.

              Over 365 or 366 days, the formula has to recognise each daily total and calculate accordingly.
              year month day hour minute
              rain depth (mm)
              rain intensity (mm/day)
              2013 5 128 1 0 0
              2013 5 128 1 10 0.4
              2013 5 128 1 20 0.1
              2013 5 128 1 30 0
              2013 5 128 1 40 0.3
              2013 5 128 1 50 1.8
              2013 5 128 2 0 1
              2013 5 128 2 10 0.8
              2013 5 128 2 20 1.3
              2013 5 128 2 30 1.4
              2013 5 128 2 40 0.4
              2013 5 128 2 50 0.1
              2013 5 128 3 0 0
              2013 5 128 3 10 0
              2013 5 128 3 20 0

              Comment


              • #8
                Originally posted by rary2013 View Post
                It seems that attaching files doesn't work.

                I created a table below; there is no rainfall after 02:50 AM in the morning.
                The days are Julian days.

                I am assuming that the rainfall intensity column should sum to total mm for the day. That is, it should equal the total amount of rain per day - 7.6 mm.

                Over 365 or 366 days, the formula has to recognise each daily total and calculate accordingly.
                year month day hour minute
                rain depth (mm)
                rain intensity (mm/day)
                2013 5 128 1 0 0
                2013 5 128 1 10 0.4
                2013 5 128 1 20 0.1
                2013 5 128 1 30 0
                2013 5 128 1 40 0.3
                2013 5 128 1 50 1.8
                2013 5 128 2 0 1
                2013 5 128 2 10 0.8
                2013 5 128 2 20 1.3
                2013 5 128 2 30 1.4
                2013 5 128 2 40 0.4
                2013 5 128 2 50 0.1
                2013 5 128 3 0 0
                2013 5 128 3 10 0
                2013 5 128 3 20 0
                I'm still confused on whether you want instantaneous or average rainfall intensity. Zero is zero, but in the first 10 minute period, 0.4 mm/10 min = 0.04 mm/min = 57.6 mm/day, but only for that period. For the 3rd period, 0.1 mm/10 min = 0.01 mm/min = 14.4 mm/day, but again only for those 10 minutes. None of the ten minute periods will have much relation to the average intensity for the whole day.

                However, for average, you have to sum the 144 ten minute periods, getting 7.6 mm, then dividing by the day, 7.6 mm/day. That will also depend on how you define your day markers, probably midnight to midnight.

                Either seems like a potentially valid approach. It depends on what you are trying to do.

                Comment


                • #9
                  Hi John and thanks for the clarification to distinguish between each 10 minute period (instantaneous intensity) and the average intensity for the whole day.

                  The purpose is to input the mm/day time series into an hydrological application that calculates surface runoff, water balance etc.
                  Unlike most other hydrological software, the precipitation time series unit must be mm/day and not mm. And it needed to be in sub-hourly time intervals.

                  My conversion formula for each cell was [depth, mm * (10/1440)] to convert from mm to mm/day for the whole day time series in 10 min intervals.

                  The reverse [intensity, mm/day / (10/1440)] to convert from mm/day to mm

                  The disruption to my thought pattern had been relating mm/day (depth) = 7.6 mm per day, to the need for mm/day (intensity) over 144 time intervals.

                  Comment


                  • #10
                    Originally posted by rary2013 View Post
                    Hi John and thanks for the clarification to distinguish between each 10 minute period (instantaneous intensity) and the average intensity for the whole day.

                    The purpose is to input the mm/day time series into an hydrological application that calculates surface runoff, water balance etc.
                    Unlike most other hydrological software, the precipitation time series unit must be mm/day and not mm. And it needed to be in sub-hourly time intervals.

                    My conversion formula for each cell was [depth, mm * (10/1440)] to convert from mm to mm/day for the whole day time series in 10 min intervals.

                    The reverse [intensity, mm/day / (10/1440)] to convert from mm/day to mm

                    The disruption to my thought pattern had been relating mm/day (depth) = 7.6 mm per day, to the need for mm/day (intensity) over 144 time intervals.
                    Note that your conversion is upside down. I recommend always keeping units attached so you can verify unit cancellation
                    (0.1 mm/10 min) (1440 min/day) = 14.4 mm/day. The" keeping units attached" is on paper or in your mind. Unfortunately, to Excel, it is all just numbers. But it is key to avoiding mistakes in formulas.

                    Also intuitively, if it rained at constant rate, there has to be more rain in a day than in 10 minutes, so you have to be multiplying by a number greater than one, not dividing by it.

                    Comment


                    • #11
                      Thanks John, keeping the units attached is good practice.

                      Just to clarify the algebra for the example cell in the spreadsheet:

                      Converting from depth, mm to averaged daily intensity, mm/day = (0.1 mm * 10) / 1440 min/day) = 0.000694 mm/day
                      Converting from mm/day to mm = (0.000694 mm/day / 10min) * (1440 min/day) = 0.1 mm

                      .

                      Comment


                      • #12
                        Originally posted by rary2013 View Post
                        Thanks John, keeping the units attached is good practice.

                        Just to clarify the algebra for the example cell in the spreadsheet:

                        Converting from depth, mm to averaged daily intensity, mm/day = (0.1 mm * 10) / 1440 min/day) = 0.000694 mm/day
                        Converting from mm/day to mm = (0.000694 mm/day / 10min) * (1440 min/day) = 0.1 mm

                        .
                        I'm sorry but that conversion is upside down. If it rains 0.1 in 10 minute,then at a steady rate, there are 6 ten-minute periods in an hour so 0.6 mm/h and 24 h in a day so 14.4 mm/day.
                        There has to be more rain in a day than in 10 minutes of that day (at steady rate). The correct formula is (0.1 mm/10 min)*1440 min/day = 14.4 mm/day

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