 So welcome to the second lecture of fourth module. So as part of the previous lecture, we were trying to get a grip on the fundamentals of radar remote sensing and in this part of the lecture, we shall examine the various applications of radar remote sensing in hydrology. See quantifying the terrestrial water budget, it is very crucial to understand the various earth system processes and we know that the terrestrial water budget is mainly composed of the fluxes of precipitation, evapotranspiration, runoff, the changes in water stored at the earth surface delta S and they are related using this following equation. Now terrestrial water changes are represented through terrestrial water budget, again which is a function of precipitation, evapotranspiration and runoff, recent as well as operational satellite missions have quantified these components either individually, independently or as an aggregate at various spatiotemporal scales, microwave remote sensing enables measuring each component of the terrestrial water storage at global scales. So what we will do is through this lecture, we shall try to understand one by one about the different applications of radar remote sensing beginning with the estimation of precipitation, okay. So all of us know how precipitation is formed, is not it? At higher altitudes of the atmosphere where the temperature is colder than that at the land surface, the water vapor condenses into tiny liquid water droplets. Now these cloud droplets, they tend to join together, they combine together to form heavier cloud drops and as they become heavy, they are no longer able to float and hence they begin to fall to the earth as precipitation or hail or snowfall, all being different forms of precipitation. So even gallons of water can fall from the sky in a small but intense storm and we all know that precipitation does not occur in the same amounts throughout the world. There are variations, variations in the intensity of precipitation within a country even within a city, is not it? A slightly more technical definition of precipitation is as a crucial variable driving the atmosphere's general circulation through latent heat release. So let us try to understand what are the different ways in which precipitation can be estimated from radar remote sensing. Now what you see here is a small sketch wherein x axis represents the time, y axis represents the rainfall say it is in millimeter per hour and precipitation values occurring at a time t over an area A is of interest, you know we are interested in measuring the precipitation that occurs at a particular instant of time over an area. Now you can see that the arrows shown here are the specific time intervals at which observations are being made and these observations can be from satellite bond radars or Doppler weather radars, you know the instant of time at which observation is made is different from the actual time of occurrence of the event. Now instantaneous rainfall rates occurring both in space and time when integrated they give us the space time average of rainfall rate, is not it? It is also known as the area time integral of rainfall. I can express it in the form of a small relationship say RAT refers to the area time integrated rainfall, I can write it as 1 upon at integral 0 to t, integral 0 to a small r x, t dx dt. So here small r x, t this is the instantaneous rainfall rate and then we are integrating it to get the space time average of rainfall rate. See the measurement scale of precipitation as such is a very interesting topic of discussion because a satellite bond radar scans the atmosphere vertically while a Doppler weather radar scans the atmosphere horizontally and there is a fundamental difference between satellite and radar remotely sensed observation of precipitation and those which are measured directly using the rain gauges. While satellites and radars they measure rainfall as a space integral at a given instance in time, rain gauges on the other hand they measure rainfall as a time integral of rain at a particular location. So let me repeat, I am talking about measuring precipitation using rain gauges in situ rain gauges as that set by the Indian meteorological department and measuring rainfall using Doppler weather radars which are also ground waste as well as measuring precipitation using radars onboard satellites. And I am telling you that there is a fundamental difference between the satellite and radar remotely sensed observation of precipitation which means the way satellite radar sees and measures precipitation is different from the way rain gauges measure precipitation which again is different from the way Doppler weather radars are measuring precipitation. While satellites and Doppler weather radars they measure rainfall as a space integral at a given instance in time, rain gauges on the other hand they measure rainfall as a time integral of rainfall at a particular location, okay. Now let us try to discuss in detail about satellite bond radars used for measuring precipitation. So in the last two decades, microwave based precipitation products have taken unprecedented satellite images of the earth's weather and they have proved to be a valuable tool for quantitative estimation of precipitation from space. And along with the widespread acceptance of microwave based precipitation products, it has also been recognized that they contain large uncertainties, okay. Which means quantitatively using these rainfall products for various scientific and hydrologic applications it requires them to be accompanied with an error estimate. We need to know how reliable is the precipitation product that we get from Doppler weather radars or satellite bond radars. In this context, we can discuss about satellite based remote sensing of precipitation because let me re-itrate satellites don't continuously look at a precipitation event because they scan and then their temporal resolution is different which means they can give you instantaneous measurement of rainfall at certain instance of time. They are not continuously looking at the same rainfall event but they are giving us the precipitation values at an instant of time that is why I have written small rx, t that is the rain rate at a point x in time t. And always when we are trying to derive precipitation from satellites, we take the accumulation integration of rainfall that has occurred over a particular region throughout the time period. So the instantaneous rain rate at a time t averaged over an area A is what is given by a satellite radar. You know I am just trying to explain the orbital data of a satellite because you know when the satellite is looking down on the earth it doesn't see the entire tropical region in one go. It is going to travel a particular path, remember there is always relative motion the earth is also rotating, the satellite is also travelling in the orbit. So a particular orbital path will be covered by a satellite and then this orbital path is getting repeated to finally give us the precipitation images that we can use for our applications. So what you see here the sample orbital data of GPM mission as captured on 4th Jan 2016 what you see in blue gives us the precipitation in millimeter per hour. So just to reiterate because this concept is important, what you see here is the rainfall at a point x accumulated during time t and what you see here is the instantaneous rain rate at a time t averaged over an area A both are different. And we do have the concept of area time integral of rainfall that we discussed. So with this background let us try to understand a few radars in space that are dedicated to the measurement of precipitation. We have TRMM that is Tropical Rainfall Measuring Mission. So the TRMM or Trim Satellite it was launched into a near circular orbit and it is a joint mission between NASA of the United States and the National Space Development Agency of Japan and Trim Satellite it studies the variability of precipitation in the tropical region using a suite of instruments namely the passive sensor called as Trim Microwave Imager TMI and the active sensor known as precipitation radar abbreviated as PR. So precipitation radar is capable of giving us a 3 dimensional structure of rainfall and the details about precipitation radar are summarized here. It operates in the KU band, it has a horizontal resolution of 4.3 kilometers in nadir, vertical resolution of 0.25 kilometers, observable range is given and the sensitivity is given that is 0.7 millimeter per hour alright and the Trim precipitation radar it is also known as the first rain radar in space. It helps us to quantitatively measure the precipitation over land as well as ocean okay, Trim Precipitation radar and as I mentioned earlier the TRMM satellite themselves it has 5 different sensors, one among them is precipitation radar but the other sensors are Trim Microwave Imager which we will discuss in the next module and in addition we also have the visible and infrared scanner, the lightning imaging sensor and so on. Now there are different data products that can be generated from Trim you know different data products. We have the level 1 radiances and the level 2 instantaneous geophysical parameters and the level 3 data which consists of the gridded Trim precipitation data products. We also have the quarter degree products from Trim and other satellites. So right now let us try to understand the different rainfall types. So if you are more interested I would suggest you to have a look at this paper. Both the precipitation can be broadly classified into two different types. One is known as convective precipitation and the other is known as stratiform precipitation. So the difference is between both the types of precipitation are given in the screen in front of you. Whenever I say convective precipitation I am referring to higher rainfall rates higher than 5 millimeter per hour and I am referring to small but intense horizontally inhomogeneous radar echo, small intense horizontally inhomogeneous radar echo. The second broad classification of tropical precipitation is stratiform precipitation, stratiform which consists of low rain rates which are lesser than 5 millimeter per hour. At the same time it consists of widespread horizontally homogenous radar echo, convective stratiform. Whenever we try to learn more about the radar based precipitation from satellite we always try to make a distinction between convective precipitation as well as stratiform precipitation. Alright, in this context let me also introduce the global precipitation measurement mission GPM that is dedicated to the measurement of precipitation. It has a dual frequency precipitation radar which is abbreviated as DPR, it has a spatial resolution of 5 kilometers and GPM is a low earth orbiting satellite, it was developed as an improvement on the trim data in numerous ways. Now although GPM has only 2 instruments versus the 5 instruments on trim they are giving us valuable sources of information which is why we have included it as part of our lecture. So there is a radiometer which we will be discussing as part of our next module but for this module we will focus our discussions on the GPM dual frequency precipitation radar, another radar in space dedicated for the measurement of precipitation. So GPM as such it has DPR as well as GPM microwave image which is a radiometer that operates in the concept of passive microwave remote sensing. They are some of the most advanced algorithms that employ the use of GPM data to estimate quantified precipitation from space and at this point let me mention that DPR is the only dual frequency radar in space and it is capable to give us the three dimensional profiles and intensities of precipitation ranging from rain to snow and ice, different forms of precipitation. What you see in front of you is showing you the liquid precipitation rate as well as the frozen precipitation rate from iMark. Now satellite based precipitation from active and passive microwave remote sensing because they have also resulted in multi-satellite precipitation products and these multi-satellite precipitation products you know they range from different satellite systems and gauge data all of them have been combined to one single best estimate. For trim satellite we have something known as the TRMM multi-satellite precipitation data abbreviated as TMPA. Similarly, what you see here shows you the iMark data product a sample data is being shown on screen. So let me write it down the iMark it stands for integrated multi-satellite retrievals for GPM which combines the information from the GPM satellite constellation to estimate precipitation globally over the Earth's surface. So remember GPM is not a single satellite it is a constellation of satellite. So more details about these can be found in the link of GPM. To a case study let us try to understand how satellite based precipitation products can be evaluated in hydrology. At this point let me try to also introduce the contingency table statistics to you you know because assume you have a precipitation data from say Indian meteorological department rain gauges that have been regraded to say quarter degree spatial resolution and daily temporal resolution which means you have an image of precipitation values for every day at 0.25 by 0.25 degree spatial resolution over India and say you have the data for multiple number of years one map per day. Similarly imagine you have the precipitation data from satellite based radars in a similar manner that is quarter degree spatial resolution and say daily temporal resolution. So how do you estimate the accuracy of the satellite based products which means you need to have a reference product that is the Indian meteorological department data rainfall data that can be used as a reference whereas you can compare the satellite based data with respect to the reference data. Now how to do this comparison that is where contingency table statistics finds its importance. So let me try to write it down ok. Say you want to estimate the rainfall that is correctly estimated from the IMD gauges as well as from the satellites and you want to write it down, tabulate it in the form of a contingency matrix. It is going to have just two possibilities isn't it either yes or no. So we call it as dichotomous classification, a classification which has just two probabilities either 0 or unity and such classification are tabulated in the form of a contingency matrix and you can derive various indices, various metrics from this contingency table. So the result of a categorical estimate can be expressed in the form of a 2 cross 2 contingency table, 2 cross 2 ok. Say for example you want to estimate the rainfall that is judged by precipitation radar ok. Say no rainfall that is just judged by precipitation radar and say the rainfall that is judged by TMI and no rain judged by TMI. Say these are your elements of a contingency table. So let me draw and give it the shape of a proper table. These are the four values that belong to the contingency table. Say I am going to name it as A, B, C and D. The elements of the table denote the number of positive estimates that is hits, positive estimates and the number of events with a negative estimate that is B, number of positive estimates that were not accompanied by an event that is false alarms C and the number of negative estimates that did not have any associated events B. Let me repeat what you see here is the rain that is judged by say precipitation radar. No rain judged by precipitation radar. Say I want to compare the rainfall measurements from precipitation radar with the radiometer TMI, TRMM microwave imager. So this is rain judged by TMI and R is no rain judged by TMI. The elements of a contingency table it is going to be I am going to write it as A, B, C and D. Now let us try to understand what each element is. A is the number of positive estimates we call it as hits where we are also says it has rained A number of times, TMI also says it has rained A number of times hits the number of positive estimates. B is nothing but the number of events with a negative estimate, we call it as misses, you know PR says it has rained but then TMI is not of the same opinion. The number of events with a negative estimate. Now the number of positive estimates that were not accompanied by an event is known as C, the number of positive estimates which were not accompanied by an event is C and the number of negative estimates that did not have any associated events is D, okay. And using the contingency table statistics we can derive different metrics, different metrics like the probability of detection popularly abbreviated as POD, the probability of detection, it is given by the expression A by A plus C. It is nothing but the likelihood that an event would be estimated given that it occurred, okay. Likelihood that an event would be estimated given that it occurred and the probability of detection POD values range from 0 to 1, okay. Probability of detection, similarly we can have another metric that is computed from the contingency table known as false alarm ratio abbreviated as FAR, false alarm ratio. Now FAR is an element of the conditional distribution of events given the estimate and FAR ranges from 0 to 1 with 0 being the ideal score, no false alarm, 0, okay. It is given by the expression B by A plus B, okay. Now when I say A and B I am referring to the contingency table which was written in the previous slide, okay. Now we also have some metrics from the extended contingency table. Now while contingency table metrics they give information regarding the hit, miss or false estimates. They have a slight disadvantage because they do not shed any light on the bias and errors in the magnitude of the variable observed. So the commonly used categorical metrics can be extended to volumetric measures. So as to decompose the total error or bias with respect to their volumetric error components. Now in this context similar to probability of detection we can have something known as a volumetric hit index that is the volume of correctly detected rainfall, okay. When it is probability of detection it is the number of times the rainfall was detected whereas when we say volumetric hit index it is the volume of correctly detected rainfall. Similarly we can also have the volumetric false alarm ratio which is the volume of false rainfall above a threshold that has been detected. Once again I am going to represent the contingency table for clarity. We have the event occurred from the reference, the event occurred from the observation, okay. So the reference can be data from India Meteorological Department gauges and the observations can be the rainfall that is observed from satellite based radars. You can see hits written here wherein both reference as well as observation agree on yes, okay. Now when the reference says no but observation says yes we call it as false. When the reference says yes, observation says no it is miss, okay. The number of missed rainfall events and of course when both say no it is contributing to a null event. Once again we can have different metrics I have explained just two but we can have different metrics that can be generated from a contingency table like we can have probability of detection. Now it will be more clear it is H by H plus M, okay probability of detection. We can have false alarm ratio which is F by H plus F. We can have the miss rate and critical success index similarly we can have an extended contingency table wherein the volume of rainfall is given, okay. In the previous case the number of events are only counted. In the volumetric indices the volume of rainfall is also counted and if you are more interested to know about these indices I would suggest you have a look at this paper, okay. So here OBS refers to observed rainfall which is from the satellite based radar and REF refers to the reference rainfall from IMD rain gauges, T is the time threshold, okay. They are direct extensions of probability of detection as volumetric hit index, a direct extension of false alarm ratio is volumetric false alarm ratio and so on, okay. So we started with an example that I give you two data sets, one from the IMD rain gauges and one from the satellite based radars and then you are given the task of comparing the satellite based precipitation with the reference data set to say the quality of rainfall that is coming out from the radar. So let me show you sample results obtained. So what we did is we compared the IMD precipitation product with the IMD precipitation product for the Indian summer monsoonal months of June, July, August, September from year 2008 to year 2015 and what you see here is the bias towards your left side, okay, bias whether it is over estimating or under estimating that is the information you get from bias and the probability of detection is shown in the figure, central figure probability of detection and the volumetric hit index is shown in the figure towards the right side, okay. Similarly, I can have diagrams that give you the false alarm ratio, okay, false alarm ratio, volumetric false alarm ratio and the categorical miss, again the data from IMD as well as IMD precipitation for the June, July, August, September months were used from year 2008 to 2015. So when you make these comparisons, please be aware of the density of IMD rain gauges because the gauges are less dense over the Kashmir region, so which is why the large amount of masses are obtained in the Kashmir region. So just be aware that the India Meteorological Department if you visit their website, they give you the location of rain gauge stations and from this data, a graded precipitation product is created and available to us for using and what we have done in this study is we have just taken the graded product and used it for analyzing the IMR precipitation product, okay. So in this part of the lecture what we did is we started to understand the applications of radar remote sensing and hydrology and we were discussing specifically about one of the applications that is estimation of precipitation from space and we also discussed a few metrics based on contingency table that can be used for comparative evaluation of the satellite based precipitation and the reference precipitation. Now hoping that you could understand what was being discussed and I shall see you in the next class. Thank you.