RELATIONSHIP BETWEEN TERRESTRIAL WATER

STORAGE AND THE OCCURRENCE AND MAGNITUDE

OF FLOODS AND DROUGHTS

WU CAIJUE

DEPARTMENT OF CIVIL & ENVIRONMENTAL

ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

AY2015/2016

RELATIONSHIP BETWEEN TERRESTRIAL WATER

STORAGE AND THE OCCURRENCE AND MAGNITUDE

OF FLOODS AND DROUGHTS

WU CAIJUE

A THESIS SUBMITTED

FOR THE DEGREE OF BACHELOR OF ENGINEERING

DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

Acknowledgement

The research for the completion of this thesis are conducted in NUS Hydrology &

Water Resources Group, Department of Civil & Environmental Engineering, National

University of Singapore, under the supervision from Dr. Pat Yeh.

All original data used in the thesis are retrieved from NASA’s Gravity Recovery and

Climate Experiment (GRACE) satellite data, Global Land Data Assimilation System

(GLDAS) data products, and Global Runoff Data Centre (GRDC), with permission.

Appreciations to Mr. Peng Xiao and Mr. Huang Zhiyong for the help on processing the

original data. Appreciations to Dr. Pat Yeh for all the instructions and encouragement

given to me over the year.

Table of Contents

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

2. Data and Methods ................................................................................................... 3

3. Results and Discussion ......................................................................................... 12

3.1. Comparison of Daily Precipitation, Evaporation, Runoff and Storage ............ 12

3.2. Preliminary Relationship between Total Runoff and Storage Anomalies ......... 23

3.3. Baseflow Separation ......................................................................................... 27

3.4. Each Year with Different Color Plots ............................................................... 34

3.5. Each Month with Different Color Plots ............................................................ 38

3.6. Baseflow-Storage Relationship in Dry Seasons and Wet Seasons ................... 42

3.7. Remove Data on Days with High Accumulative Precipitation ......................... 44

3.8. Time-Lag Modification ..................................................................................... 48

4. Conclusion ............................................................................................................ 58

5. References ............................................................................................................. 59

Appendix A. MATLAB Scripts..................................................................................... 60

A.1 MATLAB Script for Retrieving Daily Storage Anomalies ................................ 60

A.2 MATLAB Script for Baseflow Separation ......................................................... 61

A.3 MATLAB Script for Removing Values on the Days with High Accumulative

Precipitation .............................................................................................................. 62

A.4 MATLAB Script for Time Lag Modification ..................................................... 64

Summary

Currently the prediction on floods and droughts can be made with limitedly short

timescale and low accuracy, as only partial water components are under analysis. The

importance of total water storage for the predisposition of hydrological extremes are

less clear to the world by now. In this paper, the storage-discharge relationship of large

basins will be analyzed with different approaches, to determine the relationship

between terrestrial water storage and the occurrence and magnitude of floods and

droughts.

Nomenclature

E: Evaporation (mm)

GLDAS: Global Land Data Assimilation System

GRACE: Gravity Recovery and Climate Experiment

GRDC: Global Runoff Data Center

P: Precipitation (mm)

R: Total Runoff (mm)

S: Basin-scale Storage Anomaly (mm)

List of Figures

Figure 1. Selected Basin in the World Map .................................................................... 3

Figure 2. P-E-R-S Diagram of Columbia ..................................................................... 14

Figure 3. P-E-R-S Diagram of Congo ........................................................................... 15

Figure 4. P-E-R-S Diagram of Lena ............................................................................. 16

Figure 5. P-E-R-S Diagram of Mackenzie .................................................................... 17

Figure 6. P-E-R-S Diagram of Mississippi ................................................................... 18

Figure 7. P-E-R-S Diagram of Ob ................................................................................ 19

Figure 8. P-E-R-S Diagram of Volga ............................................................................ 20

Figure 9. P-E-R-S Diagram of Yenisei .......................................................................... 21

Figure 10. P-E-R-S Diagram of Yukon ......................................................................... 22

Figure 11. Runoff-Storage Scatter of Columbia, Congo and Lena ............................... 24

Figure 12. Runoff-Storage Scatter of Mackenzie, Mississippi and Ob ........................ 25

Figure 13. Runoff-Storage Scatter of Volga, Yenisei and Yukon .................................. 26

Figure 14. Baseflow Separation for Columbia, Congo and Lena ................................. 28

Figure 15. Baseflow Separation for Mackenzie, Mississippi and Ob ........................... 29

Figure 16. Baseflow Separation for Volga, Yenisei and Yukon .................................... 30

Figure 17. Baseflow-Storage Diagram of Columbia, Congo and Lena ........................ 31

Figure 18. Baseflow-Storage Diagram of Mackenzie, Mississippi and Ob .................. 32

Figure 19. Baseflow-Storage Diagram of Volga, Yenisei and Yukon ........................... 33

Figure 20. Baseflow-Storage Diagram of Columbia, Congo and Lena, with Different

Colors for Each Year ............................................................................................. 35

Figure 21. Baseflow-Storage Diagram of Mackenzie, Mississippi and Ob, with

Different Colors for Each Year ............................................................................. 36

Figure 22. Baseflow-Storage Diagram of Volga, Yenisei and Yukon, with Different

Colors for Each Year ............................................................................................. 37

Figure 23. Average Baseflow-Storage Diagram of Columbia, Congo and Lena .......... 39

Figure 24. Average Baseflow-Storage Diagram of Mackenzie, Mississippi and Ob .... 40

Figure 25. Average Baseflow-Storage Diagram of Volga, Yenisei and Yukon ............. 41

Figure 26. Baseflow-Storage Diagram in Dry Seasons and Wet Seasons .................... 43

Figure 27. Runoff-Storage Relation for Low Precipitation Days in Columbia, Congo

and Lena ................................................................................................................ 45

Figure 28. Runoff-Storage Relation for Low Precipitation Days in Mackenzie,

Mississippi and Ob ................................................................................................ 46

Figure 29. Runoff-Storage Relation for Low Precipitation Days in Volga, Yenisei and

Yukon .................................................................................................................... 47

Figure 30. Time-Lag Modification in Columbia ........................................................... 49

Figure 31. Time-Lag Modification in Congo ................................................................ 50

Figure 32. Time-Lag Modification in Lena .................................................................. 51

Figure 33. Time-Lag Modification in Mackenzie ......................................................... 52

Figure 34. Time-Lag Modification in Mississippi ........................................................ 53

Figure 35. Time-Lag Modification in Ob ..................................................................... 54

Figure 36. Time-Lag Modification in Volga ................................................................. 55

Figure 37. Time-Lag Modification in Yenisei ............................................................... 56

Figure 38. Time-Lag Modification in Yukon ................................................................ 57

List of Tables

Table 1. Areas and Other Information of Selected Basins from GRDC ......................... 6

Table 2. Wet Seasons and Dry Seasons of Each Basins ................................................ 10

1. Introduction

Floods and droughts are hydrological extremes that commonly occur in many parts of

the world. As natural hazards driven by complex meteorological and climate effects,

floods and droughts lead to major losses to the society (Van Lanen et al., 2008).

Therefore, the early prediction of such hydrological extremes are of great importance.

Due to observational limitations, the current prediction methods mostly only rely on

the forecast precipitation, incomplete measure of basin wetness and river level

information. It limits the timescale of the prediction with the high dependence on other

observed and measured values, as well as affecting its accuracy since incomplete

components of water storage are under analysis. The importance of total water storage

for the predisposition of hydrological extremes are comparatively less clear by now.

One of the studies has shown that total water storage information can be used to assess

the predisposition of flooding in selected river basin in advance for as much as 5–11

months with little referral to other hydrological parameters (Reagers et al., 2014). This

indicates that the proper analysis of water storage data might be used to help predict

the hydrological extremes. This project attempts to tackle this significant issue by

seeking for the basin-scale water storage-discharge relation over global river basins. It

is hypothesized that extremely high (low) basin water storage leads to potential flood

(drought), and their functional dependence can be identified and used for prediction. If

a clear storage-discharge relationship exists in certain river basins, then the flood and

drought can be predicted at a lead time from monitoring storage variation. The

difficulties lie in the lack of observed data to characterize S-D relation, the unknown

lags between storage and discharge variations, and the heterogeneous climate

conditions and basin properties among global river basins. In this project, a total of

nine large basins all over the world will be studied to approach the relationships

between terrestrial water storage and the occurrence and magnitude of floods and

droughts.

2. Data and Methods

The relationships between terrestrial water storage and hydrological extremes are

analyzed by approaching the storage-discharge relationship of each large river basin

with different filters and refining methods applied. Precipitation and evaporation data

is also assessed for reference and comparison purposes.

Nine basins are selected to be analyzed in this paper with the restrain of availability

and completeness of original data. The nine basins are: Columbia, Congo, Lena,

Mackenzie, Mississippi, Ob, Volga, Yenisei and Yukon, shown in the map below. The

timescale of the analysis is from 1 Jan, 2003 till 31 Dec, 2013. The data of some basins

are only available till the end of 2010 or 2011. Only the time period with complete

available data are analyzed for these basins.

Figure 1. Selected Basin in the World Map

Monthly basin-wide water storage anomaly data is retrieved from NASA’s Gravity

Recovery and Climate Experiment (GRACE) satellite data. There are three different

processing centers: GFZ (GeoforschungsZentrum Potsdam), CSR (Center for Space

Research at University of Texas, Austin), and JPL (Jet Propulsion Laboratory)

releasing GRACE data at the same time. As they are using different processing

strategies, the results released by the three centers are of slight difference, and for each

center’s data, three different filters are applied to the data for adjustment. In this

project, the arithmetic mean of a total of nine filtered results from JPL, CSR and GFZ

fields are calculated, to be used as the terrestrial water storage data for further analysis.

Only monthly storage data is available from GRACE. Thus, to retrieve the storage data

on daily basis, Global Land Data Assimilation System (GLDAS) data products are

introduced, in order to simulate the daily trend of basin-wide water storage. GLDAS

datasets are available from the NASA Goddard Earth Sciences Data and Information

Services Center (GES DISC). It ingests satellite- and ground-based observational data

products, using four advanced land surface models (CLM, Mosaic, Noah and VIC), to

generate optimal fields of land surface states and fluxes from 1979 to present, in the

time interval of one hour or three hours corresponding to different data types. The

daily water storage trend is assumed to follow the variation of the sum of soil moisture

contents in all soil layers and the water equivalent of accumulated snow in the basins.

All data is converted to be in the unit of mm. After summing up the depths of soil

moisture and snow water, the daily storage variation trend is achieved. The actual daily

storage anomalies used for analysis should follow this daily variation trend, while

ensuring the sum of each month’s anomalous values equal to monthly water storage

anomaly from GRACE. A MATLAB script used in retrieving daily water storage

anomalies is enclosed in Appendix A.1.

Precipitation and evaporation data on both daily and monthly basis are also retrieved

from GLDAS products. Precipitation depth comes from the sum of rainfall rate and

snowfall rate multiplied by the length of time intervals. Evaporation data is directly

produced by GLDAS.

The water discharge data is retrieved from the Global Runoff Data Centre (GRDC).

GRDC offers a collection of river discharge data at both daily and monthly intervals.

The original data is in the unit of kg/m2/s, therefore, a unit converting is needed. The

areas of the basins are also provided by GRDC as listed in the table below.

River GRDC No. Station Area (km2) End Year

Columbia 4115200 The Dalles, OR 613830 2013

Congo 1147010 Kinshasa 3475000 2010

Lena 2903420 Kyusyur (Kusur) 2430000 2011

Mackenzie 4208025 Arctic Red River 1660000 2013

Mississippi 4127800 Vicksburg, MS 2964255 2013

Ob 2912600 Salekhard 2949998 2010

Volga 6977100 Volgograd Power Plant 1360000 2010

Yenisei 2909150 Igarka 2440000 2011

Yukon 4103200 Pilot Station, AK 831390 2013

Table 1. Areas and Other Information of Selected Basins from GRDC

These four water components: precipitation, evaporation, water discharge and basin-

wide storage anomalies are the original data retrieved for this study. Firstly, the four

parameters of each basin are plotted on daily basis to reflect the undisturbed, natural

status of the basins over the years. The plots will serve as reference in the later analysis

process, as they provide information on seasonal cycles and annual cycles, detailed

variation status of each water component, and the potential mutual effects among the

parameters, etc. Besides plotting each component respectively, all four water

components are also plotted in one same figure in the same scale to enable the

comparison among them at the same day. As water storage anomalies have a much

higher amplitude of variation, a time series plot with only the other three parameters is

also produced, so that a clearer correlation among precipitation, evaporation and

storage anomaly could be observed.

Secondly, a preliminary relationship analysis is conducted between the total runoff and

the basin-wide storage anomalies, by drafting the scatterplots based on runoff against

storage, on both daily and monthly basis. The scatterplots provide an initial image on

the storage-discharge relationship for large-scale basins. Different filtering and refining

methods are to be applied to these original parameters further for more reasonable and

precise analysis results.

The streamflow hydrograph consists of two parts: the ‘event flow’ and the baseflow.

The ‘event flow’ is a transient response to precipitation, while the baseflow is the

underlying part of runoff that is rarely affected by sudden changes. To eliminate the

impact of precipitations on the storage-discharge relationship, a separation of baseflow

from total runoff is necessary.

An improved digital recursive filter is applied to the daily runoff data from GRDC for

baseflow separation, which follows the equation:

!" =3% − 1

3 − %∙ !")* +

2

3 − % -" − %-")*

where: !" = filteredquickresponseatthe@ABsamplinginstant > 0

-" = originalstreamflow

% = filteredconstant = 0.900 − 0.995accordingtoTat(n. d. )

For different basins, c values between 0.985 and 0.995 are adopted in consideration of

the actual separation results. Since the method is only reasonable to be applied to daily

runoff data, the monthly baseflow data is obtained through the aggregation of each

month’s everyday baseflow. Please refer to Appendix A.2 for the MATLAB script used

in the baseflow separation.

The storage-baseflow scatter diagrams of the 9 basins are then plotted on both monthly

and daily basis to achieve a visually readable relationship between terrestrial water

storage and baseflow.

To access the occurrences of hydrological extremes of the nine basins, the storage-

baseflow scatter diagrams are modified by marking each year’s data in different colors.

From these yearly plotted diagrams, it becomes more apparent that for each basin, at

what time a flood or drought happened, as well as the severity of it. With the help of

the P-E-R-S diagrams, it also becomes easier to figure out the developments of each

year’s hydrological conditions along with time.

Clear annual fluctuating cycles can be observed from the P-E-R-S diagrams for all 9

basins. And most of the peaks and nadirs occur at similar time of each year. Therefore,

to obtain a yearly pattern of the storage-discharge relationship, an arithmetic mean on

each day of the year is calculated, forming vectors with 365 mean values of baseflow

and storage anomalies. The values on the 29th of February in 2004, 2008 and 2012 are

omitted, as only three or two sample values are available, and in the case of

hydrological extremes happening on that day, the reliability would not be trustworthy

enough.

Further refining is conducted to achieve a more visually clear relationship between

baseflow and storage anomalies in scatterplots. Referring to Reagers et al. (2014)’s

paper, analysis can be conducted on only summer seasons. Inspired by the work by

Reagers et al. (2014), I modified the storage-baseflow scatter diagrams again by

marking the dry seasons and wet seasons with different colors. The sortation on wet

season’s months and dry season’s months of each basin are based on observations from

the yearly average storage-baseflow patterns attained earlier. The wet seasons and dry

seasons are distributed as in Table 2 below.

Basins Wet Seasons Dry Seasons

Columbia May, Jun, Jul, Aug Jan, Feb, Mar, Apr, Sep, Oct,

Nov, Dec

Congo Jan, Feb, Dec Mar, Apr, May, Jun, Jul, Aug,

Sep, Oct, Nov

Lena Jun, Jul, Aug, Sep, Oct Jan, Feb, Mar, Apr, May, Nov,

Dec

Mackenzie Jun, Jul, Aug, Sep, Oct Jan, Feb, Mar, Apr, May, Nov,

Dec

Mississippi Mar, Apr, May, Jun, Jul Jan, Feb, Aug, Sep, Oct, Nov,

Dec

Ob Jun, Jul, Aug, Sep, Oct, Nov Jan, Feb, Mar, Apr, May, Dec

Volga Apr, May, Jun Jan, Feb, Mar, Jul, Aug, Sep,

Oct, Nov, Dec

Yenisei May, Jun, Jul, Aug, Sep, Oct Jan, Feb, Mar, Apr, Nov, Dec

Yukon Jun, Jul, Aug, Sep, Oct, Nov Jan, Feb, Mar, Apr, May, Dec

Table 2. Wet Seasons and Dry Seasons of Each Basins

As the ‘event flow’ that should be removed from the total runoff in this study is a

transient response to precipitation, it can be concluded that the runoff on the days with

high precipitation consists of a larger portion of “event flow” that will affect the

accuracy in analyzing the storage-discharge relationship of basins. Therefore it is

logical to assume, that removing the data on the days with high precipitation will give

a clearer relationship between the storage anomalies and the water discharges.

Considering the large areas of the basins (up to millions of kilometers) and the possible

time lag in the rainfall arriving at the measurement gauges, an accumulative 7-day

precipitation depth is retrieved for each day. And all days with accumulative

precipitation values higher than a certain percentage of average 7-day accumulative

precipitation are removed from the to-be-plotted discharge-storage scatter diagrams.

This practice can be considered as another baseflow separation method. Thus in the

scatter diagram, total runoff instead of baseflow is used for analysis, as the remaining

runoff values are supposed to be the baseflow. For demonstration purpose, runoff on

the days with high precipitation and that on the days with low precipitation are

together plotted in different color also. Please refer to Appendix A.3 for the MATLAB

script on removing values on the days with high accumulative precipitation.

The last modification on the approach in getting the relationship between baseflow and

storage anomalies is to simulate a time lag on the whole hydrological system of the

large-scale basin. The lead time of the length 1 month, 2 months and 3 months are

assessed, according to the observations on P_E_R_S diagrams. For the simplicity of

the analysis, each month is assumed to be of 30 days. The MATLAB script is enclosed

in Appendix A.4.

3. Results and Discussion

3.1. Comparison of Daily Precipitation, Evaporation, Runoff and

Storage

The four hydrological parameters: precipitation, evaporation, total runoff and storage,

of each basin are plotted against time series. The main purpose of doing so is to use the

values and these four important water components in the water cycle as a reference for

the later analysis. The plots serve as references in the later analysis process, as they

provide information on seasonal cycles and annual cycles, detailed variation status of

each water component, and the potential mutual effects among the parameters, etc.

The storage anomalies have much higher amplitudes compared with other three

parameters. This could be caused by that storage anomalies are measured in basin-

scale, while the other parameters are actually calculated by dividing the total fluxes

with the whole area. As the areas of the basins are very large, and it is very rare that

rainfall or evaporation happens uniformly above every square meter of the basin. As a

result, the amplitudes of these three parameters are comparably smaller than the actual

effect on one certain portion of the basin, as well as smaller than that of storage

anomalies.

For all the basins, it can be observed that all four hydrological parameters are at the

same frequency, which is about one cycle per year. The peaks of evaporation and

precipitation occur at almost the same time, with runoff slightly earlier than

evaporation. The precipitation and storage anomalies have the peaks occur at a longer

lead time up to several months to the runoff. This makes sense as large-scale basins

have more different water sources and more complex dynamic water storage, thus it

takes time for the runoff measured at downstream gauges to response to it.

Furthermore, the system response depends on the history and the memory of the

system, and thus also creates complex relationship between storage and discharge

(Fovet et al., 2015).

Figure 2. P-E-R-S Diagram of Columbia

Figure 3. P-E-R-S Diagram of Congo

Figure 4. P-E-R-S Diagram of Lena

Figure 5. P-E-R-S Diagram of Mackenzie

Figure 6. P-E-R-S Diagram of Mississippi

Figure 7. P-E-R-S Diagram of Ob

Figure 8. P-E-R-S Diagram of Volga

Figure 9. P-E-R-S Diagram of Yenisei

Figure 10. P-E-R-S Diagram of Yukon

3.2. Preliminary Relationship between Total Runoff and Storage

Anomalies

The daily scatterplots of all 9 basins are rather messy, and no clear correlations could

be directly deduced from them. Basins such as Columbia, Congo, Lena, Mississippi

and Yenisei possess a weak trend that overall total runoff has higher value when

storage is higher, while with the existence of a large amount of noise.

In monthly analysis, the plots of Columbia, Congo, Mississippi, Volga and Yenisei

show an exponential relationship between total runoff and storage. While the scatters

of Lena, Mackenzie, Ob and Yukon have C shape loops. However, if we include a

lower envelope regression line in the plots, an exponential relationship can be seen for

these basins with less clear scatter patterns.

As the total runoff is impacted by different water components in very complex ways, it

is as expected that the scatter diagrams of total runoff against storage anomalies show

less clear relationship.

Figure 11. Runoff-Storage Scatter of Columbia, Congo and Lena

Figure 12. Runoff-Storage Scatter of Mackenzie, Mississippi and Ob

Figure 13. Runoff-Storage Scatter of Volga, Yenisei and Yukon

3.3. Baseflow Separation

An improved digital recursive filter is applied to the total runoff data to retrieve the

baseflow values. The separated results are shown in Figure 14, 15, 16. The “event

flows” removed in basins like Lena, Ob and Yenisei are of quite large portions of the

total streamflow, while for all the other basins the “event flows” removed are relatively

of low portion. That could be because all Lena, Ob and Yenisei are basins in Russia,

which is in very high-latitude area. These areas have heavy snow up to 300mm

equivalent water depths in the winter time, and sometimes icing also occurs, so when

the temperature rises and the snow and ice melts, there will be a severe rise in runoff.

Referring to the P-E-R-S diagrams in time series, the sudden rises in total runoff in

these three basins actually do occur in spring seasons, which proves that the

explanation makes sense.

The storage-baseflow scatterplots are slightly better than those plotted from storage-

runoff with clearer exponential relations in monthly analysis for basins like Columbia,

Congo, Lena, Mississippi and Yenisei. However, the daily scatters are still with less

clear correlation shown and a lot of noise can be observed. This could be because the

digital filter baseflow separation method is not effective enough, since it is a pure

mathematical approach with no physical meanings. Thus further refining practices

should be conducted.

Figure 14. Baseflow Separation for Columbia, Congo and Lena

Figure 15. Baseflow Separation for Mackenzie, Mississippi and Ob

Figure 16. Baseflow Separation for Volga, Yenisei and Yukon

Figure 17. Baseflow-Storage Diagram of Columbia, Congo and Lena

Figure 18. Baseflow-Storage Diagram of Mackenzie, Mississippi and Ob

Figure 19. Baseflow-Storage Diagram of Volga, Yenisei and Yukon

3.4. Each Year with Different Color Plots

Plotting yearly data in different colors demonstrates the developments of the

hydrological systems along with time. After plotting each year’s scatter in different

color, it is observed that northern basins in Russia, which are Lena, Ob, Volga and

Yenisei, all have very low baseflow in the year 2003, as well as having high baseflow

in 2007. Similarly, Columbia and Mississippi, which are beside each other, both have

high baseflow values in 2011. For tropical basin Congo, dry years and wet years come

alternatively, as 2003 and 2007 have high baseflow while 2004 and 2006 have very

low baseflow.

Moreover, some basins appear clear yearly paths over the whole time. Especially for

Lena, Mackenzie and Yukon, S-shape paths are observed for every single year. The S-

shape reflects the variation trend of each years’ storage and baseflow over the 12

months. Storage first increases and then decreases and increases again from January to

December.

Figure 20. Baseflow-Storage Diagram of Columbia, Congo and Lena, with Different Colors for Each Year

Figure 21. Baseflow-Storage Diagram of Mackenzie, Mississippi and Ob, with Different Colors for Each Year

Figure 22. Baseflow-Storage Diagram of Volga, Yenisei and Yukon, with Different Colors for Each Year

3.5. Each Month with Different Color Plots

Yearly baseflow-storage pattern of each basin is produced by averaging the same dates’

values of each year. The yearly tracks for most basins are zigzag lines. That is because

in every month, the storage varies a lot while the baseflow remains at similar values.

The scatters of Congo and Mississippi show an indistinctive positive correlation as

baseflow increases along with the growing of storage. Each month with different color

enables visual determination of dry seasons and wet seasons, which is adopted for

reference in further analysis. It is also easy to see that basins near each other have

similar day months and wet months’ distributions. However, these yearly plots show

no clear correlations between average baseflow and average storage.

Figure 23. Average Baseflow-Storage Diagram of Columbia, Congo and Lena

Figure 24. Average Baseflow-Storage Diagram of Mackenzie, Mississippi and Ob

Figure 25. Average Baseflow-Storage Diagram of Volga, Yenisei and Yukon

3.6. Baseflow-Storage Relationship in Dry Seasons and Wet Seasons

Figure 26 reflects the baseflow-storage relationships of all 9 basins in dry seasons and

wet seasons. Baseflow is hard to be perfectly separated by digital filter alone,

especially for wet seasons with high precipitation thus inducing high “event flow”.

Therefore, it is reasonable to deduce that the baseflow achieved in dry seasons are

more accurate and realistic. All 9 basins show clear correlations between the storage

and baseflow for dry seasons. Especially for Columbia, Congo, Mississippi and Volga,

an ideal exponential line could be observed from the plots. While for basins such as

Lena, Mackenzie, Ob, Yenisei and Yukon, the red dots form rather linear traces. Most

of the baseflow values keep at a low level, so very little noise remains to disturb the

visual-determinable relationship. Generally, it is concluded that with higher basin-scale

storage, higher baseflow will occur at the same time. The basins with less clear

exponential baseflow-storage relationships are northern basins with large areas. Larger

basins often have more different water sources and more complex dynamic water

storage. Also the snow accumulated during winter and the sudden melting in spring

will have impact on the inner rational of their hydrological systems.

Figure 26. Baseflow-Storage Diagram in Dry Seasons and Wet Seasons

3.7. Remove Data on Days with High Accumulative Precipitation

With high precipitation days removed, the runoff-storage plots of Columbia, Congo,

Mississippi, Volga and Yenisei reflect either an exponential relationship or a linear one.

While for other basins, even though the portion of streamflow separated on the right

side show effective separation results, the runoff-storage relationships are not so clear.

This may indicate that a time lag exists and is affecting the effectiveness and accuracy

of the separation practice. Simply removing the data on the days with high 7-days

precipitation is not effective enough to avoid the disturbances and attain a reliable

storage-discharge relationship.

Figure 27. Runoff-Storage Relation for Low Precipitation Days in Columbia, Congo and Lena

Figure 28. Runoff-Storage Relation for Low Precipitation Days in Mackenzie, Mississippi and Ob

Figure 29. Runoff-Storage Relation for Low Precipitation Days in Volga, Yenisei and Yukon

3.8. Time-Lag Modification

Compared with the original baseflow-storage scatterplots, and the 1-month, 2-month

and 3-month time lag applied plots, Congo and Mississippi give the best results at a

time lag of 1 month, Columbia and Volga fit best in 2 months’ lead time, while Lena,

Mackenzie, Ob, Yenisei and Yukon have better visual-determinable correlation with 3

months’ time lag applied. It is observed that basins in higher altitude have longer time

lag for baseflow variation resulted from storage change. Because lower temperature

relates to slower flow rate and less active water dynamics. Snow and icing also affect

the response time of these basins. Another point to notice is that basins with larger

areas are under longer time lag effects. As mentioned earlier, larger basins often have

more different water sources and more complex dynamic water storage, it also takes

longer for the water coming to the gauges downstream to be measured.

Lastly, it should not be neglected that errors exist in original data, and they may also

occur during the calculation process and through several times’ rounding. Most

mathematical practices applied on the data only produce approximate values. All these

factors lead to inaccuracy in all the analysis above.

Figure 30. Time-Lag Modification in Columbia

Figure 31. Time-Lag Modification in Congo

Figure 32. Time-Lag Modification in Lena

Figure 33. Time-Lag Modification in Mackenzie

Figure 34. Time-Lag Modification in Mississippi

Figure 35. Time-Lag Modification in Ob

Figure 36. Time-Lag Modification in Volga

Figure 37. Time-Lag Modification in Yenisei

Figure 38. Time-Lag Modification in Yukon

4. Conclusion

After using different approaches in analyzing storage-discharge relationship of selected

large-scale basins, with references in precipitation and evaporation behaviors, and with

different filters and refining methods applied, it can be concluded that:

(1). Terrestrial water storage information can help and should be assessed in predicting

the occurrence and magnitude of hydrological extremes such as floods and droughts

for large scale basins at a lead time.

(2). There is a positive exponential correlation existing between the discharge of one

basin and the storage of that, provided effective removal of disturbing factors as “event

flow” components caused by instant precipitation.

(3). The exponential correlation between water discharge and storage is more ideal for

basins in dry seasons.

(4). The time lag between the storage change and the response in runoff is longer for

basins with larger areas and in higher altitudes areas (for northern hemisphere only,

that is, areas with lower temperature).

(5). The variation of the basin’s runoff depends on the combined effect from storage

changes, precipitation, evaporation and other hydrological components. Therefore, the

occurrence and magnitude of floods and droughts cannot be determined solely by

terrestrial water storage information.

5. References

Fovet, O., Ruiz, L., Hrachowitz, M., Faucheux, M. and Gascuel-Odoux, C. (2015).

Hydrological hysteresis and its value for assessing process consistency in catchment

conceptual models. Hydrol. Earth Syst. Sci., 19, 105–123, 2015, doi: 10.5194/hess-19-

105-2015.

Reager, J. T., Thomas, B. F., and Famiglietti, J. S. (2014), River basin flood potential

inferred using GRACE gravity observations at several months lead time. Nature

Geoscience, 7, doi: 10.1038/ngeo2203.

Tat (n.d.). Applications of Traditional Approach and New Technique for Baseflow

Separation.

Van Lanen, H. A. J., Kundzewicz, Z. W., Tallaksen, L. M., Hisdal, H., Fendeková, M.

& Prudhomme, C. (2008). Indices for different types of droughts and floods at

different scales. WATCH Technical Report No. 11.

Appendix A. MATLAB Scripts

A.1 MATLAB Script for Retrieving Daily Storage Anomalies

% GLDAS Soil Moist + Snow to get daily storage anomaly data % unit: kg/m2 = mm % convert houly data to daily -> AVERAGE not sum dS_VIC = zeros (4018,9); for d = 0:4017 for h = 1:8 dS_VIC(d+1,:)=dS_VIC(d+1,:)+hS_VIC(8*d+h,:); end end dS_VIC = dS_VIC/8; adjust = mS_VIC - GRACE; dadj1 = zeros(132,9); for i=1:132 dadj1(i,:) = adjust(i,:)/DayofMon(i); end dadj = zeros(4018,9); m=1; for d = 1:4018 if d

A.2 MATLAB Script for Baseflow Separation

% Baseflow Separation Digital Approach Improved f = length (4018); f(1) = 0; c = 0.990; % c could be of diff value for i=2:4018 f(i)= (3*c-1)*f(i-1)/(3-c) + 2*(DailyRunoff(i)-DailyRunoff(i-1))/(3-c); if (f(i)

A.3 MATLAB Script for Removing Values on the Days with High

Accumulative Precipitation

% to remove some data with high 7-day accum precipitation days = 4018; d1P = zeros(days+6,1); d2P = zeros(days+6,1); d3P = zeros(days+6,1); d4P = zeros(days+6,1); d5P = zeros(days+6,1); d6P = zeros(days+6,1); d7P = zeros(days+6,1); d1P(1:days)=DailyPre; d2P(2:days+1)=DailyPre; d3P(3:days+2)=DailyPre; d4P(4:days+3)=DailyPre; d5P(5:days+4)=DailyPre; d6P(6:days+5)=DailyPre; d7P(7:days+6)=DailyPre; all7P=d1P+d2P+d3P+d4P+d5P+d6P+d7P; accumP=all7P(7:days); avgP = sum(accumP(1:days-6))/(days-6); percent = 0.75; % changable, percentage of avgP, above which to remove keep = zeros(days-6,1); remove = zeros(days-6,1); for i=1:days-6 if (accumP(i)

end end kpR = zeros(days-6,1); kpS = zeros(days-6,1); rmvR = zeros(days-6,1); rmvS = zeros(days-6,1); for i=1:days-6 kpR(i)=keep(i)*DailyRunoff(i); %low P kpS(i)=keep(i)*DailyStorage(i); rmvR(i)=remove(i)*DailyRunoff(i); %high P rmvS(i)=remove(i)*DailyStorage(i); end subplot(3,5,[1,2,3]) scatter(kpS,kpR,'m'); xlabel('Storage'); ylabel('Runoff'); title('Columbia (with high precipitation days removed)') legend('high P removed'); subplot(3,5,[4,5]) startDate = datenum('01-07-2003'); endDate = datenum('12-31-2013'); xData = linspace(startDate,endDate,4012); scatter(xData,rmvR,'b','+'); hold on scatter(xData,kpR,'g','+'); hold off dateFormat = 'yyyy'; datetick('x',dateFormat); title('Daily Runoff in High P Days and Low P Days'); legend ('high accum P days','low accum P days'); ylabel ('Runoff (mm)'); xlabel ('Date'); ylim([0.1,3]) xlim([731588,735599]) grid on

A.4 MATLAB Script for Time Lag Modification

% for time lag modification % 1-month / 2-month / 3-month lagD = 30*lagM; d=4018; m=132; lagM=1; subplot(3,5,[1,2,3]) scatter(DailyStorage(1:d-lagD),DailyBaseflow(lagD+1:d)); title({'';'Time Lag = 1 month'}); xlabel('Daily Storage (mm)'); ylabel('Daily Storage (mm)'); subplot(3,5,[4,5]) scatter(MonthlyStorage(1:m-lagM),MonthlyBaseflow(lagM+1:m)); title('Time Lag = 1 month'); xlabel('Monthly Storage (mm)'); ylabel('Monthly Storage (mm)'); lagM=2; subplot(3,5,[6,7,8]) scatter(DailyStorage(1:d-lagD),DailyBaseflow(lagD+1:d)); title('Time Lag = 2 month'); xlabel('Daily Storage (mm)'); ylabel('Daily Storage (mm)'); subplot(3,5,[9,10]) scatter(MonthlyStorage(1:m-lagM),MonthlyBaseflow(lagM+1:m)); title('Time Lag = 2 month'); xlabel('Monthly Storage (mm)'); ylabel('Monthly Storage (mm)'); lagM=3; subplot(3,5,[11,12,13]) scatter(DailyStorage(1:d-lagD),DailyBaseflow(lagD+1:d)); title('Time Lag = 3 month'); xlabel('Daily Storage (mm)');

ylabel('Daily Storage (mm)'); subplot(3,5,[14,15]) scatter(MonthlyStorage(1:m-lagM),MonthlyBaseflow(lagM+1:m)); title('Time Lag = 3 month'); xlabel('Monthly Storage (mm)'); ylabel('Monthly Storage (mm)');