Integration of Rainfall Data Obtained From an Isolated ...

Tel Aviv UniversityThe Raymond and Beverly Sackler Faculty of Exact Sciences

School of GeosciencesDepartment of Geophysics

Integration of Rainfall Data Obtained From anIsolated Commercial Microwave Link and Radar with

Respect to Flash Floods in the Dead Sea Area

A thesissubmitted in partial fulfillment

of the requirements for the Degreeof

Master of Science

By

Adam Eshel

Tel Aviv UniversityJune 2017

Tel Aviv UniversityThe Raymond and Beverly Sackler Faculty of Exact Sciences

School of GeosciencesDepartment of Geophysics

Integration of Rainfall Data Obtained From anIsolated Commercial Microwave Link and Radar with

Respect to Flash Floods in the Dead Sea Area

A thesissubmitted in partial fulfillment

of the requirements for the Degreeof

Master of Science

By

Adam Eshel

Under the Supervision of Prof. Pinhas Alpert and Prof. Jonathan B.Laronne.

Tel Aviv UniversityJune 2017

Acknowledgments

First, I would like to deeply thank my two supervisors, Prof. Pinhas Alpert and Prof.

Jonathan B. Laronne, for endless consultations and admirable support and care. Thank

you for the trust you gave in me and for the working freedom to follow my curiosity. It

was a pleasure learning from both of you.

I would like to heartily thank Prof. Hagit Messer, Roi Raich and Jonatan Ostrometzky

for the priceless support, help and knowledge I got from you with every step I took.

Great thanks to my group members: Dr. Noam David, Shani Gat, Yoav Rubin, Lior

Gazit, Ori Cohen, Yogev Wallach, Hai Habi and Daniel Serebrenik for the best advice on

the right times and for many fertilizing discussions.

I would also like to thank several of my colleagues: Maaian Rotstein, Avihai Tzinober,

Dr. Jutta Metzger, Beeri Kanner, Hanna Hennig, Dr. Yael Storz-Peretz, Noa Hillel, Ronen

Radian, Yotam Aud, Lior Ozer and Haya Sud for the professional support and priceless

conversations.

The German Helmholtz Association is gratefully acknowledged for (partly) funding

this project within the Virtual Institute DESERVE (Dead Sea Research Venue) under

contract number VH-VI-527.

This study was in part supported by the German Research Foundation (DFG) through

the project Integrating Microwave Link Data for Analysis of Precipitation in Complex

Terrain: Theoretical Aspects and Hydrometeorological Applications (IMAP).

Hydrometric measurement instruments were professionally installed by Yaniv Munwes

of Y ammaTM , with thanks also for essential consultations.

I thank Amit Savir, Elyakum Vadislavsky and Assaf Rayitsfeld of the Israel Meteoro-

logical Service (IMS).

At CellcomTM , I thank: Eli Levi, Yaniv Koriat, Baruch Bar and Idit Alexandrovitz.

iv

Abstract

Commercial Microwave Links are becoming a legitimate tool for environmental monitor-

ing in recent years. Ground level rain measurements obtained from cellular networks’

microwave links have been shown to be accurate in urban and sub-urban areas, but due

to the low density networks and longer links, characteristic to deserts, difficulties arise

in accurately reconstructing high resolution rain fields in rural areas. The distance from

civilization leads to considerable lack in ground level rainfall data, in the form of rain

gauges, which is crucial for runoff prediction in dry-lands. Weather radar readings in re-

mote mountainous dry areas are prone to inaccuracies. As a result of the aforementioned,

flash flood warning in deserts is a challenging task. This study presents a complementary

integration approach of these two vital, yet limited instruments providing a better under-

standing of the effect of different rain patterns on the microwave attenuation. This method

can thereby potentially contribute to improve performances of short term flash flood warn-

ing systems, as the rainfall spatio-temporal variations i.e. rainfall spottiness, which is of

high importance in surface hydrology, can be obtained by the radar, whereas more accu-

rate quantitative ground level rainfall data is provided by the long isolated link. These

parameters are essential in flash-flood generation, yet they are unreliable when the instru-

ments are considered separately. Evaluating the rain distribution along the link was done

by suggesting statistical indices, such as standard deviation, percentages and kurtosis for

classification. Moreover, when compared with precise hydrologic analyzed measurements,

the direct relation to flash flood occurrence is investigated. Wadi Ze’elim (245 km2), an

ephemeral river located in the arid to hyper-arid Judean desert, was monitored in order

to determine water discharges. Measurements of mean water surface velocity, water stage,

bed roughness, cross sectional and longitudinal profiles were undertaken in the trunk chan-

nel at the outlet of the wadi. Similar coupled values of rain spottiness and intensities are

shown to cause similar hydrological responses. Moreover, high rain spottiness along with

moderate rain intensities, as well as low rain spottiness along with high intensities where

found to result in flash floods. Findings in the Dead-Sea area are presented, where the

rain spottiness indices were validated using rain-gauges and radar images.

v

Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Related Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Desert Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Study Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1 Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Synoptic & Climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 Hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Velocity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1.2 Water Discharge Calculation . . . . . . . . . . . . . . . . . . . . . . 13

3.1.3 Error Assessment of Water Discharge . . . . . . . . . . . . . . . . . 17

3.2 Microwave Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.1 Maximum - Minimum Attenuation Method . . . . . . . . . . . . . . 18

3.2.2 The Effect of Quantization and Length on R . . . . . . . . . . . . . 21

3.3 Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.1 ARCOML- Averaged Radar Cells Over Microwave Link . . . . . . . 23

3.3.2 Spottiness Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

vi

CONTENTS vii

4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Hydrological Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1.1 The Effect of Manning’s n on the Calculation of Water Discharge . 27

4.1.2 Optimization of a Constant n Based On Velocity Measurements . . 29

4.1.3 Estimations of Manning’s n With Two d84 Determination Methods

(Limerinos) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2 ARCOML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Spottiness Indices and Discharge: a Short Term Warning Feasibility . . . . 36

4.3.1 Standard Deviation Index . . . . . . . . . . . . . . . . . . . . . . . 37

4.3.2 Kurtosis Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3.3 Spottiness Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.4 Virga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

List of Figures

1.1 Flash-flood at the gauging station in wadi Ze’elim on Feb. 20th 2015. . . . 2

1.2 World map with weather radars coverage (bright spots). Based on WMO

data 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 The effect of different rain intensities on the power loss of a microwave

signal (ITU). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Predicted portion of microwave-based communication networks worldwide

in the near future based on EricssonTM report (Ericsson, 2014). Optical

fiber ”bites” off the microwave portion but a stabilization of the microwave

on ≈ 50% is expected towards 2019. . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Commercial microwave links distribution in Israel (Ostrometzky and Messer,

2014), France (Gazit, 2016) and Netherlands (Overeem et al., 2013). In Is-

rael, the different colors represent three providers: Cellcom, Pelephone and

Partner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6 Left: existence and absence of cellular coverage (based on data obtained

by an Android application). Right: the world population density in 2000

(Overeem et al., 2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Catchment of Wadi Ze’elim (245 km2, red contour), draining into the Dead

Sea after crossing road 90 (white). More in the figure: CML across the

basin (green), Israeli Meteorological service (IMS) radar beams covering

the CML’s path (blue), trunk channel path (black), rain gauges (light blue

markers) and hydrometric station (yellow marker). The figure was taken in

perspective so that it is without scale. . . . . . . . . . . . . . . . . . . . . . 10

viii

LIST OF FIGURES ix

3.1 Downstream view of the cross-section of the Wadi Ze’elim hydrometric

gauging station site. Used for calculations of discharge, done using Eq.

3.2, is the area above the channel cross section (blue) and below the simu-

lated 1 m water depth line (orange). The location of the water depth sensor

is marked in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Longitudinal profile of the Ze’elim channel. Upper point: CML-channel

first crossing point. Lower point: Hydrometric station nearby road 90. . . . 14

3.3 Abnormal behavior of n when derived from Eq. 3.4 (solid) and the expected

behavior when a certain n − Rh inverse proportion is used: n = 0.0234 ∗Rh−0.667 (Garti et al., 1981). . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Locations of hydrometric stations (yellow markers) in the catchment of

Wadi Ze’elim (red contour). . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.5 Maximum - Minimum Attenuation Method as presented in Eq. 3.10. Points

140-160 are the showers marked in figure 4.11 for the Nov. 6th 2015 event.

B = 1.6 dB bias is prominent in the dry period (0-140). . . . . . . . . . . . 20

3.6 The effect of the length of the link on the power loss (in dB) of a microwave

signal. Quantization error for instantaneous measurements is illustrated

(dashed line) and represents a threshold which rain intensities inducing

attenuation not exceed it, will be hardly detected. . . . . . . . . . . . . . . 21

3.7 Second lowest available radar beam (0.76o). Thin lines represent the top and

bottom boundaries of the 1o aperture. Thick line is the topography surface.

The profile is from the IMS by the seashore (Bet-Dagan), to midway of

CML. The Judean Mountains create an obstacle to low radar beams. . . . 23

4.1 Calculated flow properties in wadi Ze’elim with change in water depth:

discharge (top left), wetted area (top right), wetted perimeter (bottom left)

and hydraulic radius (bottom right). The discharge rating curves represents

the calculation methods based on Eq. 3.3. . . . . . . . . . . . . . . . . . . 28

4.2 Response surface of |Q− Qv| for a range of level and n values. The graph

emphasizes the sensitivity of the calculated discharge to n in large depths.

It can be seen that with the growth of water depth, grows the dependency

on the coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3 Stage-Discharge relations for two discharge calculation methods. Qv was

calculated using the velocity measurements, as presented in Eq. 3.3 (blue).

Q was calculated using the Manning Formula with a constant preliminary

assumption of n = 0.035. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

x LIST OF FIGURES

4.4 Surface flow velocity in water with varying depth. A non logarithmic scale

is presented in the small box along with a 5% instrument error. This ex-

ceptional data base of water velocity, measured during flash flood events, is

used to estimate discharge from water depth (y = 0.549x+0.519; r2 = 0.85). 30

4.5 Histograms of the pebbles sizes samples for all four monitored channels

in the Ze’elim catchment: Ze’elim trunk channel (a), Shafan (b), Ze’elim-

Upper (c) and Harduf (d). . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.6 Probability of the sampled data (a) and the PDF of the fitted truncated

normal distribution (b) of the truck channel of wadi Ze’elim. . . . . . . . . 33

4.7 Change of n with water depth according to the two methods regarding d84

and another method for reference, as presented in Fig. 3.3 (Garti et al.,

1981), for the trunk channel. . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.8 Change of n with water depth according to the two methods regarding d84

and another method for reference, as presented in Fig. 3.3 (Garti et al.,

1981), for the three monitored tributaries in the catchment: Shafan (a),

Ze’elim-Upper (b) and Harduf (c). . . . . . . . . . . . . . . . . . . . . . . 34

4.9 Discharge of the three tributaries: Shafan, Ze’elim-Upper and Harduf, and

of their total discharge, measured at Ze’elim trunk channel’s gauging sta-

tion, all for three case studies: November 6th 2015 (a), January 25th 2016 (b)

and January 1st 2016 (c). Ze’elim-Upper contains the discharge of Shafan

tributary as it was located downstream of the confluence due to lack of

suitable spots upstream. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.10 Histograms of rain intensities of 124 radar cells on January 1st 2016 above

the CML, in a 5 minute resolution starting at 05:05 (UTC+2). Low rain

intensities are more prevalent and some kind of a decaying distribution tail

is noticeable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.11 Standard Deviation spottiness index and rain intensities during Effective

Rain Periods (ERPs), with respect to runoff at the outlet of the Wadi. The

events presented are November 6th 2015 (a), January 25th (b) and January

1st 2016 (c). Lower part: CMLR and radar STD 15 minute resolution (blue

stems and orange line respectively). Upper part: Discharge hydrograph in

Ze’elim outlet (black line). Markers on the hydrograph correspond with

their ERPs (shaded and numbered areas on the bottom part). Each ERP

represents 3.5− 2.5 h prior to the marked hydrograph point. . . . . . . . . 38

LIST OF FIGURES xi

4.12 IMS radar images of chosen times for the three case-studies as visual sup-

port for STD-spottiness relations. Since images are taken in a 5 minute

resolution, one figure was chosen out of the three taken prior to the referred

coupled CMLR-STD. Left: Nov. 6th 2015, 14:00 (ERP2); Middle: Jan.

25th, 16:15 (ERP1); Right: Jan. 1st 2016, 06:15 (ERP1). IMS radar and

CML illustrations are marked as a red semi-circle and a transparent purple

line respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.13 Radar cells QPE along the CML path (NW to SE), in the coherent times

with Fig. 4.12, for the three events. . . . . . . . . . . . . . . . . . . . . . . 40

4.14 Zoom in to Figures 4.11 b and c with kurtosis (k) spottiness index and rain

intensities during Effective Rain Periods (ERPs), in respect to runoff at the

outlet of the Wadi. The events presented are January 25th (a) and January

1st 2016 (b). ERP1a (in b) is an additional point which is not presented

in Figure 4.11. k was not calculated for ARCOML values not exceeding

0.3 mm h−1 and is given in a 5 minute resolution. . . . . . . . . . . . . . . 42

4.15 Radar measurements vs. ground rain gauges and link measurements. The

events presented are Nov. 6th 2015 (a), Jan. 25th 2016 (b) and Jan. 1st

2016 (c). Top: ARCOML is plotted along with the CMLR. Bottom: Rain

intensities of Arad IMS rain gauge are plotted along with the averaged

values of three consecutive radar cells (one just above the gauge, one on it’s

tail and another one after). . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.16 IMS radar cells intensities distribution along the CML path (NW to SE),

at times where CMLR were the same (≈ 2 mm h−1), for the three events:

Nov. 6th 2015: 12:15; Jan. 25th: 17:30; Jan. 1st 2016: 06:15 UTC+2. . . . 44

4.17 Histograms of the percentage of ones out of the 124 radar cells inMAT50 for

every non-all-zeros vector ofM . Left to right: January 25th, January 1st and

November 6th. PDF curves (red) were placed for qualitative demonstration

only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.18 The 90th percentile of the binary link coverage (percentage of ones out of

the 124 radar cells) for all three thresholds (MAT25, MAT50 and MAT75)

for every non-all-zeros vector of M . Left to right: January 25th, January

1st and November 6th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

xii LIST OF FIGURES

4.19 ARCOML (orange) and CMLR (blue stems) on May 2014. The shaded

area represents the period when the relative humidity exceeded 85%, based

on the IMS meteorological station in Arad. It is prominent that some rain,

detected by the radar, did not reach ground level fully. It can be assumed

that the virga plays a role in this event, as the low relative humidity values

fluctuated around 35%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

A.1 Histograms of the percentage of ones out of the 124 radar cells inMAT25 (a)

and MAT75 (b) for every non-all-zeros vector of M . Left to right: January

25th, January 1st and November 6th. For MAT25: θ = 16.44, 14.24, 6.82.

For MAT75: θ = 1.10, 0.82, 0.63 respectively. . . . . . . . . . . . . . . . . 52

List of Tables

4.1 Values of d84 (mm) for the four monitored channels, for the two investigated

methods: linear interpolation and a truncated normal distribution fit. . . . 31

4.2 Correlations (r) between ARCOML and CMLR for each case study. AR-

COML represents the CMLR fairly to very well. . . . . . . . . . . . . . . . 36

4.3 Correlations (r) between all four rain gauges for the Nov. 6th (a), Jan. 25th

(b) and Jan. 1st (c) events. Distances between gauges are presented in

parentheses. Both Arad IMS and Shani gauges are IMS gauges, which have

a 10 min. time resolution. Hanokdim and Arad are dedicated gauges which

measure every minute. Summation of every 10 samples was used in order

to befit the IMS sampling rate. . . . . . . . . . . . . . . . . . . . . . . . . 39

4.4 STD representative values for the three case studies. Data was obtained in

5 min. intervals, including only non-zero samples. The original sampling

duration of the data sets (prior to the exclusion of zeros) was for the entire

periods presented in Fig. 4.15. Values are given in mm h−1. N is the

number of samples (non-zero samples) which were used for the analysis. . . 44

xiii

Chapter 1

Introduction

FLASH–Floods are a common phenomenon in hyper-arid to semi-arid regions. They

serve as the main source of water to support the existence of flora and fauna, and

play an important role in ground water recharge through transmission losses. These flood

events can be generated by very short as well as by longer duration rainfall events, yet the

ones with high local and temporal intensities, which are much less predictable (David et al.,

2009), are more likely to be the cause for abrupt and large floods. When civilization meets

prone areas, severe damage can be caused to infrastructure, roads and private property,

thus a threat to human life is inevitable. High concentrations of suspended solids as

well as ultrahigh bedload discharges along with a sharp hydrograph rise emphasize how

powerful and violent these flows can be. This form of runoff is typical of desert areas due to

low infiltration rates mainly caused by poor vegetation coverage, shallow underdeveloped

rocky soils, exposed bedrock and steep rocky terrain. Indeed, it depends also on the

rainfall characteristics in such areas that include the duration, overall quantity and covered

area, but spatial distribution and rain intensity are two major ones (Pilgrim et al., 1988).

Ephemeral rivers draining the Judean Desert rain to the Dead Sea (commonly referred

to as Wadis) meet these characteristics and indeed the convective (mainly spring and

autumn) and cold front (winter) events, which occur several times a year, often generate

flash floods within these catchments (Kahana et al., 2002; Tarolli et al., 2012; Ziv et al.,

2006).

Rainfall monitoring is crucial for understanding the processes taking place in the oc-

currence of these floods. The use of Commercial (telecommunication) Microwave Links

(CML) as a rain monitoring instrument integrated with weather radar is examined in this

research with respect to generation of flows events.

At this early stage of research, as in this study, the CML data were obtained from the

local Israeli cellular providers.

1

2 CHAPTER 1. INTRODUCTION

Figure 1.1: Flash-flood at the gauging station in wadi Ze’elim on Feb. 20th 2015.

1.1 Background

The manner by which rain cells are separated, as well as the intervals between their

appearances, is referred to as the spottiness of rain (Ben-Gai et al., 1994; Sharon, 1972).

Spotty rainfall events are common worldwide, especially in semi-arid and arid areas, and

the difficulty in their monitoring is of considerable substance due to the related high

potential rain intensities (Amiran, 1995; Shentsis et al., 2012).

Advance flash flood warnings are widely based on predictions of models, which also

use field observations. Accuracy of rainfall measurements is of high importance in surface

hydrology modeling (Larson and Peck, 1974; Osborn et al., 1979; Price et al., 2014; Samuels

et al., 2011). In aim to increase the regional database, rain gauges have been deployed

throughout the desert by interested parties such as research groups and local authorities.

Providing measurements from ground level, the rain gauge is justifiably referred to as

”ground truth”. Moreover, various interpolation methods of rain field reconstruction exist

and provide spatial distribution data which are assumed to reality.

Weather radar is another widely used tool for rain monitoring. With a wide spatial

coverage for various elevations and a temporal resolution of minutes, it provides indirect

rain measurements of essential value. The coupling of radar and rain gauges is not new and

one of its most common applications is radar adjustment and calibration. Furthermore,

it has been shown that prediction of flash floods is improved when using a weather-radar,

rather than rain gauges only (Berne and Krajewski, 2013).

Difficulties in using radar exist and sometimes constitute a barrier for a wider use of

the provided data. Weather radars are used less extensively for hydrological forecasting

CHAPTER 1. INTRODUCTION 3

as expected due to the need for adjustment and various sources of errors (Joss et al.,

1990), most arising due to robust working premises (Harrison et al., 2000), ray blocking

obstacles (Alpert and Shafir, 1989) and evaporation of water droplets (Price et al., 2014),

also discussed in this study. In particular, mountainous areas induce additional factors

which affect the accuracy of radars (Germann et al., 2006). World-wide coverage of radars

is excellent in North America, Europe, along the coastlines of Australia, Japan and in

parts of South-East Asia. However, it is prominent from the Fig. 1.2 that the presence of

radars is concentrated in certain parts of the world whereas other parts remain uncovered

due to the high price of having such technology operative or due to unwillingness to share

the data.

Deployment and maintenance of rain gauges is costly and after being installed and

left in the field, the gauges are vulnerable to damage caused by nature and vandalism;

therefore, installation sites are sometimes restricted to settled areas and as a result- not

uniformly spread in space. Specifically, arid regions, as well as mountainous ones, are

known for low density rain gauge networks (Marra et al., 2014; Pilgrim et al., 1988). Fur-

thermore, rain gauge data supply point measurements, and as many flash flood generating

rainfall events are commonly somewhat spotty, the dearth of areal coverage generates

large uncertainties in identifying rainfall patterns and local high intensities (David et al.,

2013). Convective events are characterized by low correlations between nearby rain gauges

(Osborn et al., 1979).

Figure 1.2: World map with weather radars coverage (bright spots). Based on WMO data2015.


Monitoring rain through the use of CML attenuation data of existing wireless com-

munication systems, first presented a decade ago (Messer et al., 2006), is increasingly

becoming a legitimate tool in meteorological sciences (Alpert et al., 2016). The principle

of data retrieval is as follows: The transmitted signal level (TSL), given in dB, from one

cellular antenna is received by a nearby antenna i.e. the receiver. In the absence of any

technical or climatic disturbances, differences in the logged power are almost constant and

are mainly depended on the fixed distance between the towers. As the common frequen-

cies used for this purpose are within the water-sensitive spectrum, the signal power level

weakens when rain falls within the medium, resulting in a lower received signal level (RSL)

than in dry periods. The International Telecommunication Union (ITU) stated an empir-

ical Power-Law model (presented in chapter 3.2) that outputs the expected attenuation

per unit of length for different possible rain intensities (presented in Fig. 1.3), in order to

determine the needed TSL. Using the reverse form of the Power-Law one can derive the

rain intensities.

Figure 1.3: The effect of different rain intensities on the power loss of a microwave signal(ITU).

Wireless connections are known to be the easiest and fastest way of establishing a new

communication network system, yet considered to be preliminary and to be replaced with

an optical fiber connection soon after placed. This conception cast a shadow over the the

future of cellular environmental monitoring. Recently, a new publication by EricssonTM

(the biggest manufacturer of cellular antennas worldwide) revealed an optimistic future


Figure 1.4: Predicted portion of microwave-based communication networks worldwide inthe near future based on EricssonTM report (Ericsson, 2014). Optical fiber ”bites” offthe microwave portion but a stabilization of the microwave on ≈ 50% is expected towards2019.

prediction for the portion of wireless networks among telecommunication ones for different

countries and regions (Fig. 1.4), predicting a balanced state in the near future (Ericsson,

2014, 2016).

(a) Israel (b) France (c) Netherlands

Figure 1.5: Commercial microwave links distribution in Israel (Ostrometzky and Messer,2014), France (Gazit, 2016) and Netherlands (Overeem et al., 2013). In Israel, the differentcolors represent three providers: Cellcom, Pelephone and Partner.

Microwave links are spread all over the world. Maps of CML in Israel and France

presented in Figure 1.5, emphasize the not-yet fulfilled potential of these new instruments

as environmental monitors. Moreover and with high relevance to this study, populated


Figure 1.6: Left: existence and absence of cellular coverage (based on data obtained by anAndroid application). Right: the world population density in 2000 (Overeem et al., 2013)

areas can be spotted by the high density of links e.g. large cities, whereas rural areas

sometimes even lack their presence. Visual reference is found in Fig. 1.6.

1.2 Related Research

The feasibility of reconstructing 2D rain maps using the recorded TSL and RSL has been

previously shown (Messer et al., 2008). Rain maps created nowadays in several countries,

based on CMLs, use a variety of interpolation algorithms to evaluate the rain field between

the different links and along their paths (Liberman and Messer, 2014; Overeem et al.,

2013). The benefit of interpolated spatial CML rainfall data, as well as data obtained

from a single link been shown with respect to rain gauges measurements (Rayitsfeld et al.,

2012). In addition, the presented methodologies preformed better when the density of

links increased due to diminishing of the spatial uncertainty. Hence, CMLs can provide a

fair ground truth for rain in populated areas.

Rain cells detection by both rain gauges and CMLs was simulated by David et al.

(2013). The research presented the benefits in the presence of long links in sparsely

populated areas, stating a detection factor four times higher with CMLs than in the

distributed rain gauges i.e. the links detected Monte-Carlo simulated rain cells in more

cases, and earlier than the gauges.

Spatial distribution of rain is crucial for surface hydrology modeling (Morin et al.,

2006; Obled et al., 1994). Furthermore, prediction of flash-floods is improved when using

a weather-radar which has a wide spatial coverage (Morin et al., 2009). Notwithstanding,

as previously mentioned, weather radars are insufficient for hydrological forecasting as

expected due various reasons.


1.2.1 Desert Hydrology

Many studies related flash flood generation and rainfall in the Negev and Judean deserts

were done (Cohen and Laronne, 2005; Greenbaum et al., 1998; Yair and Lavee, 1982).

Differences in hydrological processes taking place in humid and arid areas are of great

importance and should be considered when trying to understand desert hydrology. Pilgrim

et al. (1988) numerated some of these distinctive features: Apart of it’s role in increasing

channel friction, soil permeability and ground water recharge, the absence of vegetation

coverage (previously mentioned) leads to significantly lower content of organic matter in

the soil. Influences can result in changes in soil hydrophobicity, infiltration, evaporation

and more. Moreover, weighting of processes must be distributed differently e.g. baseflow

absence is prevalence in desert wadies, and channel transmission losses are of significant

importance. The fact that the ground water table is usually hydraulically disconnected

from both the river bed and the drainage surface plays an important role in modeling, all

the more so today, when the vadose-zone research is accelerating.

Hydrological models nowadays still struggle in accurately predicting flash floods and

in many cases either miss detect or report false alarms (Younis et al., 2008) due to lack of

quality tempo-spatial rainfall data, especially in remote locations. A robust uncalibrated

hydrological model was used to predict peak discharges (Rozalis et al., 2010). It was

concluded that convective events are easier to predict than winter storms caused by the

governing Mediterranean lows systems, using calibrated radar data. This can be attributed

to the lower typical intensities in winter storms, and as a result- a larger sensitivity to the

model’s parameters and initial conditions such as soil moisture content.

The improvement of hydrological models is strongly dependent on the ability to de-

termine water discharge of floods. As discussed in Chapter 3.1.2, the Manning’s Formula

for discharge calculations contains the Manning’s n- coefficient of the river bed roughness.

Determination of it’s value was studied in the past (Linsley, 1958) and has great impor-

tance in discharge calculations. The value of n can be based on tables (Linsley, 1958) and

pictures (Barnes, 1967; Limerinos, 1970), as well as many other techniques. A survey of

several methods of determination included visual assessment, pebbles size measurements

and other empirical relationships (Cohen, 2005). Limerinos (1970) developed a Manning’s

n assessment method, based on data collected from 11 gravel-bed streams in California.

Sediment sizes, as well as roughness coefficients were incorporated into Limerinos’s empiric

equation. In sediment rivers, friction is induced mainly due to drag and viscous friction

at the interaction between the flowing medium and solid particles (Ferguson, 2007). Fric-

tion weighting is different in mountain river beds which contain boulders or large gravels.


Turbulence caused by the aforementioned increases friction as well. That, among other

sources, makes it very difficult to accurately describe the friction-velocity relations (Wohl,

2000). Water velocity is another useful component in discharge calculations. Welber et al.

(2016) examined the use of a Doppler effect- based acoustic velocimeter. In this study,

the aforementioned techniques were used and compared.

1.3 Thesis Objectives

A rain monitoring-based, short-term flash flood warning system can be useful as an ad-

ditional tool to models, along or even integrated with now-casting solutions. Traditional

devices commonly used for quantitative precipitation estimates (QPE), i.e. rain gauges

and radars (Cole and Moore, 2008), have various deficiencies, which create difficulties in

fulfilling this need in remote places, such as catchments in the Judean-Desert.

Integrating CML data to the world of hydrology is not trivial for various reasons,

yet one is outstanding; Resolution in space of QPE is of great importance for hydrologic

forecasting as heavy rain generates runoff faster than light rain, especially on surfaces

with low infiltration rates. Rain derived from CML is, in practice, a line-integrated rain

intensity between two antennas. Since the radio signal is affected by rain properties within

its medium, it does not distinguish between heavy but spotty rainfall to uniformly spread

but light rainfall. Each measurement can be referred to as the average rain intensity along

the path, and as a result, similar attenuation patterns can outcome, thus leading to similar

CML derived Rain intensities (CMLR).

The goal of this study is to determine whether the usage of real time, uncalibrated

data from weather radar alongside data obtained by CMLs, can contribute to our under-

standing of flash flood generation, and perhaps even to flood warning. The approach is

a complementary integration, using the advantages of each rain monitoring instrument

to cover for the weaknesses of the other, while developing a method to determine water

discharge more accurately and adding water discharge data in tributaries, not merely at

a catchment outlet.

The objective mentioned above was approached from various directions in this study,

all which require data analysis and different conceptual approaches, from the identifi-

cation of rain spottiness, through the contribution of the spatial uniformity of rainfall

regarding runoff generation, to the determination of the CML’s strengths and weaknesses

when isolated. Different hydrometric, discharge- related, approaches were examined in

order to optimize the measurements e.g. precise rare radar-based mean water velocity

measurements in flash flood events, and estimations of roughness coefficients.

Chapter 2

Study Region

The study region sprawls along the western part of the Dead Sea rift and focuses on lati-

tudes around 31.3o. The characteristic surface is mostly comprised of limestone, dolomite

chalk and cherts. The prevalence of sink-holes, the arid to hyper-arid climate, extreme

summer temperatures and the steep topography are just some of the causes of the sparse

distribution of the population. Hence, the spread of the cellular infrastructure is mostly

limited to be along roads, and the links are relatively long.

2.1 Topography

Chosen as the case study on which this study concentrates; Wadi Ze’elim is a 245 km2

catchment (to the hydrometric station located at the fan apex, Fig. 2.1) draining the

eastern slopes of the Judean Desert into the Dead Sea (−430 m). Eastwards of the

divider (the Judean mountains) an area with very moderate slopes is present, named

the desert plateau. Desert lithosols and regs characterize this upper (western) part of

the basin (Cohen and Laronne, 2005). Stony surface and exposed limestone bedrock are

common in the steep slopes of the lower (eastern) part, along with similar soil texture

on the floodplains (Yair and Lavee, 1976). The central part of the basin is underlain by

chalk which tend to generate runoff faster than many limestone and dolomite surfaces.

Topography is generally rugged and waterfalls are prevalent. Coverage of vegetation is

rare, discontinuous and can be found out of the channels only in the upper parts of the

basin.

2.2 Synoptic & Climate

Upper level troughs extending from eastern-Europe to the eastern-Mediterranean during

winter enhances atmospheric instability in the lower levels and encourage rain events

9

10 CHAPTER 2. STUDY REGION

Figure 2.1: Catchment of Wadi Ze’elim (245 km2, red contour), draining into the DeadSea after crossing road 90 (white). More in the figure: CML across the basin (green),Israeli Meteorological service (IMS) radar beams covering the CML’s path (blue), trunkchannel path (black), rain gauges (light blue markers) and hydrometric station (yellowmarker). The figure was taken in perspective so that it is without scale.

(Alpert and Reisin, 1986; Ziv et al., 2006). Negative correlations (r = −0.74) were found

between rainfall and the 500 hPa geopotential height.

The annual rainfall gradient is very sharp in the region, due to the rain-shadow effect:

the northwest corner of the catchment adjacent the 300 mm y−1 line whereas the Dead

Sea shore, considered a hyper-arid zone, averages ≈ 50 mm y−1 (Morin et al., 2009). As

can be seen in Fig. 2.1, the horizontal distance between the uppermost and outlet of the

catchment is only about 20 km. This implies that most of the annual rainfall is recorded

by gauges located in the western part of the basin, as is the studied CML. Furthermore,

also as it is a rain shadow region, the Judean Desert is characterized by very localized rain

cells, with a typical diameter of 5 km Sharon (1972). This kind of spottiness is possible

also due to the low availability of moisture in the desert air.

The synoptic systems dominating the rain events in the region are the Red Sea Trough

and the winter cyclones (Mediterranean lows) (Kahana et al., 2002; Krichak et al., 2000).

The first is a synoptic scale system, active in the region mostly during spring and charac-

terized by convective events leading to 31% of flash floods in southern Israel (Shentsis et al.,

2012). The latter often coincides with cold fronts, arriving from the Mediterranean Sea in

the west, and if conditions allow, generate rain on the lee side of the Judean Mountains,

intermittently causing the eastern drainage system of the Dead Sea to flow.

Chapter 3

Methodology

In this chapter the details of the methodology, data analysis and background of the main

three data sources worked with in this research are described: hydrologic data, microwave

attenuation and weather radar.

3.1 Hydrology

The trunk channel of wadi Ze’elim is monitored continuously throughout the potentially

active flood seasons (September-May), at a hydrometric station (Fig. 1.1) located in

close proximity to road 90 (Figure 2.1), parallel to the Dead Sea shore. Equipped with

various monitoring means, the hydrometric station continuously monitors water depth

using a recording vented pressure transducer. Because the transducer needs to be located

10 − 20 cm above the active bed due to the movement of large bedload particles, water

depth is separately monitored by an absolute pressure leveloger located at the height of the

river bed, thereby allowing to determine water depth also during the shallow recession. The

hydrostatic pressure is determined by subtracting from the ”levelogger” data (equivalent

to the atmospheric and the hydrostatic) the atmospheric pressure monitored by a separate

”barologger”. The mean flow velocity was calculated based on measured average surface

water velocity using a Doppler based hand-held radar velocimeter (Welber et al., 2016).

Measurements of water velocity in flash-floods events are very rare. The unpredictability

of these events, the large intervals between each event and the distance from populated

areas are the main reasons for the dearth of these essential data. The velocimeter required

presence during flow events. This was made possible on two occasions. Cross sectional

and bed slope measurements, undertaken using a theodolite, were used in determining

the cross sectional shape and the longitudinal slope of the reach approaching the gauging

station. These topographic measurements were repeated after sufficiently large events.

When velocity measurements are absent, water discharge (Q) calculations are done

11

12 CHAPTER 3. METHODOLOGY

using the Manning formula (also known as the Gauckler-Manning formula) for open chan-

nels:

Q = n−1Rh 23S

12A (m3 s−1) (3.1)

where A is the cross sectional area of flow (in m2), S is the hydraulic head loss (assumed to

be constant and equal to bed slope in this study) given in %, Rh is the hydraulic radius (in

m) and n (s m− 13 ) is Manning’s n. In this study Rh was used as in it’s formal definition:

Rh = A p−1 (m) (3.2)

where p is the wetted perimeter (given in m).

One of the main sources of inaccuracies in discharge calculations is the need for de-

termining a roughness coefficient,such as- Manning’s n, presented in Eq. 3.1. Another

well-known problem with Manning’s n is that in most cases it is not being changed with

different depths, as it should due to the distance increase between the friction source and

water surface. Water velocity measurements ware used to bypass the inaccuracies involved

in estimating Manning’s n thereby to calculate discharge in a more accurate manner. Fur-

thermore, estimations of different n values were undertaken using different water depths

and a least-squares method was used to determine a more accurate n which can be robustly

used in all water depths.

Velocity measurements were undertaken in this study in order to:

1. Use the continuity equation (Q = A v) for discharge calculations rather than Man-

ning’s formula.

2. Determine an approximated ni for every ith water level measurement using the re-

arrangement of Eq. 3.1.

3. 3. Suggest an additional method of determining Manning’s n and thereby suggest

a new suitable n for the Wadi Ze’elim outlet.

3.1.1 Velocity Measurements

The challenge in measuring mean surface water velocity in a channel arises from the

physics of kinetic energy loss due to friction, which determines the change of velocity with

distance from the friction source. The latter are the river bed as well as the river banks.

The Hazen-Williams equation is an empirical engineering solution for pipes, which relays

on similar principles of head loss (based on the Chezy formula) and forced a classification

CHAPTER 3. METHODOLOGY 13

of roughness coefficient for pipes, provided by manufacturers. The pipe solution is simpler

than the open channel case in a way: In channels, the water surface changes, and so

the distance from the friction plane also varies. Furthermore, it is harder to assess the

roughness coefficient in the field, not to mention the changes it experiences during a flash-

flood, where gravel to boulders are frequently deposited, thereby changing the cross-section

and also the roughness.

3.1.2 Water Discharge Calculation

By possessing seldom available measurements of mean surface water velocity in flash-flood

events, one can reduce the uncertainty in calculated water discharge (Qvi ) which here, is

based on:

Qvi = Ai · vi (L3 T−1) (3.3)

for the ith water depth measurement, sampled at a 3 minute time resolution, where

vi is the is the mean flow velocity in the channel, given in m s−1. Ai is the calculated

wetted cross sectional area (illustrated in Fig. 3.1) whereas vi was determined by the

regression of measured average surface velocity and its variation with water depth. It

is worth noting that Welber et al. (2016) suggested to multiply the obtained velocity

raw data by ≈ 0.84 − 0.85. Nonetheless, in this research all velocity measurements were

multiplied by 0.85 due to the small difference and the presence of larger sources of error.

Figure 3.1: Downstream view of the cross-section of the Wadi Ze’elim hydrometric gaugingstation site. Used for calculations of discharge, done using Eq. 3.2, is the area above thechannel cross section (blue) and below the simulated 1 m water depth line (orange). Thelocation of the water depth sensor is marked in red.


Figure 3.2: Longitudinal profile of the Ze’elim channel. Upper point: CML-channel firstcrossing point. Lower point: Hydrometric station nearby road 90.

The longitudinal channel profile of Wadi Ze’elim, from the CML-channel crossing point

to the hydrometric station at the outlet, is shown in Figure 3.2. This data was later used,

as well as the velocity measurements to determine the flood warning time, detailed in

chapter 4. As aforesaid, the velocity data can be assigned for assessing ni values for

different water depth. Rearranging Eq. 3.1 with the use of Eq. 3.3 to empirically estimate

ni:

ni = v−1i R

h 23

i S12 (3.4)

In theory, the manning coefficient is expected to decrease with water level rise as a

result of the growth of distance from rough solid matter, but as can be seen in Figure

3.3, it is not the case in this naive try. Nevertheless, it is worth noticing that the final

value, around which the roughness coefficient stabilizes (in large depths), is similar to that

for the neighboring Wadi- Rahaf (Cohen, 2005). The Rahaf has similar properties but

does not contain large boulders nearby the gauging station. The abnormal behavior of the

roughness coefficient in shallower water levels is referred to it’s nature of being an empirical

rather than a physical quantity. At first, the channel bed cross sectional relatively complex

structure i.e. the prevalence of boulders and large gravel, previously mentioned, was the

suspect to be the cause, but it is known that in the n−Rh, n is decaying with the growth

of the hydraulic radius (Cohen and Laronne, 2005; Limerinos, 1970; Wolman, 1954). In

contrary, the n − Rh relations in the Manning formula is proportional: Rh ∝ n32 . In


Figure 3.3: Abnormal behavior of n when derived from Eq. 3.4 (solid) and the expectedbehavior when a certain n − Rh inverse proportion is used: n = 0.0234 ∗ Rh−0.667 (Gartiet al., 1981).

practice, examination of different n − Rh relations using data from Wadi Ze’elim, states

that surely, there is an inverse proportion between the two. These relations were checked

and found to project a normal behavior of n with reasonable values (Fig. 3.3).

When accounting other roughness sources, e.g. vegetation, behavior as this is accept-

able as water can reach various obstacles on the banks, when rising. It is not the case here

as the vegetation in the channel is growing in higher levels.

Limerinos Method for Estimation of Manning’s n

As previously mentioned, it is customary to use the Limerinos method (Limerinos, 1970)

for the assessment of n in gravel-bed rivers. In the aforementioned study the channels

have a coarse gravel bed, so it is assumed that they are quite free from other than particle

size associated flow-retarding effects such a channel curvature, Large bars or vegetation.

The principle is based on the assumption that the range of sizes of pebbles on the river

bed is normally distributed. Altogether 100-200 particles were randomly selected from

within the channel bed, in close proximity to the gauging station based on the Wolman

method (Wolman, 1954) and according to the procedure specified by Limerinos (1970).

Assuming a normal distribution, the empirical relation of pebbles’ sizes, Rh and n made

use of the 84th percentile (pebble diameter), a well known characteristic of the normal

distribution: one standard deviation above the expected mean. d84 then, represents the


diameter (measured in mm) of the 84th percentile pebble, around the gauging station,

which the empirical model refers to:

n =0.1129Rh 1

6

1.16 + 2.01log Rh

d84

(3.5)

where both d84 and Rh are given in meters. Determination of the d84 was carried out by

two methods:

1. The commonly used method (linear interpolation): a scatter of the actual cumulative

distribution data was created and every two data pionts were linearly interpolated.

Then, all the interpolation segments were divided 100 times so that the value of the

84th constitutes d84.

2. A Maximum Likelihood estimation was used to fit a normal distribution curve to the

data. Then, the 84th percentile is actually equal to E + σ.

Results are presented in the next chapter, and a comparison with an optimization of n,

using the aforementioned velocity measurements, is presented as well.

Tributaries Monitoring

Monitoring the trunk channel of wadis in the Judean Desert has been going on for some

time, yet measurements of water depth in the tributaries were yet to be undertaken.

Within the framework of this study, three main tributaries of Wadi Ze’elim were chosen

in which water depth was monitored by deploying absolute pressure levelogers and one

barologger: Shafan, Zeelim-Upper and Harduf (Fig. 3.4). Cross sectional and bed slope

measurements were undertaken in each of these tributaries; longitudinal profiles have

slopes of 1.18%, 1.17% and 2.59% respectively. Each of these tributary sites were carefully

chosen in straight channel reaches where boulders are absent. First results of discharge

calculations are presented chapter 4.1.3. The Ze’elim-Upper contains the Shafan tributary,

as can be comprehended by looking at Fig. 3.4.

Since direct velocity measurements are absent in these tributaries, the Manning rough-

ness coefficient was assessed by similar aforementioned methods. Such data from within

the catchment can be used to learn about the lower thresholds for runoff generation, as

small flow events often do not reach the main gauging station at the outlet due to trans-

mission losses. Moreover, the data from tributaries can aid in researching transmission

losses, mean wave velocity in the channel, routing and more.


Figure 3.4: Locations of hydrometric stations (yellow markers) in the catchment of WadiZe’elim (red contour).

3.1.3 Error Assessment of Water Discharge

The estimated error in the calculation of water discharge Q is hereby analyzed:

1. Velocity measurements have a stated 5% accuracy according to the manufacturer.

Measurements were undertaken for water depths in the range 0.3 to 0.7 m and

interpolated with the best fitting logarithmic trend line using least squares, with

r2 = 0.85 and RMSD = 0.1 m · s−1 (Fig. 4.4). Hence, the error here is estimated

to be 15%.

2. As bed slope is measured rather precisely, we assume that the error in the determi-

nation of slope is very small, therefore negligible.

3. In the calculation of wetted water area (for every ith water depth), both the wetted

perimeter and water level are involved, since it is the area between the water level

line and the perimeter (pi) assuming that the water surface is horizontal. During

large floods the channel bed may undergo changes and as these are never monitored

during an event but only afterwards, the actual changes during a flood are unknown.

Nevertheless, most of the wetted perimeter at all the 4 monitoring locations is stable

on bare rock, particularly so at the tributary sites. Bed changes before and after a

moderate flow event vary around 10 cm. Relative to water levels reaching around

1 m the estimated uncertainty in area is roughly 10%.


4. The concentration of suspended solids is on average 2-3%, although it may rise to

10% at the onset and very fast rise of large floods. This affects the calculation of

water depth because the density of the water-sediment mixture is higher than that of

pure water. At this stage this induces a 1-2% positive error (water depth is slightly

lower than calculated without the effect of suspended sediment), one which will be

included in the calculation of water discharge at a later date.

3.2 Microwave Link

Current cellular communication networks are based, at least partly, on CMLs, which built

the networks’ infrastructure. Present CMLs usually operate in the K-band frequency range

(6 − 40GHz), whereas future CMLs will make use of the higher E-band frequency range

(at ≈ 80GHz, Ericsson (2014)).

A radio signal which operates either in the K-band or in the E-band frequency ranges

and travels throughout the atmosphere is sensitive to a number of environmental phenom-

ena, from which, rain is the most dominant (ITU-R, 2009). The relationship between the

signal attenuation and the specific rain-rate has been studied in the past (Gunn and East,

1954), and can be presented via a logarithmic relationship which is known to be in the

form of a Power-Law (Olsen et al., 1978):

Ai = a ·Rbi · L (dB) (3.6)

where Ai is the signal attenuation at time index i, Ri (inmm h−1) is the instantaneous rain

intensity (at time index i), L (in km) is the length of the link, and a& b are two parameters,

characterized by the frequency, polarization, and the rain Drop Size Distribution (Gunn

and East, 1954; ITU-R, 1992-1999-2003-2005; Leijnse et al., 2007; Messer and Sendik,

2015). The specific values of the a&b parameters are considered to remain relatively

constant, and were published in the technical literature (ITU-R, 1992-1999-2003-2005).

3.2.1 Maximum - Minimum Attenuation Method

Here, we use data obtained by the Israeli cellular provider CellcomTM , which uses a

Network Management Systems that records only the minimum and the maximum TSL

and RSL in 15 minute intervals. The data are being sampled every i = 10 seconds but the

Management System files available to us only contain the maximum of every 90 samples.

From the minimum TSL (defined by TSLmin) and the maximum RSL (defined by


RSLmax), the minimum channel attenuation can be approximated:

Aminj = TSLmin

j −RSLmaxj (dB) (3.7)

where j represents the jth 15-minute interval. Similarly, the approximated maximum

attenuation can be expressed:

Amaxj = TSLmax

j −RSLminj (dB) (3.8)

From the minimum and the maximum attenuation values, the attenuation caused only by

rain (defined for the jth interval by Aj) can be simply extracted, as previously presented

in (Ostrometzky and Messer, 2017):

Aj = Amaxj −min(Amin

j−1 , Aminj ) (dB) (3.9)

which in turn, can be translated directly to a rain-intensity value, by using the Power-Law

of Eq. 3.6:

Rj =b

√Aj

aL(mm h−1) (3.10)

Bias Subtraction

When using the Maximum - Minimum Attenuation Method, the quantization process is

different than in the instantaneous measurements, hereby inducing a bias of B = 1.6 dB

(Ostrometzky et al., 2017). This number is a consequence of the fact that TSL mea-

surements are quantized by a quantization level of ±1 dB, and the RSL measurements

are quantized by a quantization level of ±0.3 dB. This bias cannot be neglected, as it

can affect the rain-estimation accuracy dramatically. Visual demonstration of the bias is

shown in Fig. 3.5 for the almost-totally dry period prior to the Nov. 6th 2015 rain event.

Therefore, to finalize the rain estimation, 1.6 dB were subtracted from each attenuation

measurement:

Rj =b

√Aj − B

aL(mm h−1) (3.11)

Negative values of (Aj − B), if exist, were accounted as zeros. Naturally, the a&b pa-

rameters of the power law are assigned to an instantaneous attenuation values, but were

reevaluated to befit this currently used data storing method (a = 0.441; b = 1.074), using

extreme values statistics (Ostrometzky et al., 2016). The study mentioned above offers

a methodology to extract an a value which will refer to the mean attenuation within the


Figure 3.5: Maximum - Minimum Attenuation Method as presented in Eq. 3.10. Points140-160 are the showers marked in figure 4.11 for the Nov. 6th 2015 event. B = 1.6 dBbias is prominent in the dry period (0-140).

15 minute interval, therefore, it refers to the mean rain intensity. It is worth mention-

ing that parameter a, for instantaneous measurements, is smaller in one to two order of

magnitudes than the aforementioned. It can be learned from here that even when the

maximum attenuation (for a 15 minute interval) is used, the Rj received is not the maxi-

mum rain intensity within the time period, but a lower value which aims to represent the

mean intensity.

The above leads one a wrong assumption that rain field is constant throughout these

15 minute intervals, which is not true (Yakir and Morin, 2011) regarding convective events

in this region, but reasonable nonetheless as averaged values are accounted to.

The link in question is 16 km long, operating at 18.6 GHz, horizontally polarized,

oriented NW to SE and extends almost entirely within the Ze’elim catchment (Figure

2.1). Located close to the regional watershed, the link is placed in an optimal position of

monitoring rain; on the upstream western part of the catchment, where most of the annual

rainfall usually occurs(Morin et al., 2009; Ziv et al., 2006). Properties as these ensure that

nearly all the rain picked up by by this link will eventually fall into the Ze’elim catchment,

thereby making this situation ideal for hydrological studies. Similarly to rain gauges,

CMLs provide data from relatively close to the ground (≈ 30 m above ground level) - an


influential attribute, particularly so when compared to radar back scatter data. CMLs in

poorly gauged areas (Arava region, south of the Judean desert) have a significantly larger

detection factor of local rain events (David et al., 2013), i.e. a typical remote areas network

of links detects spotty rain earlier than gauges, when the latter at times detect no rain.

Spotty rainfall is a common type of precipitation in the Dead Sea area (Cohen and Laronne,

2005; Sharon, 1972), thus amplifying the relevance of a line integrated rain measurement

in a short term warning system. Moreover, it can be interpreted from Eq. 3.11 that as

the length of the link increases, CML sensitivity increases to lower rain intensities. This

characteristic allows the monitoring of small and low intensity rain events in rural areas.

3.2.2 The Effect of Quantization and Length on R

Figure 3.6: The effect of the length of the link on the power loss (in dB) of a microwavesignal. Quantization error for instantaneous measurements is illustrated (dashed line) andrepresents a threshold which rain intensities inducing attenuation not exceed it, will behardly detected.

As previously mentioned, both the transmitter and receiver have a quantization error

which originate from their hardware: ±1 dB for the TSL and ±0.3 dB for the RSL in the

instantaneous measurements (unlike in the 15 minute intervals, mentioned before, where

bias is present). Analyzing the error, in order to assess the arising uncertainty in the

induced attenuation in this kind of data, was done by:


δA =√δTSL2 + δRSL2 ≈ 1.1 (dB) (3.12)

If δA is an independent quantity of R or L for example, it is prominent from Eq.3.11

that longer links will be less affected by the quantization. Figure 3.6 presents the de-

tection ability as a function of length so that the advantage of long links in low rain

intensities detection is clear. The parameters assigned are aligned with the link used in

this study and are seldom the same for different lengths of links. In addition, the quantiza-

tion suits instantaneous measurements and not 15 minute intervals, therefore this Figure

demonstrates the qualitative advantage of long links over short ones but should not to be

quantitively used.

3.3 Radar

Transmitted microwave pulses are back-scattered to the emitting weather radar as a re-

sult of encountering raindrops. By evaluating the power of the back-scattered signal,

the radar returns reflectivity (Z) values (mm6 m−3), more commonly presented in dBZ

(10log10Z), the convention chosen also for this study. Z is related to rain by the Z − R

relations (Krajewski and Smith, 2002), widely examined by Marshall and Palmer (1948).

The parameters’ values used here are those developed by the aforementioned researchers

(Z = 200R1.6) and were found to be suitable to convective rainfall events. The Israel Me-

teorological Service (IMS) C-band radar samples at a 5 minute resolution when operated,

with a beam width of one degree and a 125 m radial resolution. A single elevation degree

was worked with: 0.76o (Fig. 3.7), the second lowest available. Two constrains determined

this angle: a lower one would have been almost entirely blocked by the Judean Mountains,

while although higher ones would avoid this barrier, the altitudes at which they would

reach the area of interest (distant ≈ 85 km away) would be too high and might not detect

low clouds. All of the above converges to create radar cells located roughly 1000 m above

ground level with overview dimensions of 125 m by ≈ 1200 m.

The radar’s data undergoes a Doppler correction, which filters out ground clutter.

The Bulk-Adjustment method, a multiplication factor formed by the ratio of cumulative

quantities measured by rain gauges and the radar cells above them, used for basic calibra-

tion of radars, was examined. Radar QPE are related to as unreliable in this study and

therefore are attempted to be ignored as much as possible. Due to that, neither the Bulk-

Adjustment method nor the general correction factor of f = 1.9 (also found reasonable

for the region by Morin et al. (2009)) were chosen to be worked with, so the actual QPEs

remain untouched. Basic noise reduction measures were undertaken (not mentioning the


Figure 3.7: Second lowest available radar beam (0.76o). Thin lines represent the top andbottom boundaries of the 1o aperture. Thick line is the topography surface. The profile isfrom the IMS by the seashore (Bet-Dagan), to midway of CML. The Judean Mountainscreate an obstacle to low radar beams.

default built in de-noise algorithms of the radar’s program): Z values exceeding 55 dBZ,

representing very heavy rain (≈ 100 mm h−1), were forced to this value, whereas those

not attaining 16 dBZ (≈ 0.36 mm h−1), were regarded as no-rain measurements (Morin

and Gabella, 2007). No additional calibration procedures were undertaken here, as the

aim of this study is to determine the feasibility of using real time data.

3.3.1 ARCOML- Averaged Radar Cells Over Microwave Link

Radar cells located vertically above gauges are traditionally used when the two instruments

are compared and in different radar calibration methods. Since links in rural areas are

generally longer than either dimension of the described properties of the radar cell, multiple

cells had to be included in order to properly represent the line measurement. In an attempt

to imitate the links averaging of rain intensity along the path of the signal, we created

the ARCOML; Averaged Radar Cells Over Microwave Link, namely, the mean of all radar

cells vertically in congruence with the CML.

To match with the 15 minute time-scale, the averaged rain intensity value of every

three radar observations (taken in 5 minute resolution) was accounted to. The use of

the averaged value rather than the maximum (in order to match with the maximum

attenuation of the CML) was chosen due to the assumptions used in determining the


Power-Law ’s a (Eq. 3.6). Taking the maximum value out of every three observations has

been in consideration for various reasons, but after consulting with the IMS representatives

it was decided that the mean values will be worked with, also since the radar is capable

of presenting sporadic highly inaccurate values, then when not properly calibrated and

especially when observations are far away, the actual rain intensity value is not to be

trusted.

3.3.2 Spottiness Indices

Standard Deviation Index

The distances from the mean value in a series, can explain patterns of variations. The

Standard Deviation (STD) of the rain intensities along the path of the link, i.e. the STD

of all 124 cells constructing the ARCOML, can serve as measure of rain spottiness along

the path. STD is a moment of first order and is determined by

σ =

√√√√ 1

n

n∑

i=1

(xi − x)2 (3.13)

where here n = 124. The relevant hypothesis is as follows: the greater the STD of

the radar cells series is, the more inhomogeneous is the rain distribution along the line.

Radar images (Fig. 4.12) and correlation between four rain gauges (Table 4.3) verify this

statement. Moreover, in Figures 4.15 a and b, which are considered to be the spotty

and uniform storms respectively, larger differences are apparent when comparing rain

intensities of CMLR and the Arad IMS rain gauge in the spotty event than in the uniform

one (as well as between the ARCOML and the radar cells above the gauge). This fact will

be further discussed in chapter 4 and points out the difficulty in using a line integrated

rain measurement for flash-floods, as the strong local rain showers are being smeared.

Figure 4.13 (presented in chapter 4) shows the rain intensities of the radar cells along the

link’s path for chosen periods (described in detail in chapter 4) which had not too different

CMLR values. Regardless of the radar not being properly calibrated, and therefore the

expected mean of intensities plotted can be very different both from the CMLR and QPE

logged by rain gauges (Fig. 4.15), the manner of rain distribution along the link is of great

importance and can be attained, where it is clear that in spotty events a large portion of

the link can be completely dry.


Kurtosis Index

Another approach of determining variability is by examining the distributions’ outliers.

Kurtosis is a measure of how prone to outliers a distribution is, or in other words a measure

of the ”heaviness of the tail”. This fourth order standardized moment (a central moment

divided by an expression of σ) is defined as:

k =1n

∑ni=1(xi − x)4

σ4(3.14)

In principle, the larger k is, the thicker the tail of the distribution is (k of a normal

distribution equals three). Therefore, similarly to the hypothesis proposed for the STD,

the hypothesis here is that large k values of the radar cells along the link represent a

rain structure which contains more outliers, and as rain intensity values are truncated at

zero, outliers are referred to values that are larger than the mean, under the assumption

of positively skewed series. Actual values do not play a role in k which makes it more

generic and therefore enables the comparison between periods with different intensities.

A disadvantage using this measure arises due to this property: low, and insignificant rain

intensities data series can show identical kurtosis values as higher (and therefore more

meaningful) ones with a similar distribution. This property makes it hard on the naked eye

to visually determine the contribution of k to the yearned-for spottiness-CMLR relations.

Therefore, in order to filter out low rain intensities (for convenience), a threshold for k

calculations was determined: k is not calculated for radar series with ARCOML values

not exceeding 0.3 mm h−1.

Spatio-Temporal Index

The spottiness of rain is determined by the temporal variations as much as by the spatial

variations, as mentioned in Chapter 1.1. Classification of the amplitude of the spottiness

along the link was needed to support the STD-spottiness theory. Additionally to the rain

gauges correlations and radar images, a validation which is more specific to the CML’s

path was done in order to quantify the spottiness of the tested events. The methodology

is hereby detailed: First, the radar rain intensity data above the link was arranged in an

M × N matrix i.e. 124 × 864, representing the cells above the link for every 5 minute

observation interval (total of 72 h), respectively for each event. Then, three similar size

binary matrices were formed as follows:

1. The maximum value for every N is found.

2. Three thresholds were determined: 25%, 50% and 75% of the maximum value.


3. For each threshold at a turn, the values within each M vector, which do not exceed

the aforementioned percentage of the maximum value, are assigned to zeros, whereas

the others are given ones.

4. In an attempt to reduce noise, if the mean value of a specific vector ofM (ARCOML)

does not exceed 0.3 mm h−1- the entire vector is assigned to zeros.

Visualizing the rain along the link in such perspective allows one to quantify the spatio-

temporal distribution of a storm. Further analysis was done and presented in the following

chapter. The three binary matrices will be referred to, henceforward, as MAT25, MAT50

and MAT75 respectively for the tree thresholds mentioned above.

Chapter 4

Results

4.1 Hydrological Analysis

Different methods of analyzing the hydrological data and assessing the roughness coeffi-

cient are presented in the following section. Water stage in the channel is presented as a

function of the discharge, hydraulic radius, wetted area and wetted perimeter in Figure

4.1.

4.1.1 The Effect of Manning’s n on the Calculation of Water

Discharge

It can be comprehended from the above, that the roughness coefficient can vary in different

water depths. In order to examine and visualize the sensitivity of the discharge to n and

it’s optimal values for varying depth, a comparison between the two discharge calculation

methods was conducted. The subtraction of discharge values calculated by Eq. 3.3 (Qv)

from the one calculated by Eq. 3.1 (Q), for every pair of level and n, relating Eq. 3.1, was

examined. Results are presented in Figure 4.2. The values which are the closest to zeros

represent little differences between the two methods and therefore corresponding n values

can best fit the Manning’s Formula at the certain water stage. As can be seen in Figure

4.2, since n is linearly (inverse) proportional to Q, the sensitivity of the discharge difference

to different n values is greater in larger depths. Of course, the above was done under the

assumption that the use of Eq. 3.3 provides the better outcome. This assumption is surely

debatable.

In the next chapter the use of these findings is used to determine the best roughness

coefficient for this monitoring station.

27

28 CHAPTER 4. RESULTS

Figure 4.1: Calculated flow properties in wadi Ze’elim with change in water depth: dis-charge (top left), wetted area (top right), wetted perimeter (bottom left) and hydraulicradius (bottom right). The discharge rating curves represents the calculation methodsbased on Eq. 3.3.

CHAPTER 4. RESULTS 29

Figure 4.2: Response surface of |Q − Qv| for a range of level and n values. The graphemphasizes the sensitivity of the calculated discharge to n in large depths. It can be seenthat with the growth of water depth, grows the dependency on the coefficient.

4.1.2 Optimization of a Constant n Based On Velocity Measure-

ments

In many hydrologic studies, n is considered a constant in aim of simplifying calculations or

in the absence of relevant data. For initial estimations, discharge calculations were done

by using a constant roughness coefficient. Then, the velocity measurements, mentioned

in section 3.1.1, were used to calculate discharges without the use of Manning’s Formula.

The differences between the stage-discharge curves are presented in Fig. 4.3

Optimizing Manning’s n was done by using these two curves. A correction factor

fn, which will later be referred to n, was inserted into the discharge equation using the

constant n in the form of:

Q = fc 0.035−1A ·Rh 2

3S12 (m3 s−1) (4.1)

The objective function chosen was the RMSD of the two, and it’s minimum value was

sorted using the Least Squares method. The RMSD function, from which the minimal

value was searched, is:

RMSD =

√√√√ 1

n

n∑

i=1

|Qi −Qvi |2 (4.2)

where Q is the discharge calculated by a constant n = 0.035 and Qv is the discharge


Figure 4.3: Stage-Discharge relations for two discharge calculation methods. Qv was cal-culated using the velocity measurements, as presented in Eq. 3.3 (blue). Q was calculatedusing the Manning Formula with a constant preliminary assumption of n = 0.035.

Figure 4.4: Surface flow velocity in water with varying depth. A non logarithmic scale ispresented in the small box along with a 5% instrument error. This exceptional data baseof water velocity, measured during flash flood events, is used to estimate discharge fromwater depth (y = 0.549x+ 0.519; r2 = 0.85).


calculated by the usage of water velocity data (Fig. 4.4), for the ith water depth variating

from 0 to 2 meters in 1 cm steps.

Finally, the fc which was obtained from the minimal RMSD (1.429 m3 s−1) was cho-

sen. The calculated value of the factor was fc = 1.205, thereby pointing on a ≈ 20%

difference from the initial estimation of n. It follows that the corrected value for this

specific channel is n = 0.029. This method can be implicated on different sights where

velocity measurements are available, so roughness coefficients, found in various ways, can

be compared.

4.1.3 Estimations of Manning’s n With Two d84 Determination

Methods (Limerinos)

In the previous chapter, two methods of deriving the d84 were presented: one which is

commonly used and another one, based on fitting a truncated normal distribution (non-

zero) to the data. Calculated values are presented in Table 4.1. Figure 4.5 shows the actual

distribution of pebbles’ sizes for the four monitored channels in the Ze’elim catchment. The

probabilities and PDF of both the data and the fitted normal distribution (respectively),

for the Ze’elim trunk channel, are presented in Fig. 4.6.

Table 4.1: Values of d84 (mm) for the four monitored channels, for the two investigatedmethods: linear interpolation and a truncated normal distribution fit.

Channel Linear interp. Normal dist. fitZe’elim trunk channel 57.4 71Shafan tributary 41.9 54.4Ze’elim-upper tributary 53.9 65.2Harduf tributary 84 92.4

It can also be seen, that the alternative method presented in Figures 4.7 & 4.8, does not

present stabilizing values as depth increases, but constantly decreasing ns. Thus, larger

discharges may outcome by the use of the minor most values (corresponding with the

largest water depths), which will less fit the discharge calculations done using the velocity

measurements. Manning’s n for the three tributaries is presented in Fig. 4.8.

Calculating n was done based on Eq. 3.5 for Rh, which was calculated as described

in the previous chapter. As expected, the values of n stabilize in large water depths (Fig.

4.7). It can be seen that the most common way of deriving d84 (orange line) gets to a

stabilized value of n, closer to what was reached by the optimization with the velocity

measurements,than the proposed distribution fitting method.


Tributaries Discharge

The presented plots are the very first demonstrations of discharge progression throughout

a drainage basin in the Judean-Desert. Quick visual analysis of the November case (Fig.

4.9) implies that the transmission losses have a considerable effect, by looking at the first

peak of Ze’elim-Upper (and the small ones following it within the next hour), which only

a slight sign of it remains at the outlet station. As this was the first significant event (of

the season) in the area, it can tell a lot about the decrease of the infiltration capacity, in

comparison with another event. Moreover, the travel time of the large peak (time interval

between the maximum values of the two stations) is slightly more than one hour, and

the travel distance of the channel between the two stations is 8.65 km- which makes a

(a) Ze’elim- trunk channel (b) Shafan tributary

(c) Ze’elim- Upper tributary (d) Harduf tributary

Figure 4.5: Histograms of the pebbles sizes samples for all four monitored channels in theZe’elim catchment: Ze’elim trunk channel (a), Shafan (b), Ze’elim-Upper (c) and Harduf(d).


(a) (b)

Figure 4.6: Probability of the sampled data (a) and the PDF of the fitted truncated normaldistribution (b) of the truck channel of wadi Ze’elim.

Figure 4.7: Change of n with water depth according to the two methods regarding d84 andanother method for reference, as presented in Fig. 3.3 (Garti et al., 1981), for the trunkchannel.

≈ 2.4 m s−1 wave travel speed for that segment. This value is reasonable and lies within

the measured mean flow velocities, shown in Fig. 4.4. Further research should be done

regarding this data.


(a) Shafan tributary (b) Ze’elim- Upper tributary

(c) Harduf tributary

Figure 4.8: Change of n with water depth according to the two methods regarding d84 andanother method for reference, as presented in Fig. 3.3 (Garti et al., 1981), for the threemonitored tributaries in the catchment: Shafan (a), Ze’elim-Upper (b) and Harduf (c).

4.2 ARCOML

Table 4.2 strengthens the theoretical derivation of ARCOML by presenting good cor-

relations with CML rainfall (CMLR). Justifications for the determination of spottiness

classification mentioned in the table is presented and widely explained in Chapter 4.3.3.

In this study, the ARCOML is constructed by 124 cells gathered from 5 different consec-

utive azimuthal angles (Fig. 2.1), as an outcome of the spatial orientation of this link.

Figure 4.15 shows the CMLR-ARCOML relations in parallel with the gauge-radar plot.

It can be seen that the radar is not accurately pointing on the rain intensities, but has a

consistent tendency with resembling differences from both the CML and gauge for each

storm.


(a) Nov. 6th 2015

(b) Jan. 25th 2016

(c) Jan. 1st 2016

Figure 4.9: Discharge of the three tributaries: Shafan, Ze’elim-Upper and Harduf, and oftheir total discharge, measured at Ze’elim trunk channel’s gauging station, all for threecase studies: November 6th 2015 (a), January 25th 2016 (b) and January 1st 2016 (c).Ze’elim-Upper contains the discharge of Shafan tributary as it was located downstream ofthe confluence due to lack of suitable spots upstream.


Table 4.2: Correlations (r) between ARCOML and CMLR for each case study. ARCOMLrepresents the CMLR fairly to very well.

Event rNov. 6th 2015 0.956Jan. 25th 2016 0.770Jan. 1st 2016 0.578

4.3 Spottiness Indices and Discharge: a Short Term

Warning Feasibility

In this section radar STD&k-CMLR relations were qualitatively analyzed with respect to

the hydrologic responses. Considering that rain intensities are never below zero, and that

extreme rain intensities are less prevalent than low ones in a given large enough spatial

(as well as temporal) window, let alone in the Judean desert, it is reasonable to assume

that a snapshot of the intensity-distribution of the rain in a given area (in this case along

the 16 km of the CML) will be positively skewed. Therefore, it is conceivable that in the

majority of the cases, a rise both in STD and k is a result of the presence of higher rain

intensities (rather than lower) than the mean. Based on the aforementioned assumption,

pairs of high k-CMLR or STD-CMLR were examined. Figure 4.10 presents consecutive

snapshot histograms of the rain intensities along the CML, as captured by the radar on

January 1st 2016. All these snapshots have positive skewness.

Examinations of the trunk channel route (Fig. 3.2) and measurements of water velocity

(Fig. 4.4) at the outlet lead to the preliminary working premise that a common range

of average flow velocity (for effective flows) in the wadi is similar to the one measured

at the outlet, ≈ 2− 2.5 m s−1. Sharper slopes occur downstream of the double waterfall

(located 9, 000 m upstream of the hydrometric station) than upstream of it (Fig. 3.2).

Notwithstanding, the premise remains reasonable since based on field observations, bed

roughness seems to be larger downstream of the waterfalls. Considering the distance

the water travels from the western point to the eastern one, it was assumed that the

link detects a flash-flood generating rain, hence forward: Effective Rain Period (ERP),

about 2.5 − 3.5 h before the wave is detected at the outlet. Chosen times of interest on

the hydrograph are marked and numbered in Figure 4.11. Their coherent preliminary

ERPs are respectively numbered and marked as shaded areas on the rain plot below the

hydrographs.

The three chosen case-studies: November 6th 2015, January 25th 2016 and January


Figure 4.10: Histograms of rain intensities of 124 radar cells on January 1st 2016 abovethe CML, in a 5 minute resolution starting at 05:05 (UTC+2). Low rain intensities aremore prevalent and some kind of a decaying distribution tail is noticeable.

1st 2016, represent spotty, uniform and in-between rain events respectively. Table 4.3

validates this statement by showing the correlations between four rain gauges for each

storm, and visual reference in the form of the IMS radar images is presented in Fig. 4.12

(radar cells’ QPEs over the CML for these snapshots are presented in Fig. 4.13). Further

validation can be found in Chapter 4.3.3. Flash-floods with peak discharges are present

in all three events.

4.3.1 Standard Deviation Index

Rain began falling within the basin at least 24 h prior to ERP 1 on the January 25th event,

enriching the soil moisture content. ERP 1 shows stronger rain intensities than shown in

ERP 2 (with resembling cumulative quantities), yet the latter was followed by a 36 m3 s−1

wave. Examining the STD coupled with the max. intensity of each ERP reveals that ERP

2 was more spotty than ERP 1 (0.36 vs. 1). Later, high uniform CMLR of ≈ 3.2 mm h−1

and STD = 0.1 was followed by a modest rise of ≈ 10 m3 s−1 in the hydrograph- point

3. In comparison, similar CMLR (3.9 mm h−1) was recorded in ERP 2 on the Nov. 2015

event, followed by a 29 m3 s−1 wave. A noticeable difference can be seen in the STD values

of the two as the one on November exceeds the value of 7. It is prominent that cumulative

rain depth (or in other words: soil saturation level) has to be accounted as well e.g.: ERP

1 on the November event was suitable for flow generation, but in vain. However, it was

the first rainfall of the storm, therefore speculated to be absorbed by the dry land and


(a)

(b)

(c)

Figure 4.11: Standard Deviation spottiness index and rain intensities during Effective RainPeriods (ERPs), with respect to runoff at the outlet of the Wadi. The events presented areNovember 6th 2015 (a), January 25th (b) and January 1st 2016 (c). Lower part: CMLRand radar STD 15 minute resolution (blue stems and orange line respectively). Upperpart: Discharge hydrograph in Ze’elim outlet (black line). Markers on the hydrographcorrespond with their ERPs (shaded and numbered areas on the bottom part). Each ERPrepresents 3.5− 2.5 h prior to the marked hydrograph point.


Table 4.3: Correlations (r) between all four rain gauges for the Nov. 6th (a), Jan. 25th

(b) and Jan. 1st (c) events. Distances between gauges are presented in parentheses.Both Arad IMS and Shani gauges are IMS gauges, which have a 10 min. time resolution.Hanokdim and Arad are dedicated gauges which measure every minute. Summation ofevery 10 samples was used in order to befit the IMS sampling rate.

a Nov. 6th 2015 Arad IMS Shani IMS Arad HanokdimArad IMS 1 – 0.712 0.065Shani IMS (16.40) – – –Arad (3.22) (16.93) 1 0.147Hanokdim (9.99) (20.11) (6.80) 1

b Jan. 25th 2016Arad IMS 1 0.370 0.825 0.524Shani IMS 1 0.408 0.349Arad 1 0.750Hanokdim 1

c Jan. 1st 2016Arad IMS 1 -0.036 0.589 0.238Shani IMS 1 -0.027 0.084Arad 1 0.422Hanokdim 1

Figure 4.12: IMS radar images of chosen times for the three case-studies as visual supportfor STD-spottiness relations. Since images are taken in a 5 minute resolution, one figurewas chosen out of the three taken prior to the referred coupled CMLR-STD. Left: Nov. 6th

2015, 14:00 (ERP2); Middle: Jan. 25th, 16:15 (ERP1); Right: Jan. 1st 2016, 06:15 (ERP1).IMS radar and CML illustrations are marked as a red semi-circle and a transparent purpleline respectively.

drained out by transmission losses. Furthermore, the differences in CMLRs on Jan. 1st

are not as significant as in the other two events, nevertheless, followed by a sharp water


Figure 4.13: Radar cells QPE along the CML path (NW to SE), in the coherent timeswith Fig. 4.12, for the three events.

level rise, ERP 1 containing the distinct maximal STD and a slight CMLR rise (maximal

value as well).

In case of a given low CMLR, the spottiness index is crucial for runoff generation.

Low STD may point on a rain intensity which is lower than the saturated hydraulic

conductivity representative value of the catchment, or just low enough to percolate a as

part of transmission losses. Higher STD may state that there was an area in which the

local rain intensity exceeded the saturated hydraulic conductivity value, allowing runoff

to develop. A good example can be seen in ERPs 2 and 3 on the Jan. 1st event, at a

time the surface had already been wetted: ERP 2, chosen for comparison only, was not

followed by water level rise (containing an event maximum of CMLR= 1.9 mm h−1 with

STD= 0.31), however slightly higher STD values in point 3 were followed by a minor one

(2 m3 s−1), although accompanied with even lower CMLRs.

4.3.2 Kurtosis Index

Comparing the events by using k is somewhat easier as kurtosis is not affected by the actual

intensity values. These results strengthen the aforementioned regarding STD. Enlargement

of the ERPs of the two January events can be seen in Fig. 4.14. It can be clearly

seen that ERP 1 and 3 both contain two consecutive CMLRs reaching 2 − 3 mm h−1,

on January 25th. Notwithstanding, the followed hydrological responses were poor. k

values in the first fluctuate around 4-5 whereas the higher CMLRs in the latter are even

lower. It is prominent, that even with lower CMLRs, the hydrological response of ERP


2 is substantial. The relatively high kurtosis values, corresponding with two consecutive

CMLRs ≈ 2 mm h−1 create the large water level rise (36 m3 s−1).

In comparison, ERP 1 in the January 1st event contains higher ks and one pair of

2 mm h−1 & k = 10, which is also followed by a wave. The lower amplitude of the

hydrograph can be a result of lower CMLRs prior to the high value k-CMLR pair, as well

as the absence of consecutive relatively high CMLRs. Furthermore, the very first water

level rise (prior to ERP 1) corresponds with a low CMLR accompanied by a very high

kurtosis (k ≈ 15). Similarly, the additional ERP 1a (not specified in Figure 4.11) also

contains CMLR< 1.5 mm h−1 and k = 10, resulting in a very modest hydrograph rise. It

indicates a very high and localized rain intensities, occurring at these time steps, therefore

emphasizes the probable higher dependency of the hydrological response on the CMLR

than on the spottiness index.

Kurtosis values for the November event were significantly higher, fluctuating around

15 and reaching 34 in ERP 2. By examining ERP 1, one can come to a similar conclusion,

as was done in the STD analysis (therefore it is not presented): it was indeed suitable for

runoff generation, but the flow probably was drained due to transmission losses.

4.3.3 Spottiness Validation

Examination of STD values throughout the progressions of the tree storms provides an-

other perspective. Table 4.4 demonstrates STD representative values for each event. The

mean values are aligned with the above as well. Furthermore, the additional examina-

tion of the median values emphasize how abruptly appearing and shortly-staying are the

high-intensity local rain-cells in the region: the spotty event of Nov. 6th has a resembling

median to the other events, but has a significantly higher maxima, out of the least number

of samples.

Also, examining the line averaged rain intensities against the local ones, recorded by

rain gauges, can point on the spatial distributions of the rain. As mentioned in Chapter

3, the presented QPE of the radar (as well as in the form of ARCOML) are in line

with the ground truth (Fig. 4.15). However, when the actual values are compared (point

measurement to line measurement), the differences are outstanding: Nov. 6th is considered

to be the spottiest event of all, and in a way that supports the theory, the gauge plot

(lower) in Figure 4.15 presents higher values, in an order of magnitude, from the CMLR.

In contrast, the event suggested as the most uniform of all, is the Jan. 25th, where the

gauge measurements show similar values to those provided by the line integrated rain

(Fig. 4.15 b). To complete the picture, the gauge measurements in the ”in-between”

event (spottiness-wise) of Jan. 1st 2016 (Fig. 4.15 c) logged values double the ones seen


(a)

(b)

Figure 4.14: Zoom in to Figures 4.11 b and c with kurtosis (k) spottiness index and rainintensities during Effective Rain Periods (ERPs), in respect to runoff at the outlet of theWadi. The events presented are January 25th (a) and January 1st 2016 (b). ERP1a (inb) is an additional point which is not presented in Figure 4.11. k was not calculated forARCOML values not exceeding 0.3 mm h−1 and is given in a 5 minute resolution.


(a) Nov. 6th 2015

(b) Jan. 25th 2016

(c) Jan. 1st 2016

Figure 4.15: Radar measurements vs. ground rain gauges and link measurements. Theevents presented are Nov. 6th 2015 (a), Jan. 25th 2016 (b) and Jan. 1st 2016 (c). Top:ARCOML is plotted along with the CMLR. Bottom: Rain intensities of Arad IMS raingauge are plotted along with the averaged values of three consecutive radar cells (one justabove the gauge, one on it’s tail and another one after).


Figure 4.16: IMS radar cells intensities distribution along the CML path (NW to SE), attimes where CMLR were the same (≈ 2 mm h−1), for the three events: Nov. 6th 2015:12:15; Jan. 25th: 17:30; Jan. 1st 2016: 06:15 UTC+2.

in the CMLR. This underlines the challenge this study attempts to face in order to use

long links in hydrology. The values around which the radar STD fluctuates (Fig. 4.11)

are in line with the aforementioned, showing low, high and medium values for the three

events respectively.

Table 4.4: STD representative values for the three case studies. Data was obtained in5 min. intervals, including only non-zero samples. The original sampling duration of thedata sets (prior to the exclusion of zeros) was for the entire periods presented in Fig. 4.15.Values are given in mm h−1. N is the number of samples (non-zero samples) which wereused for the analysis.

Event N Median Mean Max. ClassificationNov. 6th 2015 67 0.372 2.112 14.165 SpottyJan. 25th 2016 122 0.230 0.302 1.408 UniformJan. 1st 2016 272 0.401 0.597 4.071 Medium

Figure 4.16 shows the distribution of the radar cells’ rain intensities along the path, at

times where CMLR were similar to one another (2 mm h−1). The distribution differences

for the three events are prominent and provide a visual reference of this work’s main issue.

Spatio-Temporal Index Validation

It was shown previously that the temporal rainfall distribution can be approximated by the

Gamma distribution (Dan’azumi et al., 2010). Two parameters of the Gamma distribution

are the shape (κ) and scale (θ) parameters. The latter is a parameter which the larger it is,


the more spread out the distribution. The data analysis of MAT25, MAT50 and MAT75

(defined in Chapter 3.3.2) is hereby demonstrated. Histograms of the wet percentage of

the link for MAT50, with a fitted Gamma distribution curve (for demonstration), are

presented in Fig. 4.18 (histograms for MAT25 and MAT75 are presented in Appendix

A). Even without complex analysis, it is prominent that the histogram throughout the

three days, for each event, is most spread in the January 25th event and most spotty in

the November one. Moreover, the θ parameters of the fitted Gamma distribution curves

support the above with θ = 5.01, 3.63, 2.37 respectively for January 25th, January 1st

and November 6th. The same trend is seen in MAT25 and MAT75.

Figure 4.17: Histograms of the percentage of ones out of the 124 radar cells in MAT50 forevery non-all-zeros vector of M . Left to right: January 25th, January 1st and November6th. PDF curves (red) were placed for qualitative demonstration only.

Withal, the higher 90th percentile of the ”binary wet” percentage distributions can

also constitute as a measure of the spatio-temporal spottiness. Fig. shows that both the

thresholds of MAT25 and MAT50 create a division in which the 90th percentile shows

higher ”binary wet” portions of the link as the event is more uniform. Such statement can

not be said with confidence by considering the 90th percentile of the MAT75 alone.


Figure 4.18: The 90th percentile of the binary link coverage (percentage of ones out ofthe 124 radar cells) for all three thresholds (MAT25, MAT50 and MAT75) for everynon-all-zeros vector of M . Left to right: January 25th, January 1st and November 6th.

4.4 Virga

The virga is a common phenomenon in dry areas i.e., defined as the evaporation of water

droplets before they reach ground level (Fraser and Bohren, 1992). As radar observations,

in some distance from it (Fig. 3.7), are taken in high altitudes, it is inevitable that when

virga takes place, the reality in ground level will be somewhat different than observed

above. Figure 4.19 presents a spring event in which ARCOML is different from the CML

readings in certain periods. A glimpse on the relative humidity, measured in the Arad

IMS station, points on the possible cause. It is shown that there is little to no agreement

between the measurements when the RH values are low, whereas this agreement gets

better as relative humidity exceeds a certain value (around 80%). The above can cause

one to suspect that the virga plays a considerable role in radar inaccuracies in dry areas,

one which must attract greater attention in future studies and applications.


Figure 4.19: ARCOML (orange) and CMLR (blue stems) on May 2014. The shadedarea represents the period when the relative humidity exceeded 85%, based on the IMSmeteorological station in Arad. It is prominent that some rain, detected by the radar, didnot reach ground level fully. It can be assumed that the virga plays a role in this event,as the low relative humidity values fluctuated around 35%.

4.5 Discussion

Throughout the study a new approach of combining radar and CML measurements to in-

vestigate floods generation in deserts had been suggested. It illuminates the rain patterns

along the microwave path, so that based on this approach of integration one can better

assess the manner in which rain is distributed in the region. It was shown that some kind

of a Spottiness-CMLR relation exists, one which significantly affects flash-flood genera-

tion. Considering the foregoing, the radar’s QPE are not always representative of ground

reality, especially when high rain intensities are present (Austin, 1987). Nevertheless, it is

reasonable to assume that the majority of the radar cells have common sources of errors

for each measurement, therefore the STD and especially the kurtosis, are used somewhat

confidently.

STD, contains the actual rain intensities, as it contains actual differences from the

mean. This property makes the STD not a perfect measure of the rainfall distribution,

as the same distribution patterns with different amplitudes (absolute values) will have

different STD values, which may miss-lead when trying to assess the uniformity of the

rain using a numeric index, especially when the radar is not optimally calibrated.

As a fourth order moment, the kurtosis is not effected neither by the multiplication nor

by the addition of any value to the data, therefore may be a more robust quantity which

can be worked with. Thus a further classification analysis is needed in order to show a

significant contribution. More analyzed storms would have helped as well. Nonetheless,


kurtosis seems to be a more suitable index to work with regarding patterns of distribution

of rain along a microwave link. It is worth mentioning that the way by which the STD

and kurtosis are affected by the factors causing inaccuracies in the radar’s rain intensity

were not examined.

It was concluded that low spottiness indices allow one to project the measured CMLR

on to a larger area. Such conclusion can rise the question of quantities: if a certain (low)

rain intensity is accounted to a larger portion of the catchment, is the specific rain depth

in the catchment likely to be larger than a different rain intensity (high) accounted to a

smaller portion? This aspect is hereby suggested to be further studied.

Further research should also be undertaken in applying this method as a working

tool. Deep examination of all thresholds which possibly lead to floods and advanced

statistical tests are necessary in order to define reliability. Routing within the drainage

basin remains unclear, thus monitoring tributary water discharge can be helpful in order

to better determine the ERP. Furthermore, an integrating method of more links is required

to cover larger areas and for the detection of prone rain cells even before they reach the

catchments, thereby increasing the alarm time.

This Wadi Ze’elim case study is a single catchment scale one, and may be only a

promo to a much larger, multi catchment, future study which is proposed to be done in

this direction with more links. Of-course, larger floods than the ones presented here are

reoccurring yearly in this catchment. Nevertheless, the concentration on the ”medium”

(peak discharge wise) events is necessary in order develop the feasibility of setting thresh-

olds for flash-floods generation. By looking at Figures 4.9 (a) and 4.11 (a), the November

event, one can conclude that the absence of a water level rise at the outlet, due to ERP1,

was actually monitored by the Ze’elim-Upper station. This finer resolution of the response

of the basin can expand research into smaller events from which lower thresholds of floods

conditions can be examined.

Possessing mean surface water velocity, as well as Wolman measurements was crucial

for achieving a more accurate discharge assessment. It allowed the analysis to refer to dis-

charge values with greater confidence.Nonetheless, more measurements of various depths

could have been helpful. Velocities for higher depths than those measured are approx-

imated by an extrapolation of the linear regression trend-line presented in Fig. 4.3. It

is possible that velocities in these depths cease to obey this projected behavior, hence a

considerable error can occur in calculating peak discharges.

Different suggestions of reconstructing rain fields by the usage of CML have been

published as new more complex ones are currently under development. In many of them,

promising results are presented in comparison to ground truth. As the common ground of


these algorithms is the interpolations between multiple neighbor links. Remote rural areas

are often characterized by their low density commercial microwave networks, i.e. fewer

and longer links. These therefore have inaccurate reconstructed rain fields. It is these

cases in which our method of involving radar data becomes even more relevant.

Chapter 5

Conclusions

Concluding the ”long isolated link” issue researched in this study, it appears that beneficial

value can be gained by using additional information from a weather radar, even when

located far away, with complex terrain in the medium and without complex calibration

procedures, which thereby allow thinking of a real time use of the data.

It was found that slight changes in the line integrated rain intensities, derived from

a Commercial Microwave Link (CMLR), are affecting the hydrograph rise dramatically.

Accompanied by a spottiness index, derived from a limited far away radar observations,

the CMLRs constitute measures that can be used to predict the hydrological response

of a given catchment. For a given CMLR, stronger runoff responses were detected when

spottiness indices increased.

Projecting the spottiness, indicated by STD (Standard Deviation of the radar cells

covering the path of the link) and the radar kurtosis, spatially on the surroundings of

the link was shown feasible. Table 4.3 serves as a support to this hypothesis, presenting

correlations between rain intensities provided by four different rain gauges located around

the link. It is clear that the temporal-spatial correlations presented are aligned with Table

4.4. On the spotty November event, the furthest gauge (Shani IMS) did not monitor rain at

all prior to the hydrograph rise, whereas the correlation between the closest gauges to one

another (Arad and Arad IMS, distant only 3.22 km away) was 0.712. A poor correlation

coefficient was found some several kilometers away, with the Hanokdim gauge. On the

opposite, the correlations in the uniform event are significantly better. As expected, the

medium event of Jan. 1st showed poorer correlations with the growth of the distance.

Therefore, it can be concluded that low spottiness indices indicate that the CMLR fairly

represents not only the path of the link, but also it’s surroundings. Furthermore, from the

preliminary examination of the data, kurtosis seems to be a better measure of pointing

on the spottiness along the link than STD as it emphasizes the probability of the outliers

rather than focusing on the area closer to the mean. It also allows one to compare different

50

CHAPTER 5. CONCLUSIONS 51

events more confidently as the QPE of the radar is considered unreliable, and therefore

the STD (as well as the variance) is affected as well.

One of the most profitable properties of this approach is the attainability, in principle,

of obtaining the data instantaneously and online, proven possible previously by Chwala

et al. (2015). This enables further developed methods of flood warning, based on this

integration, to be used as a short term one, and as it relies on observations, it has the

potential of having fewer false alarms than predicted rainfall-based systems lacking the

CML backbone e.g., Cools et al. (2012).

The constant Manning’s n, found by the optimization of fitting the two water stage-

discharge curves (Eq. 4.1), was found to be 0.029, which is a lower number than expected

at the beginning of the research (0.035). The classical Limerinos method (determination

of d84 by a linear interpolation between frequencies of pebbles’ diameters) converged to a

similar, yet greater value, for high water depths, in the trunk channel of the wadi (Fig.

4.7). An attempt to approximate the pebbles distribution in the channel to a normal

distribution was done. The value which Manning’s n converged to by using this method

of deriving d84 was even greater than that achieved by the classical method. Nonetheless,

it was closer to the 0.035 which was considered reasonable by the preliminary assumptions.

Saying that, the Manning’s n curve (Fig. 4.7) obtained by using the linear interpolation

method was chosen preferable due to it’s better resemblance with the n = 0.029, derived

using the velocity measurements.

The method of harvesting the 84th percentile from the fitted distribution is logical

as the assumption of a normally distributed pebble-sizes is in the core of the method,

along with the arguable assumption of a linear growth between each maximal measured

diameter. Saying that, the need to use a truncated distribution indicates the difficulty

of the fitting assumption. Moreover, by definition, the normal distribution has some

probability for extreme values (infinity). Thus, under certain circumstances, it is possible

to get a d84 > 128 mm, which is the maximal measured diameter, and therefore the

calibration of Eq. 3.5 will no longer be valid.

Appendix A

Appendix

(a) MAT25

(b) MAT75

Figure A.1: Histograms of the percentage of ones out of the 124 radar cells in MAT25(a) and MAT75 (b) for every non-all-zeros vector of M . Left to right: January 25th,January 1st and November 6th. For MAT25: θ = 16.44, 14.24, 6.82. For MAT75:θ = 1.10, 0.82, 0.63 respectively.

52

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. תקציר

לכלים לגיטימיים בין תחנות בסיס סלולריתמיקרוגל בשנים האחרונות הופכים ערוצי תקשורת

לפני הקרקע, בקרבה ,מסוג זה, אשר נמדדים ע"י הנחתת אות מיקרוגל גשם נתונילניטור סביבתי.

אורכי ערוץנמצאו כמדויקים באזורים אורבניים ואורבניים למחצה. בשל צפיפות רשת נמוכה יותר ו

שחזור שדה הגשם הוא משימה מאתגרת באזורים ייניים לאזורים מדבריים, , האופיותר גדולים

-בעיקר מדי גשםמרוחקים. הריחוק מציוויליזציה גורם לחוסר משמעותי במדידות גשם בפני הקרקע,

מידע הכרחי לחיזוי נגר באזורים צחיחים. מדידות מכ"ם מועדות לאי דיוקים באזורים אלה, בין

השאר עקב התאיידות טיפות הגשם בטרם הגעתן לקרקע. כתוצאה מהאמור לעיל, התראה בפני

ני הכלים בין ש שיטפונות בזק באזורים מדבריים היא משימה אתגרית. במחקר זה מוצגת גישת שילוב

המוגבלים, אך חיוניים הללו, אשר מאפשרת הבנה טובה יותר של השפעת מבני תאי גשם שונים על

הנחתת אות המיקרוגל. לשיטה זו פוטנציאל לתרום לשיפור ביצועי מערכות התראה בפני שיטפונות

, אשר לה של הגשם( spottiness)מידת הנקודתיות -בזק, מאחר ושינויי תבניות הגשם במרחב ובזמן

חשיבות רבה בהידרולוגיה של מים עיליים, ניתנת לניטור ע"י מכ"ם ואילו נתונים כמותיים בגובה פני

פרמטרים אלה חיוניים בהבנת תהליך יצירת נגר עילי ואינם מובאים הקרקע מסופקים ע"י הערוץ.

הגשם לאורך בצורה מספקת ע"י כל אחד מהכלים לבדו. גישה זו מאפשרת הערכה של אופן פיזור

( מוצעים לצורך סיווג. kurtosisהערוץ ואינדקסים סטטיסטיים כגון סטיית תקן, אחוזונים וגבנוניות )

תוצאות עבור אזור ים בשימוש מידע הידרולוגי, נבחן הקשר להיווצרות שיטפונות בזק. יתר על כן,

המלח מוצגות כאשר וידוא נקודתיות הגשם נעשה בשימוש ארבעה מדי גשם ומכ"ם השירות

קמ"ר(, הממוקם במדבר יהודה הצחיח, נוטר באופן רציף 542נחל האכזב צאלים ) המטאורולוגי.

קות. מדידות של מהירות פני מים ממוצעת, רום מים, חספוס תשתית וחתכי אורך למטרת הערכת ספי

. זוגות דומים של אינדקס נקודתיות הגשם ועוצמת גשם הראו ראשיורוחב נלקחו במוצא ערוץ הנחל ה

, יחד עם תגובות הידרולוגיות דומות. בנוסף, זוגות של עוצמות גשם גבוהות ואינדקס נקודתיות נמוך

היווצרות נגר עילי בעוצמות שונות. הראומוכות ואינדקס גבוה, עוצמות נ

אוניברסיטת תל אביב

ע"ש ריימונד ובברלי סאקלר הפקולטה למדעים מדויקים

בית הספר למדעי כדור הארץ

החוג לגאופיזיקה

מסחרי תשילוב של נתוני גשם ממכ"ם ומערוץ תקשורת סלולרי לשיטפונות בזק בסביבת ים המלח ותהתייחסב בודד

הוגש כחלק מהדרישות לקבלת התואר חיבור זה

באוניברסיטת תל אביב .M.Sc -מוסמך אוניברסיטה

מאת

אדם אשל

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