1 00:00:06,250 --> 00:00:11,340 Welcome! My name is Hubert Savenije and I am a hydrologist. 2 00:00:11,340 --> 00:00:15,910 In this Module we'll discuss the runoff generating mechanisms 3 00:00:15,910 --> 00:00:20,710 Maybe the most predictable part of a hydrograph is the recession curve 4 00:00:20,710 --> 00:00:27,240 which represents the slow groundwater depletion during the base flow of a river 5 00:00:27,240 --> 00:00:34,210 The recession flow obeys the water balance of the renewable (deep blue) groundwater 6 00:00:34,210 --> 00:00:39,510 In the dry season the deep blue groundwater has no recharge and in the river there is 7 00:00:39,510 --> 00:00:41,590 no surface runoff. 8 00:00:41,590 --> 00:00:46,930 So the catchment discharge consists of groundwater and the active storage is the groundwater 9 00:00:46,930 --> 00:00:49,489 storage 10 00:00:49,489 --> 00:00:54,329 It is the water balance of the dark blue box 11 00:00:54,329 --> 00:00:58,649 This results in a very simple water balance for dry weather 12 00:00:58,649 --> 00:01:04,100 On top of that , we may assume that the groundwater discharge is directly proportional to the 13 00:01:04,100 --> 00:01:06,649 storage 14 00:01:06,649 --> 00:01:13,590 The proportionality coefficient k represents the average residence time of the water in 15 00:01:13,590 --> 00:01:15,920 the groundwater reservoir 16 00:01:15,920 --> 00:01:21,450 Mathematically , it can be easily shown that the solution of these two equations is an 17 00:01:21,450 --> 00:01:22,630 exponential function 18 00:01:22,630 --> 00:01:28,100 (please see the example and do it yourself) 19 00:01:28,100 --> 00:01:32,900 One can easily recognise the residence time k from the graph, 20 00:01:32,900 --> 00:01:39,900 because it is the time where the tangent to the curve hits the time axis 21 00:01:40,040 --> 00:01:42,720 Here you see this illustrated. 22 00:01:47,140 --> 00:01:51,460 The exponential function has special properties: 23 00:01:51,460 --> 00:01:58,259 the time derivative of Q is –Q/k 24 00:01:58,259 --> 00:02:05,259 and the integral of Q (being the remaining groundwater storage) is k*Q 25 00:02:05,689 --> 00:02:08,479 Check it yourself! 26 00:02:08,479 --> 00:02:13,480 Now let's discuss the flood generating mechanisms 27 00:02:13,480 --> 00:02:18,819 When we want to determine the runoff as a result of a large precipitation event, 28 00:02:18,819 --> 00:02:25,819 we only should consider that part of the rain which contributed to runoff: 29 00:02:26,230 --> 00:02:29,260 the effective precipitation Pa. 30 00:02:30,280 --> 00:02:37,280 We thus have to subtract that part of the precipitation that replenishes the soil moisture 31 00:02:37,290 --> 00:02:43,230 or that fills stagnant pools, later to be evaporated. 32 00:02:43,230 --> 00:02:50,230 The evaporation itself during a large precipitation events we may neglect. 33 00:02:50,739 --> 00:02:57,629 So how do we subtract this increase of temporary storage from the precipitation? 34 00:02:57,629 --> 00:03:00,430 There are different methods. 35 00:03:00,430 --> 00:03:05,050 Some subtract a certain percentage 36 00:03:05,050 --> 00:03:09,480 Some subtract a fixed threshold 37 00:03:09,480 --> 00:03:17,080 Some distinguish between a short term buffer (pool formation) and a longer term threshold 38 00:03:17,080 --> 00:03:20,379 (soil moisture storage) 39 00:03:20,379 --> 00:03:27,379 And others assume a sort of maximum infiltration capacity. 40 00:03:27,739 --> 00:03:33,780 We generally take the fixed threshold for its simplicity. 41 00:03:33,780 --> 00:03:39,569 We saw that groundwater depletion can be simulated as a linear reservoir. 42 00:03:39,569 --> 00:03:49,180 If groundwater is dominant in a catchment, we could simulate both the fill and the depletion 43 00:03:49,180 --> 00:03:51,500 by a linear reservoir 44 00:03:51,500 --> 00:03:54,310 We call that the storage principle. 45 00:03:54,310 --> 00:04:01,310 The solution is an exponential function with a fixed time scale k 46 00:04:02,000 --> 00:04:08,870 For every time increment, we can apply this principle, whereby the runoff tends exponentially 47 00:04:08,870 --> 00:04:12,360 to the effective precipitation Pa, 48 00:04:12,360 --> 00:04:17,470 starting from the discharge in the previous time step 49 00:04:17,470 --> 00:04:19,549 We can do this analytically, 50 00:04:19,549 --> 00:04:22,600 but also numerically 51 00:04:22,600 --> 00:04:29,600 The numerical approach can be easily done in a spreadsheet (please look at the example) 52 00:04:29,660 --> 00:04:35,050 The numerical solution is that the discharge Q2 at the next time step 53 00:04:35,050 --> 00:04:41,470 is a function of the effective precipitation and the discharge in the previous time step. 54 00:04:41,470 --> 00:04:48,190 The coefficients depend on both the time scale and the time step. 55 00:04:48,190 --> 00:04:53,530 It is easy to see that the sum of the two coefficients is one. 56 00:04:53,530 --> 00:04:56,820 Why is that? 57 00:04:56,820 --> 00:05:03,820 Here is what the result look like for different values of k 58 00:05:06,440 --> 00:05:11,860 If a catchment is not groundwater dominated, but rather dominated by fast runoff 59 00:05:11,860 --> 00:05:18,860 (for instance a paved area, or relatively impervious area, or a hillslope with underlying 60 00:05:18,970 --> 00:05:20,690 impervious hard rock) 61 00:05:20,690 --> 00:05:25,650 then the runtime principle can be very useful. 62 00:05:25,650 --> 00:05:28,650 This approach is also called the Rational method, 63 00:05:28,650 --> 00:05:35,330 whereby the runoff is proportional to the surface area contributing to the runoff. 64 00:05:35,330 --> 00:05:42,000 This area increases over time as an ever larger area of the catchment contributes to the runoff, 65 00:05:42,000 --> 00:05:47,320 depending on the time needed for the water to reach the outfall. 66 00:05:47,320 --> 00:05:54,919 Imagine you are in an amphitheater and ping-pong balls come falling from the sky at a continuous 67 00:05:54,919 --> 00:05:57,259 rate 68 00:05:57,259 --> 00:06:01,699 The balls that fall closest to the stage discharge first. 69 00:06:01,699 --> 00:06:07,680 Only when the balls from the highest seats in the amphitheater have reached the stage, 70 00:06:07,680 --> 00:06:13,650 is the discharge equal to the flux coming from the sky. 71 00:06:13,650 --> 00:06:16,080 This is how it would look. 72 00:06:16,080 --> 00:06:20,580 The top graph shows the precipitation rate 73 00:06:20,580 --> 00:06:24,039 The middle one the contributing area 74 00:06:24,039 --> 00:06:26,319 and the lower one the discharge. 75 00:06:26,319 --> 00:06:33,319 At the end, the discharge equals the precipitation rate 76 00:06:33,440 --> 00:06:38,389 Of course this is only correct under a range of limiting assumptions, 77 00:06:38,389 --> 00:06:45,389 But in relatively small catchments in urban or impervious areas, it may work very well. 78 00:06:47,569 --> 00:06:53,160 Mathematically it can be described by a simple threshold function, described bij the MIN 79 00:06:53,160 --> 00:06:55,460 operator 80 00:06:55,460 --> 00:07:01,289 And the interesting part is that the runoff can be described purely as a function of only 81 00:07:01,289 --> 00:07:08,130 effective precipitation and the so-called time of concentration: 82 00:07:08,130 --> 00:07:15,130 the time it takes for the most remote part of the catchment to contribute to the discharge 83 00:07:15,690 --> 00:07:21,870 If you have subsequent precipitation events of fixed time steps, then we can also transfer 84 00:07:21,870 --> 00:07:26,069 this solution into a numerical scheme 85 00:07:26,069 --> 00:07:31,330 which can be readily incorporated in a spreadsheet 86 00:07:31,330 --> 00:07:36,970 Here you see outputs of the spreadsheet for the same effective precipitation event, but 87 00:07:36,970 --> 00:07:42,039 with different times of concentration 88 00:07:42,039 --> 00:07:47,860 Here are some questions for you to reflect on 89 00:07:47,860 --> 00:07:54,759 The storage principle and the runtime principle are primarily educational tools, 90 00:07:54,759 --> 00:08:00,370 although engineers may use them for particular circumstances, as long as they realise the 91 00:08:00,370 --> 00:08:02,030 limitations. 92 00:08:02,030 --> 00:08:05,990 But real catchments are more complex 93 00:08:05,990 --> 00:08:12,949 Scientific hydrologists still don’t exactly know how water moves through the terrestrial 94 00:08:12,949 --> 00:08:15,080 system. 95 00:08:15,080 --> 00:08:20,580 I plan to make a follow-up course in hydrological modeling to help you to further explore runoff 96 00:08:20,580 --> 00:08:22,740 generating processes 97 00:08:22,740 --> 00:08:27,141 “There still is a world to discover in Hydrology”