Assessing Groundwater Quantity and Quality Variations in Arid Regions Due to Climate Changes and Anthropogenic Factors: Case Study Saudi Arabia

In the Kingdom of Saudi Arabia (KSA), water resources are limited in hyper-arid regions, which are dependent on groundwater (88 percent), desalination water (8 percent) and wastewater treatment (4 percent). The management and development of these resources are essential to sustain population growth and grow the agricultural, industrial, and tourism sectors. Since the groundwater is the most valued water resource in the country, the majority of researchers are focused on the water quantity and water quality in this region in order to find the best solution to face this issue. In 1953 the Ministry of Agriculture and Water was established and assigned the mission of identifying and managing the water resources, aiming to ensure their maximum efficient development and use. The economic future of the Kingdom and the survival of the its people depend alike on the availability of water, its prudent use, and its rational development through long-term program that aim to help fulfill the overriding goal of the government, which is to establish and maintain a better life for the people of the Kingdom. Previous researchers have focused on the groundwater resources in the Saq aquifer region in northern KSA, where the depletion is the highest, during the past 10-20 years. However, most studies focused on groundwater quality, and not quantity, which is very important in the monitoring and management of water resources, but one the other side monitoring these resources are significant to sustain and develop our resources. Since the Kingdom does not have a robust database for continuous monitoring groundwater, it is critical to find appropriate scientific methods to monitor the groundwater permanently that can be used to give us a big picture in the present time and in the future to deal with this issue. Therefore, the overall objective of this dissertation was to design suitable methods for an integrated monitoring mechanism of the groundwater quantity and quality using geophysical and geochemical information of the aquifers and their water resources, hydrologic modeling, satellite Remote Sensing data, and Geographic Information systems (GIS). In order to achieve this, I combined laboratory analysis of water quality variables with modeling of the water resources patterns, and validated the findings with field-level water use and withdrawal data, to develop a suitable scenario to monitor groundwater in this region continuously. The work has been described in the following three manuscripts, as per the Graduate School Manual guidelines: MANUSCRIPT І (published in Hydrological Processes 2017). The objective of this work was to utilize month-to-month (April 2002 to April 2015) GRACE (Gravity Recovery and Climate Experiment) data as well as applicable geologic, hydrologic, and remote sensing datasets to inspect the spatial and temporal variations in GRACE-derived terrestrial water and groundwater storage over the Saq aquifer system and to research the components (i.e., natural and anthropogenic) controlling these varieties. This study extends the investigation of the individuals who have already utilized GRACE data to monitor the Saq aquifer region (e.g., Sultan et al., 2013) by (1) using enhanced state of the art GRACE global mass concentration solutions (mascons), (2) using yields from an improved global land surface model, Global Land Data Assimilation System (GLDAS), to isolate the groundwater storage, (3) developing the area of the study zone to incorporate the Saq aquifer in the KSA and Jordan, and (4) Broadening the time traverse utilized by Sultan et al., (2013) by three years. MANUSCRIPT ІI (Submitted to Journal of Hydrology). In this manuscript, we developed and applied an integrated approach to quantify the recharge rates of the Saq aquifer system. Given the areal distribution of the Saq transboundary aquifer system, the interaction between the Saq aquifer and the overlying aquifers was also assessed. Specifically, we set out to accomplish the following: (1) examine the areal extent of the Saq aquifer recharge domains using geologic, climatic, and remote sensing data; (2) investigate the origin of, and modern contributions to, the groundwater in the Saq aquifer system by examining the isotopic compositions of groundwater samples collected from, and outside of, the Saq aquifer; and (3) estimate, to first order, the magnitude of modern recharge to the Saq aquifer utilizing data from the Gravity Recovery and Climate Experiment (GRACE) and applying the continuous rainfallrunoff model, the Soil and Water Assessment Tool (SWAT). MANUSCRIPT ІII (being prepared for Groundwater journal). The objective of this Chapter is to quantify the groundwater quality of the studying area by measuring the ionic compositions, the characterization of the water quality and radioactive materials by collecting samples and comparing the results with the Water Health Organization of drinking water. Since the Kingdom of Saudi Arabia does not have a continuous water quality control system, it is essential to check the groundwater quality in the study area and make sure it is suitable for drinking and domestic uses. In addition, comparing the previous data in the same studying area with the present data to identify the differences in the groundwater quality data in between the two periods, and understanding the factors controlling the groundwater salinity and total dissolved solids distribution in order to minimize the overexploitation of freshwater resources and to maintain the livelihood of the population and public health. In conclusion, groundwater monitoring includes both groundwater quantity (e.g., groundwater level and recharge rates) and quality monitoring (analysis of selected physical and chemical variables). The purposes of groundwater monitoring are to manage and develop the policy of the groundwater resources and to predict the groundwater quality and quantity due to natural processes and human impacts in time and space. Therefore, in this situation we need to have a useful database for assessment of the current state, anticipating changes and forecasting trends in the future. My results in this dissertation will contribute to the effective and efficient utilization of the Saq aquifer water resources and will be used to promote the sustainable development of the Arabian Peninsula and Middle East’s natural resources in general. The findings have been and will be shared with stakeholders and decision makers in relevant governmental agencies to develop viable management scenarios for the water resources of the Saq aquifer.


MANUSCRIPT ІII (being prepared for Groundwater journal).
The objective of this Chapter is to quantify the groundwater quality of the studying area by measuring the ionic compositions, the characterization of the water quality and radioactive materials by collecting samples and comparing the results with the Water Health Organization of drinking water. Since the Kingdom of Saudi Arabia does not have a continuous water quality control system, it is essential to check the groundwater quality in the study area and make sure it is suitable for drinking and domestic uses. In addition, comparing the previous data in the same studying area with the present data to identify the differences in the groundwater quality data in between the two periods, and understanding the factors controlling the groundwater salinity and total dissolved solids distribution in order to minimize the overexploitation of freshwater resources and to maintain the livelihood of the population and public health.
In conclusion, groundwater monitoring includes both groundwater quantity (e.g., groundwater level and recharge rates) and quality monitoring (analysis of selected physical and chemical variables). The purposes of groundwater monitoring are to manage and develop the policy of the groundwater resources and to predict the groundwater quality and quantity due to natural processes and human impacts in time and space. Therefore, in this situation we need to have a useful database for assessment of the current state, anticipating changes and forecasting trends in the future. My results in this dissertation will contribute to the effective and efficient utilization of the Saq aquifer water resources and will be used to promote the sustainable development of the Arabian Peninsula and Middle East's natural resources in general. The findings have been and will be shared with stakeholders and decision makers in relevant governmental agencies to develop viable management scenarios for the water resources of the Saq aquifer.

1-Introduction
The scarcity of freshwater is an issue of critical importance in arid and semi-arid countries 2014). Natural freshwater resources in the arid Arabian Peninsula, especially the transboundary aquifers of inland desert regions bordering Saudi Arabia, Syria, Jordan, and Iraq, carry critical environmental and geopolitical significance, due to the extreme water scarcity in this region throughout the year and the sensitive nature of the regional geopolitics, respectively (e.g., Pedraza and Heinrich, 2016). The Kingdom of Saudi Arabia (KSA; Figure 1) is one of the largest countries in this region that faces chronic water scarcity due to a burgeoning population and rapid growth in previously uninhabited areas.  Sultan et al., 2008). However, the major recharge process occurred only during the past wet climatic periods and only minimal amounts during the dry periods, like the current day situation (Bayumi, 2008;Sultan et al., 2008Sultan et al., , 2011Wagner, 2011;Abouelmagd et al., 2012Abouelmagd et al., , 2014Zaidi et al., 2015). The management and development of these resources are thus important to sustain KSA's population growth and grow the agricultural, industrial, and tourism sectors. In order to minimize the overexploitation of freshwater resources and to maintain the livelihood of the population and development, understanding the natural phenomena (e.g., rainfall/temperature patterns, duration, and magnitude) together with human-related factors (e.g., population growth, over-exploitation, and pollution) that affect these resources is highly recommended.
Globally, groundwater depletion is a major concern in aquifer systems across the United States, Australia, Northern Africa, South Asia, and South America (e.g., Famiglietti  A comprehensive understanding of the hydrologic and geologic settings, recharge and depletion rates, and the effect of natural and man-made practices on the Saq aquifer system is essential for the proper management of this significant aquifer system in particular and also for the management of the KSA's water resources in general. Extensive field, geophysical, and geochemical explorations are required to comprehend the geologic and hydrogeological settings of this expansive aquifer system. Additionally, the development, validation, and calibration of groundwater flow models are essential for the exploration of the effect of natural and man-made consequences for this aquifer system. However, the development of such models, for the most part, requires gathering deep subsurface and field information, including, but not limited to, temporal water levels, pressuredriven parameters, and lithological well records. Such data are hard to acquire for the Saq given its broad spatial distribution, inaccessibility, and the general absence of local funding to support the required researchrelated activities.
The use of recent Earth-observing satellites has greatly facilitated our ability to observe changes in water resources at large scales (e.g., Famiglietti and Rodell, 2013;Famiglietti, 2014 variations with field water level data from regional supply wells.

Geology, Hydrogeology, and Geomorphology
The Arabian Peninsula contains several aquifer systems sitting, in an arc shape, directly over the Precambrian Arabian Shield (Figure 1). These aquifer systems could be grouped into (1)

Shared Water Resources of the Arabian Peninsula
In 1970, the KSA started to use the water of the Saq aquifer for human consumption; however, the amount of the extracted water increased in 1980 to support wheat production. Wheat is a water-intensive crop, and this farming effort required a tremendous amount of groundwater

Data and Methods
A flowchart summarizing the main processing steps applied to GRACE and other relevant datasets used in this study is shown in Figure 2.
Generally, the soil moisture data were utilized to remove the nongroundwater storage components from TWSgrace data. Rainfall data used to explore the climatic controls on the temporal variations in TWSgrace.
Groundwater levels and irrigated areas, among others, were used to validate GWSgrace results over the Saq aquifersystem. TWSgrace trend data were then statistically analyzed by using the Student t-test to identify their significancelevels.

Land Surface Model-derived TWS Data
Since GRACE has no vertical resolution, the TWS outputs of the GLDAS

Rainfall Data
Precipitation data were utilized to explore the climatic controls on the temporal variation in TWSgrace observed over the Saq aquifer system.  Figure   6). AAP data were used to explore the climatic control on TWSgrace given the fact that a rainfall value is already a rate, and so it corresponds to a trend (i.e., a mass/time) signal in the TWSgrace; a trend in rainfall corresponds to an increase in mass rate, and so to a quadratic function of time in the mass.

Field Data
Water level data of 15 monitoring wells distributed over the entire Saq

Normalized Difference Vegetation Index (NDVI)
The spatial distribution of irrigated areas (Figure 8a

GRACE-derived TWS (TWSgrace) Trend
The TWSgrace secular trends over the Arabian Peninsula are displayed in     Figure 1). To the best of our knowledge, this is the first-time field data from water supply wells, within the vulnerable Saq aquifer region, has been used to directly validate TWSgrace and/or GWSgrace estimates.
Comparisons indicated that the GWSgrace estimates generally capture the observed groundwater level depletion shown by the analysis of water level data ( Figure 5). The observed GWSgrace depletions over the Saq aquifer are attributed to extensive groundwater extraction activities mainly from the Saq aquifer system. These activities were intended to develop agricultural communities in northern and northwestern parts of the Arabian Peninsula.
Our interpretation is supported by the reported groundwater extraction rates as well as the observed variations in the areas and the spatial distribution of the irrigated regions and irrigation wells (Figure 8a). Figure   8a shows that areas that are witnessing GWSgrace depletion (

Factor driving TWSgrace and GWSgrace depletions
Freshwater resources in the has witnessed a decline in TWSgrace that is mainly due to a decline in GWSgrace (6.0 ± 3.0 km3/yr). The observed differences between the previous and our findings could be, among others, attributed to the changes in the investigated time, investigated area, and the data source.
It is worth mentioning that, the mascons solutions, used in our study, provide higher signal to noise ratio, higher spatial resolution, reduced error, and do not require spectral and spatial filtering or any experimental scaling techniques. As a result, our results report far better accuracy and much smaller error margins (an order of magnitude lower) in the TWS and GWS estimates. Our GWSgrace depletion rates are highly correlated with the observed decline in water level measured in water supply wells within the investigated aquifer system.
The rapid declines in GWSgrace in this extremely arid, strategic, and geopolitically significant region needs to be carefully monitored and managed with competing uses within KSA and plans to use the Saq aquifer to supply freshwater to the Jordanian capital city of Amman. Our results indicate that the implications of unsustainable groundwater based irrigation and extraction practices are clear for these fossil aquifers, also warranting future investigation on the impacts on water quality changes in the valuable sources. Our study also demonstrates that global monthlyGRACE solutions can provide a practical, informative, and cost-effective method for monitoring aquifer systems in water-stressed regions across the globe.

Conclusion
Water is a valuable resource in the Arabian Peninsula's current hyper-arid conditions. In KSA, for example, there are no surface water rivers or reservoirs. To sustain its growing population, KSA is currently utilizing more of its groundwater resources and is planning to increase the         Manuscript II

Abstract
The arid and semi-arid regions of the world are facing limited freshwater resources, minimal amounts of rainfall, and increasing population and water demands. These resources, often groundwater, are vulnerable to both natural variability and anthropogenic interventions. Here, we develop and apply an integrated approach using geophysical, geochemical, and remote sensing observations to quantify the recharge rates of arid region aquifers that are witnessing rapid groundwater depletion. Focusing on the Saq aquifer system in the Arabian Peninsula, our study was three-fold: (1) to examine the areal extent of the aquifer recharge domains using geologic, climatic, and remote sensing data; (2) to investigate the origin of, and modern contributions to the aquifer system by examining the isotopic composition of groundwater samples; and (3)

Introduction
The arid and semi-arid parts of the world are currently facing more difficult problems than ever before when it comes to freshwater resources. Quantifying groundwater recharge of the Saq aquifer is thus key to the sustainable utilization of the groundwater resources in that system.
Groundwater recharge is generally assessed either by direct or by indirect methods (e.g., Scanlon et al., 2002). Some of the physical and chemical methods that are used to quantify the recharge are difficult to apply, given the sizeable areal extent of the Saq aquifer and the absence of field data that is required for implementing these methods.
In this manuscript, we develop and apply an integrated approach to quantify the recharge rates of the Saq aquifer system. Given the areal distribution of the Saq transboundary aquifer system, the interaction between the Saq aquifer and the overlying aquifers was also assessed. Specifically, we set out to accomplish the following: (1) examine the areal extent of the Saq aquifer recharge domains using geologic, climatic, and remote sensing data; (2) investigate the origin of, and modern contributions to, the groundwater in the Saq aquifer system by examining the isotopic compositions of groundwater samples collected from, and outside of, the Saq aquifer; and (3) estimate, to first order, the magnitude of modern recharge to the Saq aquifer utilizing data from the Gravity Recovery and Climate Experiment (GRACE) and applying the continuous rainfall-runoff model, the Soil and Water Assessment Tool (SWAT).

Saq Aquifer System
Saudi Arabia is divided mainly into the Arabian Shield and the Arabian

Delineating the recharge domains of the Saq aquifer
Two main peak periods characterize seasonal rainfall patterns over Saudi Arabia. The first peak comes during March and April, followed by almost no rainfall during June to August, which in turn is followed by a second peak from October to January. These precipitation events act as the main sources of recharge to the underlying aquifer systems. Recharge domains of the Saq aquifer system were defined as those areas that are witnessing annual rainfall and covered by the Saq outcrops. We examined the AAR data over the Saq aquifer using satellite-based rainfall estimates given the lack of rain gauges over the monitored area and the discontinuous nature of

Geochemical Constraints on the Modern Recharge of the Saq aquifer
The The isotopic analyses of the collected groundwater samples are listed in  Figure 3. Fig. 3 and Table 1  +0.37‰). This hypothesis is supported by the observed progressive depletion in the isotopic composition with distance from the recharge areas.

Examination of
For example, within Group (I), the isotopic compositions of the groundwater samples collected from, and/or close to, the recharge areas cropping out at the foothills of the basement outcrops (e.g., sample 9) are less depleted compared to those collected away from the recharge areas (e.g., sample 10).

Quantifying Modern Recharge to the Saq Aquifer
Two independent approaches were used to quantify the amounts and timing of modern recharge to the Saq aquifer. The first one is based on the analysis of GRACE data, whereas the second approach focused on rainfallrunoff modeling using the SWAT model was utilized. The trend results, along with their statistical significance, are shown in Table 2. Examination of Fig. 4a and Table 2  Given the fact that GRACE cannot distinguish between anomalies resulting from different components of TWS (e.g., soil moisture and groundwater), the contributions of soil moisture storage need to be quantified and removed from GRACE-derived TWS (Fig. 4a)    The GRACE-derived GWS time series over the Saq aquifer (Fig. 4c) is generated by subtracting the GLDAS-derived soil moisture storage ( Fig. 4b) from the GRACE-derived TWS (Fig. 4a). The monthly GWS uncertainties were calculated by summing, in quadrature, the contributions from GRAC-derived TWS errors to GLDAS-derived soil moisture errors. Trends in GWS time series were quantified using the same approach used for GRACE-derived TWS data.
Inspection of Fig. 4c shows that the Saq aquifer is witnessing an overall GWS decline of −6.34 ± 0.22 mm/yr (−2.79 ± 0.10 km3/yr). Piecewise trend analysis results ( To quantify the recharge rates during the investigated periods, we added the summation of natural discharge and anthropogenic groundwater extraction to the GWS trends utilizing the following equation: The discharge rate of the Examination of AAR and recharge rates over the Saq Aquifer shows an obvious correspondence of the recharge rates on the rainfall amounts. It is worth mentioning that a one-to-one correspondence, in magnitudes between recharge and AAR, is not to be expected, given that AAR could be redistributed as runoff and evapotranspiration that could affect the spatial and temporal distribution of the precipitated water, and hence the recharge locations and magnitudes.

(B) Modern Recharge to the Saq Aquifer: Modeling Constraints
The modern recharge of the Saq aquifer was quantified using SWAT, a catchment-based, semi-distributed hydrologic model that was Evaporation was estimated using the Penman-Monteith method (Monteith, 1981).
The SWAT model climatic inputs include rainfall, minimum and maximum temperature, solar radiation, relative humidity and wind speed. The climatic data were extracted from the Global Weather Data (GWD) for SWAT database (available at http://globalweather.tamu.edu/). The GWD-derived rainfall data was validated against available rain gauge records. A comparison between monthly GWD-derived rainfall records and the available rain gauges is shown in Figure 5.
Locations of the selected rain gauges are shown in Figure 6. Examination of Fig. 5 reveals satisfactory general correspondence (R2: 0.72 to 0.85) between the average monthly rainfall measured in the field and that obtained from GWD. We should note that a one-to-one correspondence between GWD and gaugederived rainfall measurements is not expected given the fact that GWD integrates measurements over a large area (~ 38 km × 38 km).
The SWAT topographic data input was extracted from the Shuttle   Finally, the initial losses were estimated by subtracting the summation of potential recharge and streamflow from precipitation. Table 3  Sustainable utilization and management of the water resources of the Saq aquifer system could be achieved by adopting the following practices.

Examination of
First, groundwater extraction areas should be located at, or near to, the center of the aquifer; areas around the aquifer borders are expected to be depleted first as extraction increases with time. Second, groundwater extraction rates should be limited to maintain the GWS trend at ≥0; positive GWS trends means the extraction is less than the recharge, zero GWS trend implies extraction equals recharge, and negative GWS trends implies the extraction is greater than the recharge. Third, utilize the well spacing act such that the effects on the aquifer are not concentrated at any spot and well yields are sustained. The optimum well spacing is a function of a total number of wells, aquifer thickness, regional groundwater velocity, and pumping rate of an extraction well (Ahmed 1995), expressed as:

Discussion and Conclusion
In Saudi Arabia, like in many other arid/semi-arid countries of the world,

Abstract:
Groundwater quality is a critical issue in the arid and semi-arid countries, where it is one of the most reliable sources on which people depend. Water quality is a vital concern in the Kingdom of Saudi Arabia (KSA) affecting as it affects the health of its people, the growth of its agriculture, and its economic development. In this study: the objectives were to (1)  In order to minimize the overexploitation of freshwater resources and to maintain the livelihood of the population in a sustainable manner, we need to understand the natural phenomena (e.g., rainfall/temperature patterns, duration, and magnitude) together with human-related factors (e.g., population growth, over-exploitation, and pollution). In spite of the significance of the Saq aquifer system in the KSA, there are some major difficulties associated with using the groundwater system. The most critical of these difficulties are the unsustainable over-exploitation of the aquifer, which also significantly influences the water quality.

Arabian Shield
The

Arabian Shelf
When the vast mass of crystalline rocks that forms the eastward

Ionic composition of Cations and Anions of GW samples
All the water samples were stored in bottles that were kept at a temperature between 1 and 5°C. The water samples for trace element analyses were collected using sterile 100ml bottles designed for bacteriological examinations. The specific sampling conditions are described in Table 1, and the methods used for the chemical analyses are shown in Table 2.Unstable parameter hydrogen ion concentration (pH), and electrical conductivity (EC) were determined at the sampling sites by using of a pH-meter, a portable EC-meter.

Piper's Diagram
Hydro chemical classification and groundwater assessment have been discussed using Piper's diagram. The Piper plot data should be in mill equivalents per liter which is converted from milligrams per liter to mill equivalents per liter.

Radioactive analysis
Radioactive materials were discussed to measure of gross α and gross to show a preliminary assessment of the radiological risk attached to groundwater use.

GWS from GRACE
The observed GRACE-derived TWS depletions over the study area are related to variations in both soil moisture storage and GWS since GRACE has no vertical resolution. To quantify the GRACE-derived GWS variations over the Saq aquifer system, the GLDAS-derived soil moisture estimates are subtracted from the GRACE-derived TWS averaged from UT-CSR mascons equation (1). Figure 4 shows the temporal variations in the GRACE-derived groundwater estimates over the Saq aquifer. Examination of ( Figure 4) reveals a groundwater depletion rate of−2.11 ± 0.13 km3/yr. Table 3

Ionic composition of Arabian Shelf and Arabian Sheild
Investigation focused on cations and anions distributions of Na+, Ca++, Mg++, K+ and Cl−, SO4−2, HCO3, NO3 respectively. Investigation Table.3 shows most of the cations and anions in Arabian Shield are exceeding the stander of WHO due several reasons that affect the water quality in that region such high evaporation, high abstraction which is affect the gradients of the aquifer, and industrial activities. On other side, the ionic composition of Arabian Shelf are within the stander of WHO, but the radioactive materials of gross alpha and beta are exceeding WHO's guidance level.

Hydrochemical classification
The classification of groundwater analysis was done using Piper's diagram (Piper 1944). The ternary diagrams (Fig. 4)

Comparison of groundwater quality in the depletion regions between 2006 and 2016
As part of the investigation, we also compared groundwater quality in the depletion regions between groundwater quality data in 2006 that was provided by MEWA and in 2016 tested in our lab from water samples directly collected from the area (Fig. 2).

Radio analysis results
We also performed radiological analysis of the Therefore, the origin of radioactivity in the Saq aquifer water seems more likely related to adjacent layers.

Conclusion
The quality of groundwater in the Kingdom of Saudi Arabia plays a significant role in maintaining the health of people, which is the most critical source of drinking water in the Kingdom. Therefore, it is imperative to monitor groundwater quality continuously and make sure that it meets the stander of drinking water is necessary for the safety and health of the people. According to WHO, there is no health concern for using these samples from both regions in the short term. These study findings are being shared with decision makers in relevant governmental agencies and decision makers to manage and develop groundwater quality in these regions.

Acknowledgments
The        The critical components of the GRACE twin satellites (Fig. 2) are listed below: 1-K-Band Ranging (KBR) system: Provides precise (up to 1 micrometer) measurements of the distance change between the two satellites.  Figure 3.
The disadvantage of having such a low (500 km) altitude is that GRACE experiences greater atmospheric drag, which can cause significant and unpredictable changes in the inter-satellite range distance (Wahr, 2002 Over the last decade, GRACE data has been successfully used to monitor the individual components of the TWS. GRACE has been widely used for: (1) Estimating regional water storage variations in the Amazon  As we discussed earlier, the long-term average distribution of the mass within the Earth system determines its mean "static" gravity field. The These data undergo extensive and irreversible processing, and are converted to edited and cleaned data products are 1-5 second rates.
The products labeled Level-1B, include among others, the intersatellite range, range-rate, range-acceleration, the non-gravitational accelerations from each satellite, the pointing estimates, the orbits, etc.
The Level-1B products are processed to produce the monthly gravity field estimates in the form of spherical harmonic coefficients. GRACE project also delivers Level-2 data products which consist of complete    3. Processing of GRACE Data: In this section, we are introducing, in brief, the general steps that most of the researchers are using in processing of GRACE level-2 data.

Removal of the Temporal Mean:
The GRACE level-2 solutions are represented regarding fully normalized spherical harmonic decompositions up to degree (l) and order (m) of 60. The time-variable component of the gravity field solutions should be calculated by removing the long-term mean (Clm (t), Slm (t)) of the Stokes coefficients from each monthly (Clm (t), Slm (t)) value to get the temporal variations in these coefficients ( ( Clm (t), Slm (t)) . The reason for removing the mean field is that it is dominated by the static density distribution inside the solid Earth (Wahr et al., 1998).

Spectral Filtering (Destripping):
After the temporal mean removal, the correlated errors (long, linear, north to south oriented features) also called "stripes" should be reduced by applying describing methods developed by Swenson and Wahr (2006). The presence of stripes implies spatial correlations in the gravity field coefficients at higher degree (short wavelength components). Swenson and Wahr (2006) show how, at a single higher (m>8) order, the even (or odd) coefficients values at each degree tend to form smooth curves. Their filter, a moving window quadratic polynomial, was used to isolate and remove smoothly varying coefficients of the same parity. In this study, the least square method was used to fit a 4th order polynomial for the odd degree and the even degree separately, then to subtract those polynomials from the original coefficients to leave the residuals (Cˆlm (t), Cˆlm (t)).

Spatial Averaging (Gaussian Smoothing):
At this point, we have a set of gravity coefficient anomalies for each month (∆Cˆlm (t),∆Cˆlm (t)) that have been described and ready to We will compute maps of water storage anomalies over the land ( ∆σ (θ,φ,t) ) directly as: Where is ρave the average density of the Earth (5517 kg m-3), ae is the mean equatorial radius of the Earth, θ is the geographic latitude,φ is the longitude, Plm are the fully-normalized Associated Legendre Polynomials of degree l and order m and r is the Gaussian averaging radius, and kl are elastic/load Love numbers of degree l. The later was calculated via linear interpolation of the original data computed by Han and Wahr (1995).
The spatial averaging, or smoothing, of GRACE data, is necessary to reduce the contribution of noisy short wavelength components of the gravity field solutions. We will generate 0.5° × 0.5° equivalent water thickness grids using a Gaussian averaging radius of 200 km. Estimates of TWS variations suffer from signal degradation due to noise. The noise is manifested as (1) random errors that increase as a function of spherical harmonic spectral degree (Wahr et al., 2006), and (2) systematic errors that are correlated within a particular spectral order (Swenson and Wahr, 2006).

GRACE Errors
Several filtering techniques are used to damp or isolate and remove the GRACE-derived TWS errors. The problem with most of those techniques is that the filters also modify the actual geophysical signal that the researchers are interested in. The following section explains the methods used to scale GRACE TWS data to account for the effect of the filter on the GRACE signal.

Scaling GRACE TWS Data
The scaling process is supposed to take care of the GRACE TWS errors that result from applying the following filters and/or  3.2.6. In some cases, you might need to format your monthly files generated from step (3.2.5). Use the code "File_Formating.f" to format your input files in such a way.

Calculate TWS Mass Anomalies:
3.3.1. Now you are ready to calculate GRACE mass anomalies. Use the code "Calculating_TWS_mass.exe" to calculate the mass anomalies.
The outputs of this code arefiles with longitude, latitude, and TWS (in cm; equivalent water thickness). The inputs for GRACE mass calculation code include: a-GRACE spherical Harmonics files. Outputs are from step 3.2.6.
Those files should be in the specific format and certain file name style.
b-File with the list of the input files listed in (a). Usually called "Month_to_process.txt." This file has to be in the specific format. The first raw in this file should contain the number of months to be processed (e.g., 138 files). The second raw all the way till the final raw should contain the number of each file to be processed.
c-Love number file.

2.2.
Visualize the GRACE Mass Anomalies: In this step, we will use ArcMap software to create maps from the outputs files of the previous step. For each of the generated files in step (3.3.2) you need to create an image/map out of them as the following: 2.2.1. Open each file using MS Excel. Use "Space Delimited" option.