 So, another method for relating the amount of precipitation that falls in an area to the amount of runoff that comes off of that area is to use something created by the Soil Conservation Service called the rainfall runoff depth relationship. And this relies on a particular value called a curve number that we associate for these. Okay, so in this particular case what we're going to do is we're going to assume that there is some area, looking at it from the side view, and that there is an overall depth, an overall depth of precipitation that is falling on this particular area. Okay, and actually we're going to go ahead and represent that depth, there's our precipitation value. But then when the water reaches the surface, some of the water runs off and the amount of water that runs off there is going to have its own depth of water. That's going to be some fraction of the depth that sort of fell there, and that's going to have a depth Q. Now that isn't exactly a flow rate, it's going to be an amount of flow in inches. It's still represented with the Q for a flow rate, but in this case we're relating inches of precipitation to inches of flow. In other words, some amount, for example, you might receive maybe two inches of rainfall in a particular area and you might only get half an inch equivalent of water that flows off of their region. But then you need to in turn multiply that to determine a volume of water and also divide by the time frame to determine the flow rate of the water. But this goal is to sort of consider a volume, just to give us a number that we can consider to be a volume of water that has flowed off of the surface, that has run off the surface. And then the rest of it is going to be assumed to have either infiltrated or perhaps to have ponded or puddled somewhere in the region or otherwise is staying there, at least within the time frame that we're considering. So, here's the rainfall run off relationship. We're going to relate this depth Q to this rainfall depth P through two other sort of values here. One of them is this IA value which stands for an initial abstraction and then the S value here is a value we call storage. And these are also going to be assumed to be an inches of depth. So we're thinking about the overall precipitation. Here's sort of our overall precipitation in being some amount of inches and we can think about Q as being some fraction of that and then there are other pieces that represent a fraction of the overall percentage but again measured in inches. This might be the initial abstraction and you also might have your overall storage. Okay, so typically, well let's go ahead and write these, we have our initial abstraction IA, initial abstraction. And effectively that is the amount of rainfall that sort of gets soaked up or stuck or stays there as a result of the area being dry or not able to store anything in the first place. It's sort of the water gets there and it stays there. It takes a little while for the water to puddle up and upon before the runoff starts. Some of it seeps in but you have the water beginning to stick or beginning to puddle and once the puddles are full or everything, all the water has coated all the surfaces so now everything is wet, then the water will start to flow. So that's the idea of our initial abstraction. But then some of the water will also get stored. That's that S is for storage. One of the standard numbers, the relationships between this initial abstraction and the storage is a very simple one. The simplest relationship is to assume that this initial abstraction is equal to 20% of the storage, 0.2 times the storage. That's a very standard value but again this can change depending on some conditions that you might look at. Okay, so again both of these are measured in inches of rainfall. And then the storage itself is the number that's a little harder to calculate. We're going to try to figure out how much rainfall ends up staying in the region. Okay, so that the rest of it can be provided as runoff. And that storage follows a formula that looks something like this. Okay, we assume a storage of 1,000 divided by something called a curve number. This is going to be in units of inches and then we subtract off a value of 10 inches. Again, this is a somewhat empirical relationship. This is a relationship that's been made by observing how much water flows off of a number of different services in both experimental laboratory settings and in field settings. But here is our relationship here where we take our value. Okay, we need to have something called a curve number. What is this curve number? Let's see, when the curve number is equal to 100, we get 1,000 divided by 100, which is just 10. And then 10 minus 10 is zero. So when the curve number is 100, we get a storage of zero. Effectively the curve number represents a percentage of sort of, well, how impervious the surface is. The higher the curve number, the less likely it is that water is going to seep in and be stored. It's going to run off. If you just had a large plastic tarp or a large metal roof, it might have, for example, a curve number of very close to 100. As you get a lower curve number, then you're going to get more storage. For example, if I consider a smaller curve number, if I consider a small curve number of a value of say 20, the storage associated with a curve number of 20 would be 1,000 divided by 20 or about 50 minus 10 or 40 inches. Well, obviously that's a very low number. If we could store 40 inches of rain, that means very little of it's going to run off. Almost all of it is going to seep in. So that curve number is extremely low and probably not very likely for most of the things we're going to use. But you can sort of see that this idea gives you a sense of how much rain can fall before we have any level of runoff. Once we've established this storage value. There is an assumption here that before we use this relationship for runoff, there is an assumption here that the precipitation has to be greater than or equal to 20% of the storage. So that you get no runoff if the precipitation is less than 20% of what the storage is. So with that 40-inch number, we would maybe need 8 inches of precipitation before we would do any calculation of runoff. And I have made a small error here in that I missed a squared value. There's a squared value there on my formula here, which makes some sense that we get our answer in inches. So this curve number, Cn, is very similar to things like a runoff coefficient, C, which we might have seen earlier, that it's something that's measured or approximated from conditions that are on the field. And those conditions again include things like the slope, the shape of the watershed, the presence of vegetation, things like that. That curve number represents the tendency of the water to sort of either runoff or stay in one place. Here's some example curve numbers. If you had a meadow, for example, that was considered to be in good condition, maybe that the grass was growing everywhere, things like that in it, it would have a curve number 78, compared to something like a residential lot. And notice they often define residential lots based on the size of the land around them. If you live on a quarter acre, you do not. Most of your lot is the house. Whereas if you live on a half an acre or a larger acre, only a smaller fraction of your lot is the house. So sometimes they'll base it on the size of the acreage for each lot that somebody lives on. In a case like this, a residential lot, most of it is going to be in pervious surface or a good chunk of it, the roof, etc. And so you're going to have a high curve number getting closer to 100 at a value of 83. So what we do in a case like that is we might say, let's say for example, we live in a location or we're interested in the runoff of an area that's maybe some wooded, for example. But the example I use here, we'll say we have a curve number of 75. We look it up in the chart and we find out that we have a curve number of 75, which means something like a wooded situation where a good portion of the rainfall is going to be able to infiltrate or end up captured by the vegetation that's there. Well, if I put that curve number in here, I get a storage value of 1,000 divided by 75 minus 10, and that's going to be in units of inches. If I actually calculate that value, I get 3.33 inches. Okay, that would give us our storage value. That's how much rainfall we consider to store. We can calculate our initial abstraction from that value. Our initial abstraction here is going to be 0.2 times s, which is going to give us 0.667 inches. Okay, that's a value that's going to sort of stick when we first calculate. And now, using those values and plugging them into this curve number equation, we can get an estimate for how many inches of this rainfall end up leaving as runoff. And in the case there, we just plug in the various numbers. We have our initial precipitation. Well, we'd have to see what the initial precipitation was. Let's say, for example, we had 7 inches of precipitation. So if I say p equals 7 inches, well, 7 inches of precipitation is greater than the 20%. I think I said that earlier. Precipitation must be greater than 20% of the storage. In this case, it is the storage is 3.33 inches. So we'll take the precipitation of 7 inches. We'll subtract the initial abstraction of 0.667 inches. We square that value. And then similarly down here, we have the same value, 7 inches, minus 0.667 inches, plus that storage value of 3.33 inches. When we do that calculation, we get a value of Q of 4.15 inches. What does that mean to us? Well, effectively what that means is that even though we had 7 inches of rainfall that fell, we can consider only 4.15 inches as flowing off of that surface. And then if we're interested in seeing if that goes through a stream or maybe storing that value, maybe we multiply that by whatever our acreage is, the area that we're interested in, and that would give us a volume of water that has run off as a result of this 7-inch rainfall event.