Question

The average temperatures (°F) for an 8-day period are: 32,35,34,36,48,43,42, and 40. If the area has an initial SWE of 2.46 in, K=0.06in/deg-day, and a runoff coefficient of CR = 0.5, plot the estimated daily runoff (in) from the watershed and determine the total melt and runoff for the 8-day period.

Answer 1

The given problem is concerned with the calculation of run-off resulting from the melting of snow.

The Initial SWE (Snow Water Equivalent) = 2.46 in (given)

NOTE: The initial snow i.e. 2.46 in is the only snow available for melting. This is because there is no mention of the generation of further snow. Hence, our total estimated melt will be limited to initial SWE.

Here, K = melt rate coefficient = 0.06 inch per degree per day

The estimated melt is calculated as follows:

M = Estimated Melt = K(T-32)        …………………………………………                   (1)

                                    =0.06*(T-32)

The available SWE = previous day’s SWE – preceding day’s melt

The available SWE is the remaining SWE that is left after a portion of snow melts. The available SWE is limited to initial SWE of 2.46 inch.

Estimated Run-off = C_RM      ……………………………………………                        (2)

C_R=0.5 , runoff coefficient,

The table below shows the values of each day.

Day	Average Watershed Temperature(0F) T	Degree-Days (T-32)	Total Available SWE (in)	Estimated Melt (in) M	Estimated Runoff (in) CRM
1	32	0	2.46	0	0
2	35	3	2.46	0.18	0.09
3	34	2	2.28	0.12	0.06
4	36	4	2.16	0.24	0.12
5	48	16	1.92	0.96	0.48
6	43	11	0.96	0.66	0.33
7	42	10	0.30	0.30	0.15
8	40	8	0	0	0
Total				2.46	1.23

Calculations:

Day 1:

Degree Days = (T-32) = (32-32) = 0

Total Available SWE = Previous Day SWE – Preceding Day Estimated Melt

                                     = 2.46 – 0 = 2.46 in

Estimated Melt = M = 0.06 * (T-32) = 0.06 * 0 = 0 in                                       (As per Equation 1)

Estimated Runoff = C_RM=0.5*0 = 0 in                                                                 (As per Equation 2)

Day 2:

Degree Days = (T-32) = (35-32) = 3

Total Available SWE = Previous Day SWE – Preceding Day Estimated Melt

                                     = 2.46 – 0 = 2.46 in

Estimated Melt = M = 0.06 * (T-32) = 0.06 * 3 = 0.18 in                                   (As per Equation 1)

Estimated Runoff = C_RM=0.5*0.18 = 0.09 in                                                       (As per Equation 2)

Day 3:

Degree Days = (T-32) = (34-32) = 2

Total Available SWE = Previous Day SWE – Preceding Day Estimated Melt

                                     = 2.46 – 0.18= 2.28 in

Estimated Melt = M = 0.06 * (T-32) = 0.06 * 2 = 0.12 in                                 (As per Equation 1)

Estimated Runoff = C_RM=0.5*0.12 = 0.06 in                                                      (As per Equation 2)

Day 4:

Degree Days = (T-32) = (36-32) = 4

Total Available SWE = Previous Day SWE – Preceding Day Estimated Melt

                                     = 2.28 – 0.12 = 2.16 in

Estimated Melt = M = 0.06 * (T-32) = 0.06 * 4 = 0.24 in                                 (As per Equation 1)

Estimated Runoff = C_RM=0.5*0.24 = 0.12 in                                                     (As per Equation 2)

Day 5:

Degree Days = (T-32) = (48-32) = 16

Total Available SWE = Previous Day SWE – Preceding Day Estimated Melt

                                     = 2.16 – 0.24 = 1.92 in

Estimated Melt = M = 0.06 * (T-32) = 0.06 * 16 = 0.96 in                                 (As per Equation 1)

Estimated Runoff = C_RM=0.5*0.96 = 0.48 in                                                         (As per Equation 2)

Day 6:

Degree Days = (T-32) = (43-32) = 11

Total Available SWE = Previous Day SWE – Preceding Day Estimated Melt

                                     = 1.92 – 0.96 = 0.96 in

Estimated Melt = M = 0.06 * (T-32) = 0.06 * 11 = 0.66 in                                 (As per Equation 1)

Estimated Runoff = C_RM=0.5*0.66 = 0.33 in                                                         (As per Equation 2)

Day 7:

Degree Days = (T-32) = (42-32) =1 0

Total Available SWE = Previous Day SWE – Preceding Day Estimated Melt

                                     = 0.96 – 0.66 = 0.30 in

Estimated Melt = M = 0.06 * (T-32) = 0.06 * 10 = 0.6 in                                        (As per Equation 1)

However, the amount of snow, SWE left is 0.30 in which is less than 0.60 in

Hence, Estimated Melt =M = 0.30 in (whatever snow is left will go into runoff)

Estimated Runoff = C_RM=0.5*0.30 = 0.15 in                                                         (As per Equation 2)

Day 8:

Degree Days = (T-32) = (40-32) = 8

Total Available SWE = Previous Day SWE – Preceding Day Estimated Melt

                                     = 0.30 – 0.30 = 0 in

Estimated Melt = M = 0, As, now SWE is available for further melting.

Estimated Runoff = 0

Total Melt = 2.46 in (Adding Melt of all days)

Total Runoff = 1.23 in (Adding runoff of all days)

Shown below is the plot of the Estimated Run-Off of the watershed