MASTER's THESIS the Lifetimes of Tropical Cloud Regimes

2010:080 CIV MASTER'S THESIS

The Lifetimes of Tropical Cloud Regimes

Mattias Häggkvist

Luleå University of Technology MSc Programmes in Engineering Space Engineering Department of Applied Physics and Mechanical Engineering Division of Physics

2010:080 CIV - ISSN: 1402-1617 - ISRN: LTU-EX--10/080--SE

Preface After ﬁve years of studies at the MSc programme in Space Engineering at Lule˚a University of Technology it was time for me to write my thesis. I had recently taken a course in atmospheric physics that I found very interesting. So I asked Professor Sverker Fredriksson if he could help me ﬁnd a thesis project within this subject. This is how I got in contact with Professor Christian Jakob at the School of Mathematical Sciences, Monash University, Melbourne. He suggested that I could work with studying the lifetime of tropical cloud regimes. Feeling a bit nervous, not knowing if I would be able to manage this with my prior knowledge, I left for Melbourne in the fall of 2009. Once there, any doubt I previously had disappeared. I got a very warm welcome to the university and everyone was very helpful. After three intense months it was time for me to leave and return to Sweden. I did this with a lot of new knowledge and with a feeling of gratitude to all those who helped me. First I would like to thank my supervisor at Monash University, Professor Christian Jakob, for all the time he spent helping me, always with a smile. I am deeply grateful for all your help. I would also like to thank my examiner at Lule˚aUniversity of Technology, Professor Sverker Fredriksson, for helping me to get this thesis project and for all his good advice. I would also like to thank Sven Molin at Lule˚aUniversity of Technology for his help with the trip to Melbourne.

Abstract

This MSc thesis in Space Engineering is about the lifetime of cloud regimes over the tropical and subtropical regions of Earth. The International Satellite Cloud Climatology Project D1 dataset and the cloud regimes, derived using a cluster algorithm on cloud top pressure and optical thickness, form the basis of the analysis of the lifetime. The cloud regimes are measusered how long they appear at a certain location. Signiﬁcant diﬀerences were found, among other things between convectives cloud states and suppressed ones. Transitions between the eight regimes were also examined and it was found that some regimes transformed to regimes with similar physical properties whereas others didn’t, suggesting that some regimes are transition regimes and others represent a more stable or unstable end state.

iii

Contents

1 Introduction 1

2 Theory of the atmosphere 3 2.1 Physics of the atmosphere ...... 3 2.2 Cloud formation ...... 4 2.3 Cloud properties ...... 4 2.4 Climate ...... 6

3 Tropical cloud regimes 9 3.1 ISCCP D1 dataset ...... 9 3.2 Cluster regimes ...... 10 3.2.1 CTP-τ diagram ...... 10 3.2.2 Anderberg k-means clustering algorithm ...... 12 3.3 The eight regimes ...... 13

4 Cloud regime lifetime 17 4.1 Global results ...... 17 4.2 Tropics ...... 39 4.3 Subtropics ...... 40 4.4 The Pacific ...... 42 4.4.1 Tropic Pacific ...... 42 4.4.2 Subtropic Pacific ...... 45

5 Summary and ﬁnal thoughts 47 5.1 Conclusions ...... 47 5.2 Future work ...... 49

Bibliography 52

Appendix A Lifetimes plots for the entire region 53

Appendix B Probability for the entire region 55

Appendix C Result for the tropics 59

v Appendix D Paciﬁc plots 61

vi Chapter 1

Introduction

All of us have probably at one point in our lives laid on our back in the green grass, staring up at the blue sky covered with white clouds in differents shapes, letting our imagination run wild, fantasizing of what the clouds look like. Maybe we have looked with fascination at noctilucent cloud shimmering in the evening, awaited with anxiety as a wall cloud approaches from the distance or gazed from our airplane window over a seemingly endless white ocean of clouds. But clouds are not just beautiful to look at, they affect us in our everyday life as well. Clouds play a major role in Earth’s climate. The Sun is the driving force behind our climate and life here on Earth. Around 30 percent (Goode et al., 2001) of the incoming solar radiation is reflected from Earth, a part of this is due to clouds. But the atmosphere is a complex system and in order to enhance our knowledge of it, further studies must be conducted, to gain a better understanding of the Earth’s climate. One of the hottest, and most controversial, political issues today is that of global warming. But no matter in what political camp one stands, learning more about the climate will help us with our everyday lives. The climate is not just something that will happen in our future, it is something that is happening today. The weather is something that affects us everyday. It affects the business man flying to his meeting, it affects the farmer growing his crops and the family spending the weekend by the sea. Getting a better understanding of Earth’s atmosphere and climate will help getting better weather and climate models and hence better predictions and forecasts. In this thesis the lifetime of tropical cloud regimes will be investigated. An- alyzing cloud data deduced from satellite observations and sorting them into groups using clustering techniques have privous been used by Jakob and Tse- lioudis (2003). Using data from ISCCP (International Satellite Cloud Clima- tology Project), they showed that one can identify four physically interpretable cloud regimes over the tropical West Pacific. In later studies (Jakob and Schu- macher, 2008; Jakob et al., 2005) the cloud regimes’ precipitation, radiative and thermodynamical properties have been examined. In Rossow et al. (2005) and Singh and Jakob (2010) the region was first expanded to the latitude band

1 15◦ S−15◦ N and later to 35◦ S−35◦ N and eight regimes were then identified. It is the time scale of these cloud states that will be investigated in this thesis. The data used will be derived from the ISCCP D1 dataset, and the same region as in Singh and Jakob (2010) will be examined. Different aspects of the time scale will be examined, such as for how long time the clouds regimes live and the probability of the transition from one regime to another. Chapter 2 gives a brief overview of fundamental atmospheric physics relevant to clouds. An introduction to the parcel concept and how clouds are formed will be described. A brief description of different cloud types will also be included in this chapter. Since the data used in this thesis are gathered from tropical and subtropcial areas, the climate in these regions will be discussed as well. This is meant to give a basic understanding of the atmosphere and familiarize the reader with some of the terms that will be used. Readers already familiar with these concepts can skip this chapter and go on to Chapter 3. Here the data used will be presented. The chapter will give a look into how clouds are analyzed in ISCCP from satellite measurements. Then the cluster algorithm, as well as its application to the ISCCP data, will be described. The regimes themselves and their physical interpretation will be examined. What other information is included with the cluster data will also be described, helping with the analysis in Chapter 4. The analysis will be carried out in several steps. First a global view of the lifetime will be provided. The lifetime will be examined in several different ways and with different goals in mind, such as how long a regime occurs at a certain spot or what regime is most likely to follow it. This will highlight different aspects of the lifetime of the tropical cloud regimes, but also tell something about what the physcial properties of the regimes are, and thus how these two different parts are connected. Since the regimes all have different physical properties, they are expected to be more common in smaller regions. To examine if this influences the lifetime, a comparison will be made between the tropical and the subtropcial region on Earth as well as some selected ocean basins, such as the Pacific.

2 Chapter 2

Theory of the atmosphere

2.1 Physics of the atmosphere

The Earth’s atmosphere stretches out from the surface and roughly 100 km up into space. It is made up of several layers with the one closest to the ground called the troposphere. The extent of the troposphere, which varies depending on the current conditions, is around 10 − 15 km. It is in the troposphere where most of the weather takes place and it is thus the most important part of the atmosphere for this thesis. In order to get a better comprehension of what might affect the lifetime of the cloud regimes, let us start by looking at the fundamental physics of the atmosphere. A simple way of explaing the physics, and more specifically circulations and uplifting, of the atmosphere is the so-called parcel concept (Andrews, 2005). This can be visiulized as a small volume of air, a parcel, which is affected by the surrounding air but does not effect its surrounding environment. This will make it easy to understand how air reacts in differents physical environments, e.g., a parcel that is warmer than its surrounding, will due to a buoyancy effect be lifted until it reaches equilibrium. It should be noted that the parcel concept is merely a way of understanding what happens in the atmosphere rather than an exact description of it. A small parcel of air would in reality quickly get mixed in with its surrounding. The temperature differs throughout the atmosphere. The rate of which the temperature decreases with height is called dry adiabatic lapse rate, DALR, or saturated adiabatic lapse rate, SALR, depending on if the air is saturated or unsaturated. Now once again consider a parcel at a certain height with temperature Tp and a temperature in the environment around it Te. Let Tp = Te for a parcel forced to rise by an external force. Now if the SALR for the parcel is greater than that of its environment, here called environment lapse rate, ELR, the parcel will cool more quickly than its surrounding. This causes it to become colder, more dense and less buoyant than its environment, according to the ideal gas law. This will then cause the parcel to sink and return to its initial position.

3 The air is then said to be absolutly stable (Aguado and Burt, 2009). Now consider the same case but this time the DALR or SALR is less than the ELR. This will cause the rising air parcal to get warmer and more buoyant that its environment. The air is then said to me absolutly unstable. A third case exists as well, conditionally unstable. In this case DALR≥ELR≥SALR. Consider that a dry parcel rises because of an external force and the temperature decrease according to the DALR. This will, as in the absolutly stable case, cause the air parcel to get colder and denser and hence the upward motion will stop. Now consider that the parcal get saturated somewhere during its upward motion. The parcel’s temperature will now decrease with the SALR, which in this case is less than the ELR, causing the parcel’s temperature Tp to be greater than the temperature of the environment Te. Hence the upward motion will continue. What happens with the parcel, in the condtitionally unstable case, depends on how high the parcel gets lifted and if it gets saturated. As seen, warmer air rises when it is surrounded by colder air. Another way of saying this is that air will move from an area of high pressure towards an area of low pressure. This is basic physics but still of importance for understanding some of the complex processes that occur in atmosphere.

2.2 Cloud formation

Clouds are made up of liquid and frozen water droplets. Thus in order for clouds to form an air parcel must be cooled until saturation occurs. As discussed in the previous Section (2.1), saturated air will cool according to the SALR when it is lifted. There are four princple mechanisms how uplifting can take place; orographic uplift, frontal lifting, convergence and localized convection (Aguado and Burt, 2009). Orographic uplift is the displacement of air due to a hill, mountain or other object that forces the air to move upward. The second way, frontal lifting, takes place when two regions with diﬀerent temperatures overlap. A front is a sloped transition zone between a region with cold air and warm air. When a region of cold air moves into a region of warm air is situated, the lighter warm air will rise. The same applies when a region of warm air moves into a region of cold air. The warm air will be forced to rise. The third case happens at the centre of a low pressure cell. The surrounding air with higher pressure will converge into the centre of the cell causing the air in the centre to get lifted. The ﬁnal way air can be lifted is through convection. As the air gets heated it gets warmer than its environment, causing it to lift because of it being more buoyant than the air around it.

2.3 Cloud properties

There are ten pricipal clouds types (Aguado and Burt, 2009), which are cathe- gorized depending on their shape and at what altitude they appear. They are named based on four basic cathegories. Cirrus, which are thin clouds of ice,

4 Stratus, which are layered clouds, Cumulus, clouds that have vertical development and finally Nimbus, which are rainproducing clouds. These are then compounded into other name, e.g., a cirrostratus clouds resembles both a cirrus cloud and a stratus cloud. There are also four cathegories that divide the clouds depending on their height. High clouds extend 6000 m or higher, middle clouds around 2000 − 6000 m and low clouds below 2000 m. There are also clouds with extensive vertical develoment throughout the large part of the troposphere, such as cumulonimbus clouds. The clouds with vertical development are often convective clouds. They are common in the tropics where the intense heating of the surface warms the air around them, leading to convection. Typical convective clouds are cumulonimbus, cumulus congestus and cumulus humilis. Cumulus humilis clouds, also called fair weather cumulus, are small single plume-like white clouds formed from localized convection. As the name fair weather cumulus suggests, they usu- ally do not yield precipitation and can evaporate soon after they have formed. Cumulus congestus have, contrary to cumulus humilis, several plume towers. They also have a greater vertical extent suggesting that they are formed from unstable air. The vertical difference between top and bottom also implies great temperature differences within the cloud, making it possible for the cloud to have supercooled droplets in the top of the clouds, which eventually can turn into ice. The anvil shaped cumulonimbus are one of the most violent clouds and can produce intense thunderstorms. They can extend from a couple of hun- dreds metres above to ground up into the stratosphere. The extensive vertical development again suggests that they are formed by unstable air. As with the cumulus congestus the temperature difference in the clouds results in the upper part of the cloud being made up of ice crystals. These ice crystals are more long lived than the rest of the cloud, forming cirrus clouds after the rest of the cloud has dissappeared. The thin cirrus clouds have a low ice content. This is due to their altitude. The low temperature at these altitude makes for a low amount of water vapour availible, from which they can form. Stratocumulus are low clouds with no real convection inside them, hence the layered shape. Stable air above them, such as inversion layers, prevent them from growing upward. A notion that will be frequently used in this thesis is cloud optical thickness. Optical thickness is a way of measuring the transparecy of an object, in this case a cloud. It is a measure of how much of the incoming radiation that is scattered and absorbed by the object. The optical thickness of clouds is controlled by their physical thickness, ice or water content and particle shape and size. In general, but not always, for visible radiation physically thicker clouds are also optically thicker. Higher ice/water content means higher optical thickness and smaller particles, which lead to optically thicker clouds (Jakob, 2010).

5 2.4 Climate

Around the Equator, where the heating by the sun is on the average most intense, a band of low pressure cells is formed due to the previously described effects. This is called the Intertropical convergence zone, ITCZ. Because of the rising air around the Equator, air flows equatorwards to take its place. The rising air by the Equator however, is prevented from rising any further once it has reached the tropopause, which is an inversion layer. Since the air that flows towards the Equator must be replaced in the same way that the rising air at the Equator is, air from higher altitudes sinks to the ground and takes it place creating high pressure cells. This sinking air is, in turn replaced by the rising air from the Equator that was prevented from further uplift. This means that the rising air flow poleward at the top of the troposphere to replace the sinking air. This creates a circulation cell known as the Hadley circulation, with air rising at the Equator and sinking around latitude ±30◦, and air flowing polewards at the top of the troposphere and equatorwards near the surface. The air flowing equatorward at the surface is effected by the coriolis force, pushing it westward. This results in what is called the trade winds. They blow northeast to southwest in the northern hemisphere and southeast to northewest in the southern hemisphere. The tropical climate around the Equator is mostly a result of the Hadley circulation. The heating of the surface does not only result in rising air and convection, it produces evaporation as well. As the air becomes more moist and rises it cools down and creates clouds. Tropical climates are in general warm and the clouds form heavy precipitation, although this is recieved in different portions in different regions, monthly or seasonly. Areas with tropical climates are warm all year around with only small seasonal variations in temperature. The subtropical climate is roughly defined as the region between latitude 20◦ −40◦ N/S. The sinking column of air in the Hadley cell will not create clouds like the rising air. This is because as the air sinks it gets warmer, preventing condensation. Thus these region are predominatly dry with mostly clear skies in the middle and upper troposphere. However, evaporation from the ocean surface still moistens the lower atmospheric levels and convection does develop. Since this convection is capped by an inversion created by the sinking air above, the so-called trade inversion, the convective clouds formed are generally quite shallow and only occupy the lowest 2 − 3 km of the atmosphere (Jakob, 2010). A region of specific interest for this thesis is the Pacific ocean. The Western Pacific has the highest sea surface temperatues in the world and is a region of much convection while the East Pacific has much colder water. The reason for this is an east-west circulation, superimposed on the Hadley cell. While air flows eastward in the top of the troposphere it flows westward at the surface. The eastward moving air subsides near the coast of South America creating a high pressure area, whereas the rising air creates a low pressure area around Indonesia. The westward flow of the wind drags the sea surface water with it from the East Pacific to the west, piling it up in the tropical warm pool in the West Pacific. This, in turn, make the water taken from the East Pacific to be

6 replaced by colder water. Every now and then this circulation is disrupted by a phenomenon called ENSO, El NiñoSouthern Oscillation. ENSO has two phases, El Niño,the warm phase, and La Niña,the cold phase. In an El Niñoevent, the easterly winds are reduced in strength, causing the pile up of warm water in the West Pacific to stop. Instead the warm pool of water is shifted to the Central Pacific. Also, the upwelling of cold water is reduced in the East Pacific. This changes the atmospheric circulation. The reverse sitiuation occurs in a La Niña event. During this the westward blowing trade winds strengthen, causing an intensification of the cold pool in the Eastern Pacific. Two particulary strong ENSO events (Eliasson, 2006) are the La Niñaevent of July 1988 to June 1989 and the El Niñoevent of May 1997 to April 1998, which will be used when comparing the lifetime during non-ENSO and ENSO events.

7 8 Chapter 3

Tropical cloud regimes

The data used to investigate the lifetime of the tropical cloud regimes come from the International Satellite Cloud Climatology Project, ISCCP. The IS- CCP data are collected globally every three hours. Each pixel with collected radiance data is then analyzed and different datasets are produced containg daily, monthly or yearly information. The ISCCP data analysis comprise three fundamental steps, which are described in Rossow et al. (1991). The first one is to determine whether the pixel is clear or cloudy. The second step is to determine the cloud properties using an atmospheric radiative transfer model and the measured radiative properties of the cloudy pixel. The final step is a statistical analysis of the data where it is mapped into grid cells, labeling them whether they are over land, coast or water. This is stored as the C1 dataset. The D1 dataset, which is used in this thesis, is an improved version of the C1 dataset. The new changes and improvments in the D1 dataset are presented in Rossow and Schiffer (1999). After this a cluster analysis has been performed using the D1 dataset, grouping the cloud data into 8 different regimes depending on their physical state, i.e., the cloud properties.

3.1 ISCCP D1 dataset

The D1 dataset contains three hourly data in 280 × 280 km 2 grid cells globally, roughly representing a 2.5◦ × 2.5◦ grid cell at the Equator. Each grid cell contains several pixels, representing the satellite’s field of view, ranging from 4 − 5 km in size. The radiance of each pixel is measured in infrared wavelength (IR) 10 − 12µ m and in visual wavelength (VIS) 0.5 − 0.7µ m. Before a pixel can be determined as cloudy or clear, a clear sky radiance value must be determined for every three-hour period. Measured radiance data are compared for a 25 km wide area at a specific time with radiance data for the same area at different times. Two assumptions are made in order to differentiante a clear pixel from a cloudy one. First clear sky radiances are assumed to exhibit lower variations in space and time. Clear sky values are also assumed to be

9 varmer than cloudy areas. Both these tests must concur to a clear sky area in order for the radiance value to be used as a clear sky value. Once the clear sky value is known, a pixel can be determined to be cloudy or clear. The radiances are measured and compared to the clear sky value for the pixel. If the measured radiance difference is higher than a predefined threshold value, which differs depending on if its wavelength is VIS or IR and the pixel’s location, the pixel is defined as cloudy. Only one of the two wavelength, VIS or IR, has to be above the threshold value. In order to calculate cloud properties, such as cloud top pressure and optical thickness, an atmospheric radiative transfer model is used. A number of assumptions are made, such as that all properties are spatially uniform and completetly covering the pixel and that clouds are single thin layers (no vertical tempreature gradient). First the surface temperature and surface reflectance is calculated from the clear sky value. Once this is known the vertical structure of the atmosphere at the given pixel is also known with help from the model. The next step is then to compare the values from cloudy pixels. Using both the IR and VIS reflected radiance cloud top temperature is derived as well as cloud optical thickness (τ). Using the radiative transfer model, the cloud top temperature is converted into cloud top pressure. Since cloud optical thickness is calculated using VIS this data is only availble during the day. The pixels are now mapped into a grid, where each grid cell is 280×280 km 2. Besides cloud top pressure and cloud optical thickness, each cell is labeled as being over land, water or coast. If the grid cell’s land fraction is ≥ 65% it is labeled land, if its land fraction is ≤ 35% it is labeled water and if it is inbetween it is labeled coast. Pixels are also labeled as day or night, but since cloud optical thickness is required to construct the CTP-τ diagrams explained in Section 3.2 this is not important in this thesis.

3.2 Cluster regimes

With the information about cloud top pressure and cloud optical thickness for each pixel in a grid box available, the different characteristics of the cloud fields within a the grid box can be investigated. This is more easily understood by plotting the data in a CTP-τ diagram, where CTP is Cloud Top Pressure and τ is cloud optical thickness (see below). These diagrams then form the basis for the application of a cluster algorithm to define recurring cloud regimes.

3.2.1 CTP-τ diagram The CTP-τ diagram is a box-histogram plot. Each pixel in a grid cell will have a certain cloud top pressure and cloud optical thickness associated with it every three hours, which results in several pairs of data during a day (varies since daylight varies with time). The number of pixels in the grid-cell and over three hours in each combined CTP-τ class can then be counted. Dividing by the total number of pixels in the grid cell (clear or cloudy) then provides the relative

10 fraction of pixels of a certain CTP-τ combination. This can then be plotted in a diagram as shown in Figure 3.1. The y-axis contains seven levels between ≤ 180 hPa and ≥ 800 hPa and gives information about the height where the cloud top is situated. The x-axis has 6 boxes with τ from 0.02 − 60 ≤ where each step represent a 15% − 20% increase in albedo.

Figure 3.1: A CTP-τ diagram showing the cloud top pressure on the y -axis and the cloud optical thickness on the x -axis. This box histogram shows where the cloud top are located and how thick they are.

Data for a certain day and grid box will occupy one or more boxes in the diagram representing its physical properties. Figure 3.1 shows the total number of occurrences for a regime over the entire region and for the entire time period. Several boxes contain data and it is most intense in the top left corner with a cloud top pressure less than 180 hPa and τ in 0.02 − 1.3. This means that the clouds represented in the diagram are high up in the troposphere (low cloud top pressure) and quite thin (low optical thickness). This part of the CTP-τ diagram therefore represents a cirrus cloud. Clouds that are situated to the left in the diagram are thin, clouds situated to the right are opaque, and a higher position vertically represents a higher altitude of the cloud top. Exactly what altitude it is depends on the current conditions but as guidance ≥ 800 hPa is about 2 km and lower, and ≤ 180 hPa is well above 10 km. The diagram gives a easy view of low top, middle top and high top clouds, as well as their optical

11 thickness. This means that it is possible to get a statistical view of a physical phenomenon. On top of the diagram the total cloud cover, TCC, is shown. TCC is a measure of how big fraction of the sky that is covered by clouds at the given moment. This is calculated by taking the integral over the CTP-τ diagram.

3.2.2 Anderberg k-means clustering algorithm Cluster algorithms are used to identify data points that are ”close to each other” and ”far from other data points” in a data set. For example, in Figure 3.2 it is clear that data points 1 and 6 form a cluster, 3, 4 and 5 another one and 2, 7 and 8 a third one. They are all linked together by the shortest distance to their centroid value. Instead of 8 data points to compare data with, three clusters can be analyzed.

Figure 3.2: Three clusters of data. The data in the three groups are connected together by having the shortest distance to a centroid.

Hence, to form clusters one has to measure the ”distance” between the points in a dataset and ﬁnd those points that are closer to each other than to other points. This is the way the k -means cluster algorithm works (Anderberg, 1973). Each day for every grid point the CTP- τ data are used giving m numbers of data points (each ”data point” is a vector of length 42, containing the frequencies of occurrence of the 7×6 CTP- τ classes). A predeﬁned number of sought of k clusters are to be decided. To start the algorithm k data points are randomly chosen from the data set and used as centroids for the k clusters. The remaining m − k data points are assigned to their nearest centroid by calculating the Euclidean distance of the vector to each centroid. Once this is done a new centroid is calculated for each cluster, including the data assigned to it in the

12 previous step. This process is then repeated until a satisfactory result has been determined, i.e., when data points do not change the cluster they belong to. Since the number of clusters must be predefined by the user, the method is somewhat subjective. There are, however, ways to lower this influence. The algorithm is run for several different number of clusters. As the clusters become more, they will start to have similarities with each other. The correlation can then be checked between the data to see how similar they are to each other. For the D1 dataset and the region used, it has been found that 8 clusters optimally describe the data set. Each of these eight clusters’ centroid diagram can be seen in Figure 3.3.

3.3 The eight regimes

Even though the cluster algorithm resulted in eight diﬀerent regimes there are some physical similarities between some of them. Over all there are two groups of three similar regimes, one with convective clouds and one with stratocumulus layers, leaving two remaining regimes, one a cirrus regime and the other a clear sky/fair weather cumulus regime. The three convective regimes are Regime 2 (Figure 3.3b), which are convective active active cirrus clouds (CC), Regime 5 (Figure 3.3e), which are convectivly active deep clouds (CD) and Regime 6 (Figure 3.3f), which is a mixture between the two previous ones (MIX). The CC regime is made up of high top, optically thin, deep clouds, whereas the CD regime also has high top, deep clouds but is less optically thin. The CTP- τ diagram for the MIX regime has a wider spread of cloud top pressure and optical thickness over the entire diagram and no real clear point where there are most occurrences for this regime. But there are still deep clouds making it to be a mixture of diﬀerent cloud types where there is convection. The three regimes have a TCC in the interval 0.79 − 0.95. The three stratocumulus regimes, having a TCC between 0.62 and 0.86, are Regime 1 (Figure 3.3a), which is made up of supressed thin low top clouds with medium optical thickness, here called SC1. The second one is Regime 4 (Figure 3.3d), stratocumuli clouds (SC2), and the third one is Regime 8 (Fig- ure (3.3h), which is also a stratocumuli regime (SC3). Both of the latter ones contain less optically thin low top clouds than SC1. In SC3, cloud top pressure and optical thickness are not as spread out as in SC2. Regime 7 (Figure 3.3g) is a supressed thin cirrus regime (STC), which holds a notably large amount of clouds in the top left box of its CTP- τ diagram. It is likely (Singh and Jakob, 2010) that most clouds that are undetermined by the ISCCP algorithm are supressed thin cirrus clouds and these are then binned in the top left box of the CTP- τ diagram and hence grouped into this regime. This would also explain why the other regimes often contain slightly more clouds in the top left box in their CTP- τ diagrams. But this presents a certain source of error, since it is not known how many undetermined clouds that are binned into this box and if there are any trends in this. The STC regime has a TCC

13 of 0.68. The last regime is Regime 3 (Figure 3.3c). This is fair weather conditions optically thin clouds or clear sky (in this study called FW). This also means that it has the lowest TCC of only 0.25. The clouds are mostly low top clouds, for instance, cumulus humilis clouds. The eight cloud regimes described in this section form the basis of the lifetime analysis carried out in this thesis. Each grid cell between latitude 32.5 N and 32.5 S for each day between January 1985 and December 2006 is assigned to one of the eight regimes. Studying the number of days a particular grid cell remains in the same regime, as well as transitions between the regimes, then allows us to gain insight into the geographical and temporal distribution of regime lifetime. This will be the subject of the next section.

(a) Regime 1 - SC1 (b) Regime 2 - CC

Figure 3.3: CTP- τ diagram of four of the eight cloud regimes. The y -axis shows the cloud top pressure and the x -axis shows the cloud optical thickness. Data from each gridcell, everyday, are assigned to one of the 42 boxes.

14 (e) Regime 5 - CD (f) Regime 6 - MIX

(g) Regime 7 - STC (h) Regime 8 - SC3

15 16 Chapter 4

Cloud regime lifetime

4.1 Global results

The lifetime of a regime is deﬁned as the number of consecutive days a regime occur at a speciﬁc grid cell.

Figure 4.1: Lifetime for the eight regimes. The diagram shows the total number of days spent in a spell of certain length versus the spell length.

17 First the lifetime for the entire region, latitude ±32.5◦ and longitude 0−360◦, and for the entire time, 1 January 1985 to 31 December 2006, is calculated. Since the time period is defined it is also of importance to define when a regime ends to know whether or not it ended within the time period. A regime is said to end once a new regime occurs at the grid cell. For example, if Regime A occurs for the first time in a grid cell on the January 1 and on the second Regime B occurs at the same grid cell, it is said that Regime A was one day long and it ended on the January 2. If a spell of days for a certain regime and grid cell stretches across two month it is said to end in the month when a new regime occurs in that grid cell. For example, if Regime A starts on January 21, 1985 and a new regime occurs at that grid cell on the February 1 it said that Regime A was 10 days long and ended in February. Since the time period for this study is January 1 1985 to December 31 2006 this means that data from 1984 has to be used in order to check if any spell stretches back from 1984 into 1985. This is not done for 2006 and 2007 since it is of no interest to know if a regime ended in 2007 for this study. The statistical significance for this is probably small and can be neglected. The result for the entire region is shown is Figure 4.1. The plot is constructed so that every occurrence of spells that live for, e.g., ten days is represented by the total number of days a grid cell was in that spell. The x -axis shows how long the spells are (in this case ten days). The y -axis shows the total number of days spent in spells of a particular length. For example, 15 ten day spells is represented by a y -value of 150 and an x -value of 10. The plot has a logarithmic y -axis. It is also divided with two different logarithmic y -scales in order to get a better view of what happens where the lines are very close to each other. The same plot is available in the Appendix A but on a linear y -scale instead of a logarithmic. From Figure 4.1 it looks as if two convective regime, CC and CD, have the least number of days the longer the lifetime is. One regime, FW, stands out from the other with many occurrence well beyond a lifetime of 30 days. Inbetween these a group of four regimes can be found, SC1, MIX, STC and SC3. Between this group and the one with the two convective regimes, the SC2 regime can be found. It is worth noting that FW and MIX hold the highest number days for one day spells, followed by SC2 and then by CC, STC and SC3 close together. CD and SC1 have the least number of one day spell occurrences. So even though SC1 has the least number of one day spells, it has more days of long-lived spells than CC, CD and SC2. One possible explanation for the large difference in days spent in say the FW regime versus the CD regime could be that the FW regime occurs much more frequently (in space and time) than the CD regime. This will be investigated in the following.

18 Table 4.1: Relative frequency of occurrence of the eight regimes.

Regime Relative frequency of occurrence (%) SC1 3 CC 9 FW 36 SC2 11 CD 5 MIX 14 STC 12 SC3 10

Table 4.1 shows the overall frequency of occurrence of the eight regimes for the entire dataset. The FW regime stands out being the most common, something that would have been expected by looking at Figure 4.1. The CD regime on the other hand is a rare regime. Given the large difference in the frequency of occurrence between the regimes, the data displayed in Figure 4.1 for each regime are normalized by the frequency of occurrence of the regime. The resulting curves are shown in Figure 4.2. As a result of the normalization described above, the area under each curve in Figure 4.2 adds up to one. This has the advantage that the lifetime of the regimes can be compared without the influence of how frequent a regime is. It also leads to another opportunity. Now that all curves are normalized in the same way, a curve fit can be calculated and the parameters of the fitted function provide a simple way of comparing the different shapes of the curves. The curve fit is calculated using Matlab’s curve fitting routine fit. It is pro- grammed to look for an exponential function to the curves. No special method, e. g., nearest interpolant or linear least square fit, is used. An exponential function is sought first of all because of the shape of the curves, but also because it is easier to compare one parameter for each curve than several, which would be the case if a Fourier series would be used to describe the curve. Several different curve fits were tried in order to check if they gave a better result (lower root- mean-square error), but it was shown that the exponential fit gave an adequate result. To avoid problems with the fitting of the exponential functions resulting from the values at long lifetimes, the tails of the curves were removed by only including the first 90% of the curve area. The curve fit yields an equation of the form y = αeβx, where β describes how the curve is shaped and α is a scalar that adjusts the position on the y -axis. To compare the lifetime or how rapidly the the number of days decreases as the lifetime increases, it is possible to use the only the β value between the different regimes, since the α value does not affect this property for the curves. A low negative β value means that the curve has a long slope, i.e., a significant fraction of occurrences of long lifetimes. A high negative β value means and that the curve has a steep slope and that the regime is dominated by short lifetimes.

19 Figure 4.2: Lifetime of the eight regimes normalized to one. The y -axis shows the fraction of time spent in a certain spell length. The x-axis represents the spell length.

20 Figure 4.3: β values for the eight cloud regimes. The β value describes the slopes of the normalized curves, and thus, how long-lived the regimes are.

The normalized plot, Figure 4.2, gives a different view than before. Instead of showing the highest frequency of occurrence for all lifetimes, the FW regime now dominates the long lifetimes, but is in fact the least frequent (in a relative sense) at short lifetimes. Instead it is now the three convective regimes that have the shortest lifetime with the remaining four in between. Figure 4.3 confirms the result from the the normalized plot. The FW regime has a the smallest negative β value in comparision to the other regimes. The three convective regimes, CC, CD and MIX, have the lowest values of them all. SC1, SC2, SC3 and STC have slightly higher values than the convective regimes, where STC has the highest value of the four. Once again this shows that the FW regime is the most long-lived of the eight, while CC and CD are the ones with the shortest lifetime. To see how the β value is distributed geographically, the individual β value for each grid cell and each regime is plotted. The results are shown in Figure 4.4. Since some grid cells contain no or too little information to make a curve fit, these grid cells are then assigned with β = −8 (the lowest β value on the scale).

21 (a) Regime 1 to 4

Figure 4.4: β values for the eight regimes. A β value is calculated, from a normalized curve, for each grid cell between latitude 32.5 N and 32.5 S. Grid cells where there are insuﬃcient amounts of data to make a curve ﬁt are assigned β = −8.

22 (b) Regime 5 to 8

23 The black areas in Figure 4.4 are grid cells with rapid decline in lifetime or where there are not enough data to calculate a β value. For the SC1 regime large areas of the map are dominated by this type of area, with hints of whiter areas at some locations. For the other two stratocumuli regimes, the black areas are not as dominant. Instead they are evenly distributed over the region, with only small areas where the lifetime is longer. The CC regime has an evenly distributed β value over the region only with slightly lower β value over certain areas. The CD regime shows some black areas whereas the MIX regime does not. The most long-lived regime from the previous results, the FW regime, shows low β values over the entire region. In order to get another point of comparison, the mean length lifetime for a spell is calculated. However, the curves from Figure 4.2 representing the lifetime for the eight regimes, look exponential and a mean might be not an appropriate measurement of the lifetime. Although it may not say anything about the lifetime, a mean can be a good landmark for comparison between the eight regimes. But more importantly it will also tell us something about the geographical distibution of the regimes.

24 Figure 4.5: The mean length lifetime for a spell at each grid cell. The maps show the mean lifetime for Regime 1 to 4, between latitude 32.5 N and 32.5 S. The maps are centered over the West Paciﬁc, a region of interest for the convective regimes.

25 Figure 4.6: The mean length lifetime for a spell at each grid cell. The maps show the mean lifetime for Regime 5 to 8, between latitude 32.5 N and 32.5 S. The maps are centered over the West Paciﬁc, a region of interest for the convective regimes.

26 As seen in Figure 4.5 and Figure 4.6, the mean lifetime is short, and rarely goes above five days. This comes as no surpise because of the exponential look of the curves. Mostly the mean is around two to three days except for FW where there are large regions over the Pacific and Africa with the mean is five days or higher. For SC1 there are some regions over Indonesia and Africa, where there are no data availible. It also has two small regions where the mean is around five days, off the coast of Peru, Namibia and California. SC2 seems to have an increased mean slightly west to those of SC1. The MIX regime has a small number of increased mean lifetime around Kenya, central Asia and northwest South America. STC has an increased mean of around four days around Chile, whereas the remaining regimes seem to be pretty evenly distributed with no real areas where the mean is significantly higher. In Figure 4.5 and Figure 4.6 the mean lifetime is around two days for most places and most regimes and on rare occasions it goes above five days. To further compare the lifetime it would then be appropriate to see how many spells that is longer than two days, five days and ten days. The last limit, ten days or longer, is to see how many percent of the regime that are really long-lived.

Table 4.2: Spells longer than 2, 5 and 10 days for the eight regimes.

Percent longer than Regime 2 days 5 days 10 days SC1 62.7 21.4 6.8 CC 51.2 6.9 0.4 FW 83.1 43.9 18.5 SC2 56.4 10.1 1.1 CD 49.8 6.3 0.4 MIX 53.2 8.7 1.5 STC 65.1 18.3 3.5 SC3 63.1 16.6 3.3

Once again it is the FW regime that has the most long lived spells. For the FW regime, 83.1% of the spells live longer than two days. A large fraction of the spells live longer than five and ten days as well. In comparison, the CC and CD regimes are again the shortest-lived with only about 50% of the spells being longer than two days. Only 0.4% of the spells for the two regimes are longer than ten days. They are accompanied by the MIX regime with similar fractions. Looking at the stratocumuli regimes, SC2 has a slightly higher fraction of cases longer than two and five days than MIX, but when comparing how many percent live longer than ten days, SC2 has a lower fraction than MIX. SC1, STC and SC3 all have around 60%−65% of their spells longer lived than two days. While the SC1 regime has the lowest percentage of the three living longer than two days it has the highest percentage with spells longer than ten days. These result give a slightly different view on things from what the β values did in Figure 4.3. Again the FW regime is the most long lived one of them all, but here it is the

27 SC1 regime that is the second longest lived regime followed by STC. To see if this changes, test were performed to see how many percent that were longer than 20 and 50 days as well. This did not change the outcome. So far it looks like there are some groups of regimes that seem to have similar lifetime properties. The FW regime is by itself as it is the most long- lived, while the three convective regimes are a group because of their short lifetime. Inbetween these two groups are the remaining four regimes. It would be interesting to see if there is any link between the diﬀerent regimes. Is it for example more likely that the following regime is from the same group? To investigate this, the probability of transition is calculated. At every grid cell, for the entire period, the current regime is registered as well as the following. It is then a simple matter to collect all the ones for Regime A and looking at how many of Regime B, Regime C etc. followed it the next day. Of course the possibility that Regime A follows itself must also be taken into account. No respect has been taken for how frequent diﬀerent regimes are. But since the probability is calculated with respect to the total occurrence of each regime (see Equation 4.1), it is not necessary to normalize the results any further.

Number of times Regime X followed Regime A P robability = (4.1) T otal number of occurrences of Regime A This means that the result for each regime is independent of the other in the sence of how frequent they are. However, since more frequent regimes have a higher probability of having longer spells this will increase the probability of the following regime being the same as the current. For instance, if a spell occurs for 20 days for Regime A, this will add the 19 occurrences to Regime A being the regime following Regime A. How much this will inﬂuence the results is hard to say, but most of the regimes have very few long lived spells and will probably wont aﬀects results to any great extent.

Table 4.3: Probability of transition for the eight regimes.

Current Next regime (%) regime SC1 CC FW SC2 CD MIX STC SC3 SC1 42.4 0.8 6.5 27.2 0.6 6.0 1.3 15.3 CC 0.2 31.1 13.7 3.5 14.5 20.9 13.5 2.5 FW 0.7 3.7 62.3 7.5 1.4 8.1 9.0 7.3 SC2 7.4 3.0 23.5 35.3 1.9 12.7 3.8 12.5 CD 0.5 19.9 8.6 4.3 29.8 24.1 9.2 3.8 MIX 1.2 12.2 19.8 9.9 8.9 33.3 8.0 6.5 STC 0.3 10.3 27.9 3.0 4.1 8.9 43.5 2.0 SC3 5.7 2.2 25.2 14.4 1.2 7.5 2.2 41.5

Table 4.3 shows the transition probabilities for each regime. Not surprisingly,

28 the diagonal, which indicates the probability of the next day being in the same regime as today, is the most likely. Once again, to no surprise, it is the the FW regime that holds the highest chance (62.3%) of being the same regime tomorrow as it is today, far greater than the regime with second highest chance, the STC regime with 43.5%. The three convective regimes are again a group, with a probability of around 30% of being in the same regime tomorrow as they are today. And the SC2 regime finds itself between the convective regimes and the group with the other two stratocumuli regimes. Looking at the four different groups defined above we now investigate the probability that the next regime is one from the same group. Let us start with the group of the SC1, STC and SC3 regimes. For the SC1 regime, after having itself as the highest probability, it is the SC2 regime that has the second highest probability of showing up at the same grid cell a day later. The SC3 regime has the third highest probability, while the STC regime has the sixth highest probability with only a 1.3% chance of being the next regime. This suggests that rather then having the lifetime binding the regimes together, it is here the physical properties that increases or decreases the probability of being the following regime. This is further demonstrated by the STC regime, where the stratocumuli regimes have a low probability of being the following regime, while the FW regime has a high chance. Looking at the last regime in the group SC3, one would expect that the other two stratocumuli regimes are most likely to follow it. This is not the case though. Although SC1 has quite a high chance of being the next one defined above, it is not the second highest probabilty, which is held by the FW regime. The SC1 regime has only a 5.6% chance of being the next regime after SC3. This is in contradiction to what would have been expected after looking at the SC1 regime. Now let us look closer at the SC2 regime and see if the results are the same. The most common regime to follow SC2 after itself is the FW regime. The other two stratocumuli regimes have 7.4% and 12.5% chance, less than the MIX regime. The remaining three regimes have a probability that ranges from 1.9% − 3.8%. Even though their probability is small, it is not as small as in some of the other regimes and also in comparison to the rest of the probabilities for SC2. This might suggest that the SC2 regime is a transition regime, primarily between the two stratocumuli regimes to the FW regime. This is further supported by the fact that the SC1 and SC3 regimes are likely to transform into the SC2 regime, but the probability of transition is not as strong the other way around. The three convective regimes all possesses the lowest probability of being the same regime the following day. At the grid cell where a convective regimes is found, there is a high chance of finding a convective regime the following day. This is true for all three converctive regimes. The CC regime is most likely to transform into the MIX regime followed by the CD regime. However, the chance is almost the same for the CD regime and the FW regime. For the CD regime the other two convective regimes are heavily favoured and the FW regime has a fairly low chance. For the MIX regime, even though there there is a fairly high chance of finding a convective regime the following day, there is a higher chance of finding the FW or the SC2 regime. Given the probabilities of the other two convective regimes and their chance of transition into the MIX regime this

29 suggests that the MIX regime is what the SC2 regime is for the stratocumuli regimes, a step on the way to another regime. Table 4.3 showed the probability of what the next regime would be at any given time. It also showed that there are some links between the regimes. Some regimes with similiar physical properties are more likely to follow each other. But as time goes the physical properties at a given grid cell are likely to change or evolve. We now extend our analysis of transition probability to include the length of the spell a grid point was in a particular regime before making a transition. To easier understand how this is calculated, imagine that all spells for a regime (say, Regime A) are lined up vertically next to each other. One day spells at the top and long day spells further down. To further enhance this image, let the length of the spells, i.e., the number of days, be represented by a bar, going horizontally to the right. Now let us see what the following regimes are. Start at the one day spells and look what the following regime are at that grid cell. Since the spells are already lined up according to their length it cannot be Regime A again. However, all the spell that are two days or longer will add to the count for Regime A being the following regime. Continue with the two day spells, and so on and so forth. This means that there can only be a different regime following when there exists a spell of a certain length. As the spell length gets longer the plots will get noisier. Longer spells means fewer spells, which means that a shifting between two spells has a greater influence than before. The figures below shows how the probability changes between one and 30 days for the three convective regimes. The plots for the remaining five regimes can be found in Appendix B.

30 (a) CC

Figure 4.7: Probability of transition and how it changes with respect to spell length for the three convective regimes. The y-axis shows the probability and the x-axis shows the spell length.

31 (b) CD

Figure 4.7: Probability of transition and how it changes with respect to spell length for the three convective regimes. The y-axis shows the probability and the x-axis shows the spell length. 32 Figure 4.7 shows how the probability changes as the spells get longer. As explained above, the plot only shows transitions to a new regime as a function of the length of spell for the current regime. Starting with the CC regime, the MIX regime is the most likely to follow it when the spell length is short (less than five days). This is in line with the results from Table 4.3 with the MIX regime being the most likely to follow, excluding the CC regime itself. The probability for the CD, STC and FW regimes being the next starts at roughly the same chance. However, these split up fast. The STC and FW regime following each other in a steady decline whereas the chance for the CD regime increases to being around the same as for the MIX regime. Around 15 days the results start to become too noisy and should be discarded. The results look similiar for the CD regime with the MIX regime being the most likely successor when the spell length is short, in this case only a few days. However, quickly this is changed and the CC regime becomes the regime with highest chance of following CD at a given grid cell. For the MIX regime, the probability of the CD regime seems to increase with the length of spell of the MIX regime up to about 5 days, after which it decreases. Looking at Figure 4.7c one might ask what is the reason for the decreasing probability of the FW regime as the lifetime increases, while the two convective regimes seem to become more and more likely spell length increases. This could be the result of the geographical variation of the frequency of convection in general. If one looks, for instance, at the tropical Western Pacific where there are a lot of convection occurring. There is also a high chance of one of the regimes being a convective regime. This means that even in this area there is a high chance of finding a convective regime, while there is also a higher chance of the regimes being longer. Hence the probability for the next regime being a convective regime would be fairly high even at spells with the length of several days. Looking at a different area that does not have so much convection and instead often more stable air. If a convective regime occurs there, where it is not so common, it is more likely that spells are shorter, and the following regime being a more stabled air regime like the FW for instance. A couple of different ways of looking at the lifetime have been tested so far. And though the results are similar there are some important differences. It has been mentioned before that some results are due to the different relative frequency of occurrence the regimes have. A method that does not have this problem is the comparison between the β values because of the normalization. It is also a method that gives a straightforeward result, and it is in turn easy to compare. So far, it has been shown that there is a distinct difference in lifetime between the different regimes. Figure 4.5 and Figure 4.6 also gave a hint that the lifetime varies in different regions. This is not surprising at all, given the different physical properties a regimes possesses. A regime that is more common in one place would also more likely have a longer lifetime in that area. Two particulary interesting regions to look at would be grid cells over land compared to grid cells over water. This should yield an interesting result, given the difference in the diurnal cycle of the surface forcing, as well as in the amount of water available, and hence the possiblities of cloud formation in the different areas.

33 To investigate land-sea diﬀerences the data are divided into two groups, one containg all the data for the grid cells over water and the other one containing all the data for the grid cells over land. The data is then normalized to one in each group and the curve ﬁtting routine is applied to the normalized data. Figure 4.8 below show the β value for each regime both over land and over sea, as well as for the entire region (which was calculated earlier) to get a point of reference to compare to.

Figure 4.8: β values for the eight regimes over land, over sea and for the entire region. The β value describes the slope of the lifetime curves. A lower β value means a shorter lifetime.

Looking at Figure 4.8 there are four regimes that have a diﬀerent lifetime over land from that over water. These are two convective regimes, CC and CD, and two stratocumuli regimes, SC1 and SC2. To get an understanding why this is let us get back to Figure 4.5 and Figure 4.6. These four regimes had a higher mean length lifetime over certain areas of ocean, which it its turn mean that they are more common over oceans and would therefore have a shorter lifetime over land. But why is this? Starting with the stratocumuli regimes, these are cloud types that in general are found over oceans and areas where there is moisture, i.e., access to water vapour to form clouds. Looking at the convective cloud types, their short lifetime over land does not come as a surprise either. As mentioned before, the tropical latitudes over the Earth is a place where much

34 convection takes place. The CC and the CD regime are common over places with warm water (Figure 4.5 and Figure 4.6). Water has a high specific heat capacity, which means that temperature variations from day to day are small. This means that when convection occurs it will likely do so for longer. Water availablility is more sparse over land and the temperature differences are greater as well. This means that convection will occur much more sporadic and for a shorter time. But why is the third convective regime not more long-lived over sea than over land. To understand why, again a look at the mean length is necessary. Remember that most of the places where the MIX regime had a high mean lifetime were over areas with high altitudes. Since the MIX regime is a middle/high top cloud regime clouds at these places are probably grouped into this regimes because of their cloud top pressure even though their physical properties are different from those grouped into the MIX regime say over the ocean. For instance, a cloud that is a couple of kilometres above the surface over the land at sea surface level might have been grouped into the SC3 regime. But a cloud at the same distance over land at a high surface altitude might be grouped into the MIX regime. The remaining three regimes, FW, STC and SC3, all have small differences in β value. The previous discussion and results show that there is a difference in β value depending on where the regimes are occurring. To further examine where different regimes are more common the total number of days a regime occur at a specific grid point is examined. This should give a similiar result to the mean length that was shown in Figure 4.5 and Figure 4.6. The difference is that, whereas the spell length was used to measure the mean length, here it is the total number of days that is the base for this plot. It is probable, in line with previous discussions, that areas with a lot of occurrences also have a longer mean lifetime and hence also mean length lifetime. Thus the areas where regimes are common and have many days of occurrences are also the areas where the mean length lifetime is higher.

35 (a) Regime 1-4

Figure 4.9: Total number of days a regime occurs at a grid cell from latitude 32.5 N to 32.5 S.

36 (b) Regime 5-8

Figure 4.9: Total number of days a regime occurs at a grid cell from latitude 32.5 N to 32.5 S.

37 Beginning with the SC1 regime, it appears to be more occurring in areas of cold water and with almost no occurrences over land. It also seems to be more frequent in subtropical areas than in the tropics. This makes sence since the SC1 regime is composed of shallow and low clouds with not much vertical devlopment and should therefore be more likely to appear in areas where there is stable air, such as over cold oceans. The CC regime does not have the same intense areas as the SC1 regime. However, there is a rather large area around the Western Pacific and Eastern Indian Ocean, where the CC is quite common. Again this might be expected since this is an area with a lot of convection. The FW regime is the most common occurring regime, something that is again evident when looking at Figure 4.9. It is more common in the subtropics over dry areas such as the Sahara, but over the oceans as well. Again this is perhaps an expected distribution, since it is the clear sky and fair weather cumulus regime, which should be more common in dry areas. Over the oceans this is as clear as the sky can get, with the all the water availible for evaporation. The SC2 regime appear around the same areas as the SC1 regime, as well as slightly west of it. Since it is a similar regime with a bit more vertical development this makes sence. It is also worth keeping in mind that the SC2 regime is likely to be the regime following the SC1 regime at a grid cell. With this in mind it is possible to explain why it is situated slightly to the west of the SC1 regime. The tradewinds are blowing westward around the Earth and the SC1 regime would then move to the west as it gets older, and the chance of it becoming an SC2 regime would also be fairly high. The CD regime is, like the CC regime, common around the Maritime Continent. It not as common as the CC regime, but as expected it is appearing around places where convection is known to take place. The final convective regime, MIX, has a fair amount of days around areas where convection is known to take place, predominatly in the tropics. But it is as mentioned before also common around areas at high altitude like the Andes and the Himalayas. It is worth noting that around these two areas no other regime is very common, further confirming that it is an inherited feature in selecting cloud tops by pressure rather than height above the surface. The STC regime is widespread but not as common over the East Pacific and the Sahara. The SC2 regime is also quite wide spread over the globe. However, there are certain areas that seem to have a higher concentration of the SC3 regime. As with SC2 regime, the SC3 regime was likely to follow the SC1 regime and the regions of increased concentration are around the areas where the SC1 regime was common. As the different results showed when the lifetime was compared for the grid cells over land and over water it would, with this new knowledge of where the regimes are more common, be a good thing to compare the lifetime for different areas as well. Two natural areas to explore would be the tropics and the subtropics. But the Pacific would be of great interest as well, given the convective feutures of the West Pacific and the colder water in the east.

38 4.2 Tropics

Since the convective regimes are occurring more here they are probably also more long-lived. The opposite can be said for the SC1 regime since it is not as common in the tropics. Before making any calculations, what is regarded as the tropics must be defined. It is here set to be latitude ±15◦. The grid map previously used has been irregular, meaning that a grid cell with data at a certain latitude does not necessarly align, longitude-wise, with the grid cell at the latitude above. Although this is not initially a problem, since the tropics is a region defined by a straight latitude boundary, it will eventually become a problem when comparing different regions that are defined with a longitude. For the of sake simplicity the regular grid will from now on be used. Each grid cell in the regular grid is 2.5◦ × 2.5◦ ranging from 32.5◦N to 32.5◦S around the globe. The distance from the centre of each grid cell in the new grid is measured to the centre of every grid cell in the irregular grid. The irregular grid cell is then assigned with the data from the regular grid cell with the shortest distance to it. Figure 4.10 shows the β value for land and sea data in the tropics. The β value is calculated like it has been done in previous sections. Later on these β values will be compared with the ones from the subtropics as well, but for now let us just focus on the difference between land and sea in this plot. In Appendix C a table of transition probabilities for this region is also included. There are differences compared to the entire region but they are relatively small. All regimes except the MIX regime show a lower β value over land than over sea, which means that they have a shorter lifetime over land than over sea. Some of these differences can most probably be due to the lower fraction of land in the tropics. But let us focus on the two convective regimes, the CC and the CD. The CD regime shows a clear difference in the β value over land and over ocean. The same goes for the CC regime, interestingly, the sea value is almost the same when compared to the entire region for both the regimes. The results are interesting because even though there is a lower fraction of land than water in the tropics, the two convective regimes appear over areas known to have lot of convection, like the Amazon rainforest. This would imply that there is a difference in the lifetime, just as Figure 4.8 showed, between regimes over land and over sea. Given the low fraction of land data that are available, the question arises if the results are useful at all, and also if a comparison between regions with different amount of data are even possible. There are roughly 12 million events, meaning that even if a regime would only have a RFO of 1% it would still leave more than 100, 000 events, or datapoints that are the base for the results. This should be more than enough to get a result that can be used.

39 Figure 4.10: β value for data over land and sea in the tropics. The β value is calculated from making a curve ﬁt on the lifetimes curves of the regimes. A lower β value, mean that the curve has a rapide regression. This means that the regime has a shorter lifetime.

4.3 Subtropics

The subtropical region is deﬁned as 15◦ − 32.5◦N and 15◦ − 32.5◦S. Since the SC1 and SC2 regime were common in the subtropics these should be of interest. It could be expected, as well that these two regimes have a longer lifetime in the subtropics than they have in the tropics. Figure 4.11 shows the result for the subtropics. The two stratocumuli regimes, SC1 and SC2, both have a diﬀerence in lifetime between land and sea, just like the the CC and the CD regime. The SC1 and SC2 regimes were common over water and also in the subtropics, so this is in line with previous results. It comes as no surprise that the two convective regimes are short-lived over land in subtropical areas since these are dry areas with low convection.

40 Figure 4.11: β value for land and sea in the subtropics. The β value is calculated from making a curve ﬁt on the lifetimes curves of the regimes. A lower β value, mean that the curve has a rapide regression. This means that the regime has a shorter lifetime.

How does these two regions, subtropics and tropics, compare to each other? Although the subtropical region is larger than the tropical region, the discussion held in Section 4.3 argued that the sizes, or the rather the amount of data, for the regions should be enough and not necessarly contribute to shifting the result. But even though this still can be a factor, the argument here is that a smaller area does not necessarly mean a lower β value. Nevertheless, care must be taken when interpreting the results. A better comparison might be done by looking at the diﬀerent regimes, like the CD and MIX regime in Figure 4.12. For the CD regime the β value is lower in the tropics than the subtropics. However, for the MIX regime it is the other way around. It is not possible to say that the MIX regime is an artefact from two sets of data that is smallar than a third. Especially since the subtropical region is larger but the β value is lower. The point is that it might be wise to see the trend for a region and all the regimes and then compare this with the trend for another region. For the CD and MIX regimes the trend was a higher β value for the MIX regime in the tropics compared to the CD regime. In the subtopics this was altered and the MIX regime now has a lower β value.

41 Figure 4.12: β value for entire region, tropics and subtropics. The β value describes the slope of the lifetime curve for a regime. A lower β value means that the lifetime is there are few long-lived spells, hence the lifetime is shorter.

The shorter lifetime in the subtropics for the MIX regime and the CC regime is expected. However, for the third convective regime, CD, it shows signs of a longer lifetime in the subtropics.

4.4 The Pacific 4.4.1 Tropic Pacific The Pacific is a region of much diversity. The Eastern Pacific has a relatively low sea surface temperature while the Western Pacific contains a much warmer pool of water. It is therefore a good idea to divide the Pacific into different regions. Here three equally large regions are defined, the Western Pacific at longitude 115◦ − 170◦, the Central Pacific at 170◦ − 225◦ and the East Pacific at 225◦ − 280◦. Since the region of interest is the Pacific, a special concern must be made about the influence of El NiñoSouthern Oscilation, ENSO, in this region. Looked at from a global point of view an ENSO year did not seems to influence, relative frequency of occurrence, RFO, or the lifetime of the regimes. But given the shift of the tropical warm pool this might not be the case when

42 looking at the Pacific alone, and especially when subdividing it by longitude. Two particulary strong ENSO year are used, one for the warm phase, El Niño, and one for the cold phase, La Niña.The test showed that there seems to be a difference in RFO in the different parts of the Pacific, but the data are mostly too noisy to draw any conclusions of how the lifetime is affected.

43 (a) CC

(b) CD

Figure 4.13: The lifetime curves, normalized to one, for the three convective regimes over tropical the Paciﬁc. The three lines represent the East, Central and West Paciﬁc. The x-axis shows the spell length and the y-axis the fraction of time spent in a certain spell length. 44 (c) MIX

Figure 4.13 shows that there is a difference in lifetime for the CC regime. The regime has shorter lifetime in the East Pacific than the Central and West Pacific. This comes as no surprise since the CC regime is very rare in the East Pacific. The FW regime (availible in Appendix D) has an interesting peak at 2 days in the Central Pacific. This means that a two day spell is more common than a one day spell for a regime. However, after the two day spell the decrease in lifetime is about the same as in the East and West Pacific. Given the scarce data, together with the water-land fraction in the region, a comparison between the regimes over land and sea are not possible.

4.4.2 Subtropic Pacific The subtropical Pacific is defined by the same longitudinal borders as the tropic Pacific. Probabilities and a comparsion with land and water areas were calculated but discared as it they were too noisy. Figure 4.14 shows the normalized plot of the SC1 regime. In Appendix D the normalized plot for the FW regime can be found.

45 Figure 4.14: Normalized plot of the lifetime curves in the subtropic Paciﬁc for the SC1 regime. The region divided into three equally large areas, The East, Central and West Paciﬁc, represented by the three curves. The x-axis shows the spell length and the y-axis the fraction of time spent in a certain spell length.

For the FW regime a similar peak of two days is found, as in the tropical Central Pacific. This time the peak is also present in the West Pacific, as well as the Central. The FW regime has a high RFO in the Pacific, especially in the West and Central part, so the result is not surprising. The SC1 regime shows a decrease in lifetime as it moves from the east to the west. This is not surprising, since it is more common in the East Pacific than in the Central and West Pacific.

46 Chapter 5

Summary and ﬁnal thoughts

5.1 Conclusions

Starting with the entire region, one regime showed to have a significantly longer lifetime the the other, the FW regime. But since this was the most occurring regime, vigilance had to be taken about the result. Therefore the results were normalized so the regimes could be compared regardless of their RFO. However, the FW regime was still the most long-lived. Three other regimes also differed from the rest, the CC, CD and the MIX regime. They all have a short lifetime. That the FW regime is the most long-lived does not come as a surprise since this represent fair weather cumulus and clear sky conditions, two common cloud states in the atmosphere. That the three convective regimes showed to have the shortest lifetime can be explained by the unstable conditions they appear in. But the different properties possessed by the clouds showed that they are more common in certain areas. Therefore the lifetime was compared between land and sea. This result showed that four regimes have a very different lifetime over land than over water. The SC1, SC2, CC and CD regimes all had shorter lifetime over land than they had over water. For the CC and CD regimes this was most probably beacuse of the larger variation in temperature and water availability over land. For the SC1 and SC2 regime this can be explained by the fact that these two regimes represent cloud states that are formed in areas with stable air and much water content, i.e., areas with cold water. The rest of the regimes showed no or little variation in land/water lifetime except for the MIX regime, but the results from the MIX regime must be taken with care since clouds at high altitude areas are grouped into this regime. To further break down the results, the tropical and subtropical regions were studied. The land/water results in the two regions were in line with the previous results with some small variation, but all too small to really draw any conclusions from them. An unexpected result from the comparison between the two regions were

47 that the CD regime had a shorter lifetime in the tropics than it had in the subtropics. Other than that regimes that are less likely to occur in one region showed a shorter lifetime there. The difference in lifetime between the East, Central and West Pacific was also studied. In the tropical region of the Pacific the CC regime showed to have a shorter lifetime in the East Pacific, whereas the other two convective regimes had roughly the same lifetime in the three parts of the Pacfic. Since the East Pacific does not have the same amount of convection as the West Pacific, this also comes as no surprise. In the subtropical region of the Pacific the SC1 regime showed a decreasing lifetime when moving westward. For the FW regime it is more common with two day spells than one day in certain parts of the Pacific. However, the decrease in lifetime is the same throughout the entire area, with the exception of the West Pacific. This is most likely due to the fact that the West Pacific is an area where much convection takes place, and the FW regime is unlikely to appear there. The probability of transition between the regimes was also studied. The SC2 and MIX regimes were suggested to be transition regimes from regimes with similar physical properties. It can be debated whether or not the SC3 also should be regarded as a transition regime, since it shows similar properties to those of the SC2 regime. However, the SC2 regime was chosen beacause of its shorter lifetime, and the fact that the SC2 regime was more likely to transform to the SC3 regime and not the other way around. The transition properties with the regimes showed some variations depending on how long the spells had been going on, particulary between the first few days of the spell with respect to the rest of the spell. This can be because of regimes that appear at more unlikely locations and hence have a shorter lifetime at these grid cells. It can also be discussed whether or not the RFO and the sizes of the different areas have an effect on the result. The effect of the RFO is not seen as a problem, although a normalization could enhance certain areas containing low amounts of data. Most of the results are based on sufficient data points with only a few exceptions, but those have already been discarded. The same arguement can be made for areas of different sizes. Given the distribution of the regimes over the Earth, it shows that low top, layered clouds form over oceans with cold water. This means that the cluster regimes represent something that is physically visible, and thus that the data used to calculate the lifetime, are reliable. The probaility of transition showed that almost ten percent of the time, the CD regime became the STC regime. This can, e.g., be an anvil shaped cumulonimbus cloud that leaves a cirrus cloud behind, after its presence. Something that is known to happen. This means that the results are reliable as well. So even though the data are mathematically processed, the results are something that can be observed by the human eye. Thus, the cluster algorithm and the statistical analysis, are a good way of studying the atmosphere and clouds.

48 5.2 Future work

The next step in investigating the cloud regime lifetime, would be to track the regimes as they move across the sky. The method used in this thesis is stationary and gives a result, somewhat biased, based on where the regimes are more common. Tracking the regimes would give more information of how the regimes are related to each other, in a transition sense. Another aspect that would be interesting to analyze, is the spatial distribution of the regimes, i.e, how big they are and if the size have an eﬀect on cloud regime lifetime.

49 50 Bibliography

Aguado, E. and Burt, J. (2009). Understanding weather and climate, chapter 6, 7, 15. Pearson Prentice Hall, (New Jersey).

Anderberg, M. R. (1973). Cluster analysis for applications. Academic Press, (New York). p. 160. Andrews, D. (2005). An introduction to atmospheric physics. Campbridge Uni- versity Press, (Cambridge).

Eliasson, S. (2006). An extrapolation technique of cloud characteristics using tropical cloud regimes. Master’s thesis, Uppsala Universitet. Goode, P., Qiu, J., Hickey, J., Chu, M., Kolbe, E., Brown, C., and Koonin, S. (2001). Earthshine observations of the Earth’s reﬂectance. Geophysical Research Letters, 29(9):1671–1674.

Jakob, C. (2009-2010). Private communication. Monash University. Jakob, C. and Schumacher, C. (2008). Precipitation and latent heating characteristics of the major topical western cloud regimes. Journal of Climate, 21:4348–4364.

Jakob, C. and Tselioudis, G. (2003). Object identification of cloud regimes in the tropical Western Pacific. Geophysical Research Letters, 30(21):2082. Jakob, C., Tselioudis, G., and Hume, T. (2005). The radiative, cloud, and ther- modynamic properties of the major tropical Western Pacific cloud regimes. Journal of Climate, 18:1203–1215.

Rossow, W., Garder, L., Lu, P., and Walker, A. (1991). International Satillite Cloud Climatology Project (ISCCP), Documentation of cloud data. WMO/TD 266 (rev.), World Climate Research Programme. Rossow, W., Tselioudis, G., Polak, A., and Jakob, C. (2005). Tropical climate described as a distribution of weather states indicated by distinct mesoscale cloud property mixtures. Geophysical Research Letters, 32(L21812).

51 Rossow, W. B. and Schiﬀer, R. A. (1999). Advances in understanding clouds from ISCCP. Bulletine of the American Meteorological Society, 80(11):2261– 2287. Singh, M. and Jakob, C. (2010). ISCCP cloud regimes and the tropical warm pool.

52 Appendix A

Lifetimes plots for the entire region

Figure A.1: Lifetime for the eight regimes. The diagram shows the total number of days spent in one spell versus the spell length.

53 54 Appendix B

Probability for the entire region

Figure B.1: Probability of transition as a function of spell length for the SC1 regime. The y-axis shows the probability and the x-axis represent the spell length.

55 Figure B.2: Probability of transition as a function of spell length for the FW regime. The y-axis shows the probability and the x-axis represent the spell length.

Figure B.3: Probability of transition as a function of spell length for the SC2 regime. The y-axis shows the probability and the x-axis represent the spell length.

56 Figure B.4: Probability of transition as a function of spell length for the STC regime. The y-axis shows the probability and the x-axis represent the spell length.

Figure B.5: Probability of transition as a function of spell length for the SC3 regime. The y-axis shows the probability and the x-axis represent the spell length.

57 58 Appendix C

Result for the tropics

Table C.1: Probability of transition in the tropics.

Current Next regime (%) regime SC1 CC FW SC2 CD MIX STC SC3 SC1 45.0 0.5 7.4 23.4 0.5 4.1 0.9 18.2 CC 0.1 34.2 13.2 2.3 14.7 19.6 14.4 1.5 FW 0.5 4.6 61.8 6.4 1.9 8.6 10.4 5.7 SC2 5.8 3.9 25.9 30.7 2.8 14.3 4.1 12.4 CD 0.1 24.9 7.4 2.5 29.2 24.0 10.8 1.2 MIX 0.6 15.4 20.0 7.2 10.4 34.3 8.5 3.8 STC 0.1 12.6 26.6 2.1 5.1 8.6 43.4 1.4 SC3 5.9 2.6 24.5 13.9 1.5 7.6 2.5 41.5

59 60 Appendix D

Paciﬁc plots

Figure D.1: The lifetime curves normalized to one for the FW regime in the East, Central and West tropical Paciﬁc.The y-axis represent the fraction of the time spent in a certain spell length, and the x-axis represent the spell length.

61 Figure D.2: The lifetime curves normalized to one for the FW regime in the East, Central and West subtropical Paciﬁc.The y-axis represent the fraction of the time spent in a certain spell length, and the x-axis represent the spell length.