A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt

ARTICLE IN PRESS The Egyptian Journal of Remote Sensing and Space Sciences (2016) xxx, xxx–xxx

H O S T E D BY

National Authority for Remote Sensing and Space Sciences

The Egyptian Journal of Remote Sensing and Space Sciences www.elsevier.com/locate/ejrs www.sciencedirect.com

RESEARCH PAPER

A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt El-Sayed E. Omran * Soil and Water Department, Suez Canal University, 41522 Ismailia, Egypt Received 17 August 2015; revised 24 February 2016; accepted 6 March 2016

KEYWORDS Water table depth; Gaussian simulation; Stochastic model; Time-series; Goodness-of-fit model; Risk assessment; Remote sensing

Abstract Water table depth (WTD) is an important map layer for many environmental models’ assessments. To develop an early water table prediction model for North Sinai, Egypt, four approaches were considered in this study: GIS, remote sensing, simulation and stochastic methods. Stochastic (using time-series) modeling enables us to characterize the water table dynamics in terms of risk, and it allows model uncertainty to be taken into account without the complexity of physical mechanistic models. The results indicate that, time-series modeling is an effective method to characterize the seasonal patterns of WTDs in the area. The model performs very well using Nash and Sutcliffe coefficient of efficiency (NSE) which indicates a fit of the model to the data. Sequential Gaussian Simulation was explored as a way to model water table spatial variability. A 95% probability level was calculated as a measure for risk of shallow water tables. The limits established for risks of shallow WTDs at April 1st were 0.5 m below the ground surface. A map showing the risk that the WTD at April 1st and October 1st in a future year will be shallower than 0.5 m was presented. If the risk is close to 50%, it will be difficult to take a decision in water management or land use planning. The results found a negligible risk of shallow water tables for this date. The level of WTD will be about 0.30–0.45 m higher than the present level in the next 20 years. There is a better agreement between the simulated and measured data (8 cm difference) which may be associated with an overestimation of the evaporative losses from the surface. Finally, Landsat image was not useful for WTD prediction; however, it may be useful for soil moisture prediction. Ó 2016 Authority for Remote Sensing and Space Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

1. Introduction

* Tel.: +20 12 02628180; fax: +20 64 3201793. E-mail address: [email protected]. Peer review under responsibility of National Authority for Remote Sensing and Space Sciences.

The depth of phreatic water below the surface is called water table depth, WTD (Knotters, 2001). WTD influences several soil characteristics, like temperature, aeration, nutrients, soil trafficability, water availability, aquifer susceptibility to contamination, and thickness of the root zone. In contrast with

http://dx.doi.org/10.1016/j.ejrs.2016.03.001 1110-9823 Ó 2016 Authority for Remote Sensing and Space Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

ARTICLE IN PRESS 2 WTD, these features are hard to be observed (Knotters, 2001; Thompson et al., 2012). There is a need for reliable information on the configuration of the water table for agricultural sustainability. Knowledge about the spatio-temporal dynamics of the water table is important (Von Asmuth and Knotters, 2004). Predicting susceptible areas to water table rising in both space and time in arid and semi-arid areas are challenging. Different approaches for WTD prediction in which remote sensing is one of these approaches were reviewed. (Gong et al., 2004) found that the normalized difference vegetation index (NDVI) has a better correlation with WTD. Al-Khudhairy et al., 2002 estimated the width of wet water channels from Landsat TM data to correlate WTD. Al-Saifi and Qari, 1996 analyzed Landsat thematic mapper (TM) imagery over saltenriched flat areas and suggested that WTD can be differentiated by image colors. However, no quantitative analysis was done with remote sensing which was not useful for predicting WTD (Becker, 2006; Meijerink, 2007). Only, microwave remote sensing (i.e., passive radar) data can be used for the estimation of the shallow water table (less than a few meters). However, it has not yet been investigated in various conditions and very little is known about the accuracy of such assessment (Meijerink, 2007). Ground penetrating radar (GPR) seems to be the most suitable tool for efficient water table depth assessment (Meijerink, 2007). The most accurate, non-invasive assessment of water table depth seems to be possible with the magnetic resonance sounding (MRS) method. However it is not yet widely used for such application, mainly because it is too expensive and too time consuming to be efficient in surveys focused on water table assessment only (Lubczynski and Roy, 2003, 2004). Other approaches for predicting the spatio-temporal variation of WTD use either physically-deterministic flow models (McDonald and Harbaugh, 1988) or space–time geostatistics (Arun and Katiyar, 2013; Omran, 2012; Rouhani and Hall, 1989). The full-fledged models require a large amount of information (disadvantage) to be able to predict WTD at sufficient accuracy, while building and calibration of these models is time-consuming. The problem with purely statistical approaches is that they require many observations to be accurate and they often become overly complicated when accounting for nonstationarity in space and time (Angulo et al., 1998). Statistical spatio-temporal prediction methods can roughly be divided into three approaches: (i) methods starting from geostatistical methodology (Kyriakidis and Journel, 1999), (ii) methods based on multivariate time-series modeling (Pfeifer and Deutsch, 1998), and (iii) methods based on time-series models with regionalized parameters (Van Geer and Zuur, 1997). Time-series modeling provides an empirical stochastic method to model monitoring data from observation sites without the complexity of physical mechanistic models. In addition, the stochastic component in the model allows model uncertainty to be taken into account. Time-series modeling allows us to simulate and predict the system behavior and to quantify the expected accuracy of these predictions (Salas and Pielke, 2003). In time-series analysis, transfer functionnoise (TFN) models describe the dynamic relationship between climatological inputs and WTDs (Von Asmuth et al., 2008; Von Asmuth and Knotters, 2004). The behavior of linear input-output systems can be completely characterized by their impulse response (IR) function (Von Asmuth et al., 2002a). The dynamic relationship between precipitation and WTD

E.S.E. Omran can be described using physical mechanistic flow models. However, much less complex TFN model predictions of the WTD can be obtained which are often as accurate as those obtained by physical mechanistic modeling (Knotters, 2001; Von Asmuth and Knotters, 2004). Risk assessment is also needed to find optimal solutions for water management in areas where WTD is a problem. Therefore, there is a demand for stochastic methods that enable to describe the water table dynamics in terms of probabilities. Such probabilities are underestimated when using only the deterministic model (Knotters and VanWalsum, 1997). To develop useful models, the uncertainty of the predictions to increase the value of the water table models in decision-making should be considered. However, observed time-series of WTDs are generally not long enough to represent the prevailing climatic conditions. Thus, simulation models are applied to extrapolate the observed time-series. By using stochastic methods the probability distribution of the WTD can be estimated more accurately than by applying deterministic methods, because the unexplained part or noise component is taken into account. All existing methods fail to include observation uncertainty; and produce poor measures of prediction uncertainty. It may be desirable, however, to not only be informed about the dynamic behavior of the water table at the observation sites, but also at other locations. To this end, the WTD needs to be early predicted in both time and space. Nourani et al. (2011) believe that problems in data interpretation given by the lack of strong predictive tools contribute to a failure to reach consensus water management actions. So, in order to overcome these limitations and to make better use of the observation data, the main objective of this study is to develop an early warning technique incorporate GIS, simulation method and stochastic methods for spatio-temporal WTD prediction. A stochastic model is interesting for estimations of WTDs because uncertainties can be quantified. Using a time-series model, it is possible to simulate over periods that do not have observations, as long as data on explanatory series are available. The uncertainty about the true WTD can be accounted for in stochastic methods by generating large numbers of possible realizations using simulation. In order to achieve the main objective, the following specific objectives are identified: (1) Propose a methodology to model and map the water table elevation by different approaches. (2) Modeling the systematic changes in WTDs from 2005 to 2007 in North Sinai, Egypt. (3) Develop stochastic methods to predict WTD probabilities for application in regions where suitable observations are scarce. (4) Predict the potential susceptible ‘‘areas at risk” for water table rising in any future date.

2. Materials and methods 2.1. Study area and time-series database The study area, El-Salam Canal basin, is located (30°4000 –31° 0500 N, 32°200 –33°1500 E) in the North Sinai province, Egypt (Fig. 1). WTDs across much of the El-Salam basin have been

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

ARTICLE IN PRESS Stochastic simulation model to early predict susceptible areas

3

Figure 1 Locations of 33 piezometer boreholes (open circles) and 545 observations (closed circles) where WTDs data are available in the study area.

increasing for at least the last 10–15 years. This is attributed to the consistent irrigation agriculture, but over the same period there has been a substantial change in land use, with desert land replaced by cropping and tree plantations. Hence, it is important to determine the relative effect of the climatic and land use factors on the water table changes which is helpful in indicating the degree of threat facing agricultural and public assets. Fig. 1 shows the digital elevation model and locations of 578 water table observations and piezometer boreholes which were collected from previous projects in the area (Atta, 2006; DRC, 2006). Thirty-three piezometer locations were selected where time-series (2005–2007) of WTDs are available and 545 observations were selected where WTDs are available. In El-Salam Canal basin, only a few time-series of WTD are available, and the opportunities for collecting additional data in space and time are limited. In general the number of observed time-series will be too small to make reliable spatio-temporal predictions of the WTD by using observed time-series only. Therefore, prediction methods are needed which incorporate additional measurements and information of the WTD. The information on water table dynamics should reflect the prevailing climatic conditions, i.e., the average weather, over 30 years, rather than the meteorological circumstances during the monitoring period. Thus, methodology is needed to extrapolate observed time-series of water table depths to series of 30 years length from which characteristics can be calculated. Series of 30 years length of precipitation and evaporation were available from the climate station nearby the study area. Fig. 2 shows the methodology applied in this study.

water table at a certain date. To develop it, the water level data were converted from the form of depth below surface to the form of water table elevation (water level height above a datum plane, e.g. mean sea level). The map is prepared by plotting the absolute water levels of all observation points on a topographical map. To draw the water table contour lines, water table levels between the observation points must be interpolated. This can be done by linear interpolation. The locational result arrived at was interpolated in a GIS environment to derive a water table elevation model (WTEM). 2.3. Sequential Gaussian Simulation (SGSIM) of water table depth and elevation SGSIM was explored as a way to model water table spatial variability using Geostatistical Software Library (GSLIB). Since SGSIM requires data to exhibit multivariate Gaussian behavior (Deutsch and Journel, 1992), this behavior was tested with results indicating reasonable correspondence between at least 3 of the 4 indicator semivariograms. The water table dataset was considered to exhibit multivariate Gaussian behavior and SGSIM was used. Omnidirectional variograms for WTD were computed using lag increments of 500 m and 1000 m. The 90 degree azimuthal tolerance and wide bandwidth were resulted in an omnidirectional variogram. The number of lags was 10 and lag tolerance 1000 m. The number of data pairs is important since we need a reasonable number of pairs to get a reliable estimate. Increasing lag increments and lag tolerances will increase the number of pairs but might also smooth out significant variations (Clark and Harper, 2000; Shepherd, 2009).

2.2. Estimating water table depth and elevation model 2.4. Stochastic Simulation of time-series models Mapping of water table level often makes very little use of auxiliary data (Kumar and Ahmed, 2003). A number of geostatistical methods have emerged that significantly improve estimates by incorporating the land surface elevation (Desbarats et al., 2002; Peterson et al., 2003). A water table contour map shows the elevation and configuration of the

To model the water table dynamics, time-series models were used. These time-series models can be seen as multiple regression methods, where the system is seen as a black box that transforms series of observations on the input (the explanatory variables) into a series of the output variable (the response

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

for WTD

Semivariogram

Determine

Database

Combine WTD

Final WTD Map

version1 of WTD Map

WTD Map from

Calculate Average

WTD Map (version1)

Create Preliminary

WTD

Perform Krriging for

Measurements

Level

WTD from Water

WTD from

Features

Surface

Perform Krriging for WTE

Series

Risk Maps of Future Water Table

techniques

with geostatistics

Spatial structure

and 95th ) for WTD

Percentile values (5th

Values

Function of these

Distribution

Probability

WTD values

April 1st) and

(October 1st and

30 years Precipitation

Evaporation

Elevation Prediction

Water Table

Realizations

Water Table

Simulated

SGSIM

Analysis

Variograms

LandSat Image

Retrieve Soil

DEM

Current Hazard Area , 2014

Current Soil Moisture Content

NDVI surface temperature

Temperature

Table Depth, 2014

Current Water

Current Water Table Depth

Simulation

Best Model

Evaluation the

Cokriging Kriging

By

Moisture Index

Ordinary

Extraction (NDVI)

Correction

Atmospheric

Land Surface

Retrieval Biophysical Parameters

Calibration

Radiometric

Pre-Processing

2005-2007, 2014

Vegetation Indices

sensor Radiance

Convert DNs to at

Remote Sensing Approach

4

Methodology and procedure used to develop a warning model to early predict water table depth.

WT Elevation Model

Final WTE Map

Average WTD from LES to get WTE

Subtract

(version2)

WTD Map

Preliminary

Subtract to get

WTD series

Time

Selected date

Stochastic simulation of

WTD

Modeling

WTE

Spatial Variability

GSLIB Software

Simulation

Model

Modeling

Software

TOPMODEL

Gaussian

RARX

Semivariogram for

Create Preliminary WTE Map

Figure 2

MODFLOW

Menyanthes

PIRFICT

Model Calibration

Time Series

(LSE) from DEM

Land Surface Elevation

Modeling Approach

Stochastic Models and Simulation

Prediction

WT Dynamic

Determine

LSE to get WTE

Subtract WTD from

Water Table Elevation (WTE)

Water Table

Depth (WTD)

Geostatistical Approach

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Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

ARTICLE IN PRESS Stochastic simulation model to early predict susceptible areas

Figure 3

5

Histogram of the water table values, location map and variogram modeling using an exponential model.

variable, WTD). The first step in time-series analysis is to identify a model able to describe the time processes which should not be based just on statistical methods, but should also include some physical insight about water table dynamics. 2.4.1. Time-series model selection The popular TOPography based hydrological MODEL (TOPMODEL) approach (Beven and Kirkby, 1979) is based on a linear relationship between WTD and a DEM-derived quantity known as the topographic index. TOPMODEL is not suitable to apply in the study area related to the assumptions that underlay the TOPMODEL index approach which are a crude approximation of reality that will not hold everywhere. However, the approach is simple, inexpensive calculations and has a minimum number of‘ effective parameters, with a quasiphysical interpretation. Most importantly, the predictions

can be mapped back for comparison with local field measurements where available. Of the concerns about using the MODFLOW (Beven and Kirkby, 1979) in the study area is in the estimation of an effective value of each point. Transfer function-noise (TFN) models and autoregressive exogenous variable (ARX) models are used to describe the dynamic relationship between the explanatory variables and the WTDs (Knotters and VanWalsum, 1997; Van Geer and Zuur, 1997). A regionalized autoregressive exogenous variable (RARX) model (Knotters et al., 2001) has proved to be useful tools in describing the dynamic relationship between precipitation surplus and WTD. However, the parameters of these models can be estimated where sufficiently long time-series of precipitation surplus and WTD are available. However, in El-Salam Canal basin, only few timeseries of WTD are available.

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

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Figure 4 The Sequential Gaussian Simulation generates four realizations of the WTD (upper) and four realizations for the elevation prediction (lower).

The Predefined Impulse Response Function In Continuous Time (PIRFICT) model (Von Asmuth et al., 2002a) was used to study the dynamic behavior of WTD. The PIRFICT model can describe a wide range of response times with differences in sampling frequency between input and output series. Using a time-series model, it is possible to simulate over periods without observations, as long as data on explanatory series are available. Long series on precipitation and evapotranspiration (30 years length) can be assumed to represent the prevailing climatic conditions (Knotters and VanWalsum, 1997). Compared to the combined ARX model and Kalman filter, the PIRFICT model offers a further extension of the possibilities of calibrating TFN models on irregularly spaced time-series, because the shape of the transfer function is not restricted to an exponential (Von Asmuth and Bierkens, 2005). From the simulated realizations, statistical characteristics of future water table dynamics can be calculated, such as mean, standard deviation and limits of prediction. The mean highest groundwater level (MHGL), mean lowest groundwater level (MLGL) and mean spring groundwater level (MSGL) are calculated based on two weekly measurements (Van der Sluijs and De Gruijter, 1985).

2.4.2. Modeling and regionalizing the trend parameter of the time-series models Menyanthesis is a powerful tool for modeling a series of groundwater level observations which is applied to the PIRFICT model (Von Asmuth et al., 2002b). Time-series analysis models model the course of the water table at a single point in space. They do so by using the relationship between water table level observations and data on factors that influence the groundwater level, such as precipitation, evapotranspiration, groundwater abstraction, etc. From the original 33 piezometer, the PIRFICT models were calibrated to 30 series of WTDs, using the Menyanthes program. Three boreholes were considered outliers and removed from the further analyses. The predefined impulse response (IR) function describes the model response (water table variation) to the system inputs. In addition, the PIRFICT model has a stochastic component (noise term) that accounts for model uncertainty. The parameters of the adjusted IR functions have a physical meaning, since they represent the influence of drainage resistance, storage coefficient of the soil and the dispersion time of precipitation through the unsaturated zone (Von Asmuth and

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

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Figure 5

7

Water table elevation model (WTEM) which determine the water table level at any location.

Knotters, 2004). After selecting an IR function that represents the underlying physical process, the available time-series have to be transformed to continuous series. The parameters of time-series models can be regionalized using ancillary information related to the physical basis of these models (Knotters and Bierkens, 2001, 2000). Regionalization of time-series parameters is not based on interpolation from observed time-series. It is obtained from landscape analysis using DEM and soil maps. In principle, the method does not require observed time-series to produce space–time predictions of water table elevation. However, if such time-series exist, they can be used to calibrate the space–time model and improve predictions. 2.4.3. Monitoring the spatio-temporal analysis of water table depths The aim of this study is to analyze how WTDs vary in space and time, and modeling their dynamics over a certain period in time. The target variable is the increase or decrease of water levels from one month to another at each observed piezometer. Geostatistics provide conceptual point of view to solve problems with space–time indexation (Kyriakidis and Journel, 1999). The trend parameter reflecting systematic changes of WTDs of the PIRFICT model was interpolated spatially using universal kriging (Pebesma, 2004). An alternative way of using data from a secondary variable to improve estimation of a sparsely-sampled primary variable is the method of kriging with an external drift. The transfer function-noise models, once calibrated to a set of time-series observed in various locations in an area, can have their predictions interpolated spatially, using ancillary information (Knotters and Bierkens, 2001) which incorporate physical meaning to the predictions (Manzione et al., 2007a). So water table elevation is expressed as a linear function of topographic elevation, a DEM-derived quantity that characterizes landform and drainage. It is possible not only to improve the accuracy of the spatial predictions, but also to yield more plausible spatial patterns and enhance the physical meaning of the maps,

using DEM (Hengl et al., 2007; Manzione et al., 2010; Peeters et al., 2010). The corresponding values of DEM at each observation were extracted and the numerical values were obtained for each observation (Arun, 2013). 2.5. Goodness-of-fit of the model In data-driven modeling, it has become standard practice for data-driven modelers to assess the performance of their models against a large number of different metrics with a host of different combinations potentially being applied to a particular solution. Among others, Legates and McCabe (1999) discuss the misuse of Coefficient of Determination R2 as a frequently applied goodness-of-fit measure. So, as a dimensionless goodness-of-fit indicator, the Nash and Sutcliffe coefficient of efficiency (NSE) (Nash and Sutcliffe, 1970) is selected and calculated as follows: NSE ¼ 1 

Nk N X X ðOi  PiÞ2 = ðOi  OÞ2 i¼1

ð1Þ

i¼1

where Oi and Pi represent the sample (of size N) containing the observations and the model estimate, respectively; O is the mean of the observed values. Thus, NSE represents the complement to unity of the ratio between the mean square error of observed versus predicted values and the variance of the observations. The coefficient of efficiency takes values 1 6 NSE 6 1. A NSE = 1 indicates a perfect fit, while a NSE = 0 suggests that the mean of the observed values is a better predictor than the evaluated model itself (Ritter and Mun˜oz-Carpena, 2013). 2.6. Risk assessment and simulation of shallow water table depths Time-series models using precipitation surplus/deficit calibrated on time-series of WTD with limited years enable us

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

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Figure 6 Regime curves and water table visualization which plots the WTD frequency as a function of the percentage of time that the WTD is equaled or exceeded. The dash lines are the maximum high WTD level (145 cm) in the next 20 years.

to simulate series of extensive length (Knotters and VanWalsum, 1997). Nevertheless, variation of the water table cannot be completely explained from the precipitation and evaporation series. So, the models must contain a noise component which describes the part of water table fluctuation that cannot be explained with the used physical concepts or empirically from the input series. The unexplained part (noise component) has to be taken into account in the simulation procedure, since we are interested in statistics of extremes, like the probabilities that critical levels are exceeded (Hipel and McLeod, 1994). After modeling the WTDs using the PIRFICT model, series of WTDs are extrapolated to a time-series of precipitation and evaporation of 30 (1984–2013) years length. As a result, deterministic series of predicted WTDs are generated. Realizations of the noise process are generated by stochastic simulation and next added to deterministic series resulting in realizations of

series of WTD. With a probability density function of the WTD distribution, the statistics to set up situations risk of shallow WTD and representing the prevailing hydrologic conditions can be calculated. The estimations of process characteristics were made for two specific interesting dates in the region: beginning of the winter planting season (October 1st), and beginning of summer planting season (April 1st). At the beginning of the planting season, shallow water tables can be a problem for machinery. They can make it impossible to plow and execute planting operations. In addition, they can influence soil conditions, soil redox potential, pH, and the conductivity and ion exchange reactions. For risk of shallow water tables, the 0.95 percentile was selected. The areas have just 5% probability to have higher WTD than these values and 95% probability to have lower values. The limits established for risks of shallow WTDs were 0.5 m below the ground surface.

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

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Figure 7

9

Model calibration example of WTD time-series at different piezometer locations.

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

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2.7. Remotely sensed data approach Another mapping approach is the classification of water table depth based on remotely sensed data. In this approach, Landsat imagery, which was acquired during April and October 2006 coincident with the period of data acquisition, was used to retrieve soil moisture index. These images were used to derive normalized difference vegetation indices (NDVI) and surface temperature to support soil moisture analysis as NDVI is typically negatively correlated with soil moisture (Adegoke and Carleton, 2000). A cross-correlation between soil moisture and NDVI can be applied which may help bias our interpolation of soil moisture in unsampled areas. Cross-correlation may also be employed where soil moisture measurements were under sampled as compared to the exhaustively sampled NDVI (where each pixel has a value specific to that location). The processes involved in cross-correlation are further explained through cokriging. The following steps were followed: – Surface temperature is interpreted from the Landsat thermal band. – NDVI is calculated using the Landsat Red and Near Infrared bands. – Calculations are run on the image matrix to obtain maximum and minimum surface temperatures at each unique NDVI value. – Values are obtained using an algorithm based on established relationship between surface temperature and NDVI. – Linear regression is applied to a scatter plot of the resulting max/min temperatures. – From the regression equations, the slopes (a) and intercepts (b) are obtained. – Soil moisture index (SMI) is calculated using the following equations:

SMI ¼ Tsmax  Ts=Tsmax  Tsmin

ð2Þ

Tsmax ¼ ða1  NDVIÞ þ b1

ð3Þ

Tsmin ¼ ða2  NDVIÞ þ b2

ð4Þ

Tsmax = maximum surface temperature (K), Ts = temperature value of the pixel, Tsmin = minimum surface temperature (K). Higher values near 1 (areas with low surface temperature and low vegetation amounts) represent higher estimated soil moisture levels. Values near 0 (areas with high surface temperature and high vegetation amounts) represent the lowest soil moisture values. 3. Results and discussion 3.1. Water table depth and elevation model 3.1.1. Exploratory and variogram analysis of water table depth Fig. 3 shows the summary statistics for the WTD. The first exploratory statistics is a histogram of the values, particularly to know the data limits for subsequent analysis. The most interesting at this point are the minimum and maximum water

table values, which are 0.3 m and 2.3 m. The mean water table value is 1.27 m and median is 1.40 m. Fig. 3 also shows a location map as another basic exploratory plot for the measured water table values which was represented by a range of colors posted at the locations. Fig. 3 shows the variogram analysis using 10 and 20 lags with a lag separation distance of 500 and 1000 m and a lag tolerance of 500 m. A lag tolerance of more than half the separation distance will result in some pairs being counted in multiple lags, resulting in a smoother variogram. The variogram with the 1000 m lag looks like a smoothed version of the one with the 500 m lag (Fig. 3), as expected. More to the point, the shorter-lag variogram does not seem to show inordinate variation, so it will be used. The variogram seems to reach a sill of around 0.75 at a range of about 5000 m. In addition, the shape of the variogram looks similar to that of an exponential model. The model fit to the variogram in the direction 135° E as representing the trend-free variogram. Variogram modeling involves using the model to generate a variogram file, which can then be plotted together with the empirical variogram for comparison. 3.1.2. Stochastic Sequential Gaussian Simulation (SGSIM) of water table depth and elevation Fig. 4 shows the SGSIM used to generate one hundred realizations of the WTD. Indicator transformation data, theoretical semivariograms and cumulative probability distribution curve were input data for SGSIM. The SGSIM model does not offer an option for kriging with a trend. Therefore, ordinary kriging was used as the kriging type, hoping that the locally varying

Table 1 Summary statistics, model calibration, estimated parameters and characteristics for piezometers 1, 4 and 11. Piezometer

PIZO001

PIZO004

PIZO0011

R2adj

69.09 0.99 0.194 m 0.201 m 0.79 39.86 0.01 45.41 39.59 7.66 1.17 104 150 126.4 20.5 0.54–0.92 0.96–1.31

74.24 0.99 0.177 m 0.180 m 125.72 5.02 2.83 5.90 125.72 0.816 4.12 0 102 46.3 31.1 0.03–0.51 0.31–0.99

37.6 0.99 0.108 m 0.096 m 4138.64 17.67 1.4 17.56 113 0.4 0.37 0 60 36.8 16.7 0.11–0.32 0.37–0.50

NSE RMSE RMSI A a n a IR LD E Min Max Mean SD MLGL, MGL, MSGL, MHGL

R2adj, percentage of explained variance; NSE, Nash and Sutcliffe coefficient of efficiency; RMSE, root mean squared error (meters); RMSI, root mean squared innovation (meters); A, drainage resistance (days); a, decay rate (1/days); n, convection time (days); E, reduction factor (); a, decay or memory of the white noise process (); IR, impulse response (days); LD, Local Drainage Base (meters); Min, minimum; Max, maximum; SD, standard deviation; MHGL, MLGL, MSGL, together referred to as MxGL statistics mean highest, mean lowest and mean spring groundwater level.

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mean estimate will be adequate to account for the trend. The water table values follow a Gaussian (normal) distribution closely enough to begin with. One hundred realizations were generated and eight realizations for both WTD and elevation were selected just for the sake of visualization. The realization num-

bers 1, 35, 70 and 100 in both WTD and elevation are shown in Fig. 4. Each realization has considerably more characters than the kriged map of water table. These realizations look quite as ‘‘trendy” as the data, meaning that the ordinary kriging approach was perhaps not adequate for reproducing the

Frequency of Exceedence

WTD 3 2

1.5

1

1

-1

0.5 0

96 88 80 72 64 56 48 40 32 24 16 8 0

0

2012 2010 2008 2006 2004 2002 2000 1998 1996 1994 1992 1990 1988 1986 1984

WTD 2

Frequency

Time-series

Regime Curves

Figure 8 The main Menyanthes screen which shows time-series of climatological data for 33 years. Performance of water table dynamics simulation compared to statistics, regime curves and frequency of exceedance graph for the PIZO 1, 4, and 11. The maximum WTD level frequency curve in the next 20 years was increased from 145 cm (Fig. 6) to 100 cm.

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ARTICLE IN PRESS 12 underlying trend. However, no single realization can be taken as a better representation of reality than any other without applying some external criterion such as a ranking based on matches to production history produced by running a set of realizations through a flow simulator. 3.1.3. Water table elevation model (WTEM) Fig. 5 shows the result of the WTEM to estimate the average depth at any point that one would drill a borehole to get water. A depth-to-water table map shows the spatial distribution of the depth of the water table below the land surface. Fig. 5 shows the locational result of water table which was interpolated in a GIS to derive a water table elevation model (WTEM). The result was represented as an image and therefore a query on the image would determine the depth for that location.

E.S.E. Omran 3.2. Modeling the systematic changes in water table depths 3.2.1. Data analysis and visualization In Menyanthes, characteristics of water table level time-series may be presented in various ways, in time-series plots and in 2D or 3D. As it is easier for the brain to comprehend images than words or numbers, analysis and visualization tools are the primary means of transforming crude data into useful information. Figs. 6 and 7 show the specific methods developed to visualize and extract information of the WTD dynamics in overall graphs such as frequency of exceedance (FOE) graphs or regime curves (Fig. 6), and for statistically characterizing the dynamics with a limited set of parameters (for which time-series models can be of use). The exceedance probability for WTD is used as the basis for annualizing the risk estimate. FOE graph is one way of

Figure 9 TFN model results in which three water table depths respond differently from the same inputs. The observations taken about the 14th and 28th of every month in the period from 2005 until 2007.

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representing the cumulative probability of WTD. This graph gives the expected number of days per year that the WTD exceeds a certain level. The curve plots the empirical cumulative frequency of WTD as a function of the percentage of time that the WTD is equaled or exceeded. The curve is constructed by ranking the data, and for each value, the frequency of exceedance is computed. Visualization also aids ‘visual system identification’ (Fig. 7).

Observations of the precipitation and evaporation are used starting from 1-1-1984 until 31-12-2013. Some problems with the calibration were diagnosed by checking the impulse response function for each piezometer. After several calibrations, root mean squared error (0.194, 0.177, and 0.108 m for pizo 1, 4, and 11, respectively) and root mean squared innovation (0.201, 0.180, and 0.096 m for pizo 1, 4, and 11, respectively) values were the minimum founded for each piezometer. RMSE is the average error of the transfer model. An individual check at each piezometer denoted small errors, considered reasonable for the target variable (WTDs). RMSI is the average innovation or error of the combined transfer and noise model. A common method to illustrate and quantify the long-term variability of the water level at a certain location is to plot both water regime (depth, duration, and frequency) curve and two more percentiles of distribution function. An alternative is the use of frequency of exceedance graphs, which do not contain information about the period of occurrence of the extremes (Fig. 8). The performance of the water table dynamics is compared to that of MxGL statistics, regime curves and frequency of exceedance graph. The MxGL statistics (MLGL–MGL–MSGL–MHGL) that describe the groundwater regime of the selected piezometers are plotted in Fig. 8, together with a regime curve obtained. The figure shows that MGL are not equal, while MHGL–MLGL is greater than the annual amplitude for the

3.2.2. Time-series modeling simulation Table 1 and Fig. 8 summarize the parameters and the statistics results of time-series modeling. Due to spatially varying hydrological conditions, a wide range of calibration results was found for the observed boreholes. The accuracy and validity of the model were checked using the autocorrelation and cross-correlation functions of the innovations, the covariance matrix of the model parameters and the variance of the IR functions. The parameters that have to be estimated are A (drainage resistance, days); a (decay rate, 1/days); and n (convection time, days) from the transfer model, along with a from the noise model. For this purpose, all available observations in the period were used. From Table 1, the percentage of NSE and variance accounted for indicate a very good fit of the model to the data. Low percentages of variance might be caused by errors or lack of data, or possibly other inputs that affect the water table dynamics, which are not incorporated into the model.

Figure 10 Variograms fitted for the trend parameter predicted WTD without including a trend that depends on land use (left), with including a trend (right), and the corresponding kriging map.

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40 87 111 0 88 117 37 86 137 47 87 138

35 87 132

67.18 53.751 2889.164 .202 1.871 136 0 136 86.36 46.191 2133.655 0.223 1.570 120 30 150

54 91 103 49.5 87 112.5 45 82 115 36 83 104 55 85 112

83.18 31.638 1000.964 .016 1.119 92 41 133

50 85 131 45 85 150 Percentiles Tukey’s Hinges

Mean Std. Deviation Variance Skewness Kurtosis Range Minimum Maximum

Fig. 10 presents the results of variograms fitted for the linear trend parameter predicted WTD from October 2005 to March 2007 without including a trend that depends on land use and with including a trend. Including the land use variables into the geostatistical model caused a decrease in the variance. The nugget parameter of the variogram reflects the precision of the WTD and the short distance spatial variation in WTD. Fig. 10 shows the interpolation results of the PIRFICT model using universal kriging and land use classification as a drift. The validation results indicate large interpolation errors. These errors can be explained from the uncertainty about the WTD parameters at the piezometer locations, the poor relationship between land use and WTD and the poor spatial correlation structure in the stochastic residual of the universal kriging model. 3.3. Integration of GIS and simulation modeling to predict the current and future water table depth 3.3.1. Spatio-temporal analysis of water table depths

25 50 75

90.18 45.751 2093.164 0.212 1.425 124 26 150

85.77 42.262 1786.068 0.064 1.309 127 23 150

81.36 39.998 1599.855 0.039 .767 130 20 150

70.27 41.699 1738.818 .251 1.114 131 0 131

82.95 31.957 1021.273 0.478 0.925 92.5 33 125.5

82.73 34.485 1189.218 .610 .297 110 25 135

90 43.25 1870.6 0.142 1.239 120 30 150

81.27 49.508 2451.018 0.239 1.694 130 20 150

February January December November October August

September

piezometers. Consequently, they do not differentiate very well between the dynamics of these different systems. The high frequency fluctuations influence the extremes. Apparently, the different behavior in the high frequencies compensates the difference in the annual amplitudes, and results in comparable MHGL–MLGL. The factor that does differentiate between the piezometers is the mean water level (or more exactly MSGL–MGL) which is, in contrast to MHGL and MLGL, not a result of fluctuations in several frequencies, but is in fact an ordinate of the annual water table cycle. The results of the TFN model are given in Fig. 9, as time plots of the observations and predictions, and of the residuals and innovations. The autocorrelation function of the innovations, for which a time lag increment of one month is chosen in order to reveal seasonal patterns in the autocorrelation, indicates that the white noise assumption holds (Fig. 9). Because of the large number of available observations, the autocorrelation function is rather smooth and the companying confidence interval narrow. As an example of the varying conditions, three boreholes piezometer distributed over different soil types, and land uses were selected. Fig. 9 shows the WTDs respond differently from the same inputs. 3.2.3. Modeling spatial trends in water table depths

July June May April

Descriptive statistics of the water table depth variation, in centimeter. Table 2

76.27 41.064 1686.218 .302 1.201 122 13 135

E.S.E. Omran March

14

Table 2 presents the descriptive statistics of the WTD variation during the years 2005–2007. The frequency distribution of the WTD increase/decrease has high negative skew and kurtosis coefficients. It is a result of extreme values found from the different responses of WTDs over the area, which influence the frequency distributions. At some places, WTDs had few centimetric variations. At other sites, the WTDs varied some centimeters during the monitored period. From a visual inspection of the frequency histograms, the frequency distribution presented deviates when compared with a normal distribution. The results presented non-normal distributions for the months under investigation. The distributions started to present shapes close to a normal distribution after removing some outliers (possibly from error measurements). This procedure reduced skewness and kurtosis. Based on Table 2, the scenario for September (end of dry season) is very different from April (beginning of the season), not only in WTDs but also in their

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

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Figure 11

15

Water table depth (meters) variations estimated by cokriging over the months.

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

ARTICLE IN PRESS 16 Table 3

E.S.E. Omran Correlation coefficient of WTDs for the study period using Gaussian model with 2000 m range.

April May June July August September October November December January February March

April

May

June

July

August

September

October

November

December

January

February

March

1 .534 .471 0.541 .436 0.269 0.585 .453 0.513 .518 0.316 .826

1 .525 0.912 .603 0.325 0.640 0.751 .484 .351 .289 .453

1 .538 0.728 0.241 .594 0.654 0.467 .003 .110 0.118

1 .599 0.334 0.914 .884 0.387 .622 0.848 .846

1 0.432 .897 0.681 0.259 0.365 .737 0.755

1 0.341 0.413 0.428 0.431 0.461 0.372

1 .932 0.512 .469 0.835 .741

1 0.385 0.304 .783 0.803

1 0.378 0.429 0.438

1 .609 0.584

1 .993

1

Figure 12 Simulated WTD that will be exceeded with 5% probability, areas with risk of WTDs shallower than 50 cm (right) on April 1st (actually 28 cm), and areas with risk of WTDs deeper than 50 cm (left) on October 1st (actually 78 cm).

Table 4 Parameters of the adjusted semivariograms for the selected percentiles from the simulated WTD at October 1st and April 1st. WTD

Model

Nugget

Sill

Range, m

April 1st October 1st

Stable Stable

5 6

10.3 19.0

2400 2400

standard deviation, kurtosis, and variance. It can be checked at Fig. 11, which presents the increase/decrease of WTDs estimated by cokriging. Some areas present systematic decreases in WTDs, verified over the months. Table 3 shows the structural correlation coefficients of WTDs. The direct variogram contributions for each month

are in the diagonal of the matrix, and out of the diagonal are the contributions of the cross variograms (covariances between months). The highest contributions for the model were given by May, June, July and October which had the highest values for the Gaussian structure. August and September had the highest nugget effects, being the months which more influence the model random component. The temporal correlation is highest at small temporal lags. The correlation is lost in time because of the changes in water table patterns during the dry season. 3.3.2. Generalization and simulation versus estimation Fig. 12 shows the distribution function of WTD for October 1st from the simulated data. The WTDs which are expected to be exceeded with 5% and 95% probability at October 1st were used for spatial interpolation.

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17 y = -0.0005x2 + 0.0485x + 0.0085 R² = 0.7637

1.8 1.6 1.4 Depth, m

1.2 1

WTDm= 0.24

0.8 0.6 0.4

WTDs = 0.32

0.2

Jan-05 Feb-05 Mar-05 Apr-05 May-05 Jun-05 Jul-05 Aug-05 Oct-05 Nov-05 Dec-05 Jan-06 Feb-06 Mar-06 Apr-06 May-06 Jun-05 Jul-06 Aug-06 Oct-06 Nov-06 Dec-06 Jan-07 Feb-07 Mar-07 Apr-07 May-07 Jun-07 Jul-07 Aug-07 Oct-07 Nov-07 Dec-07

0

Time-series

Figure 13

Table 5

WTDm WTDs

The comparison of average measured (0.24 m) and simulated (0.32 m) water table levels in the period from 2005 until 2007.

Descriptive statistics of crossvalidation and sensitivity analysis for the spatial interpolation of WTD. Minimum

Maximum

Mean

Std. Deviation

Variance

Skewness

Kurtosis

0.0 0.0

1.55 1.56

0.7696 0.7727

0.42005 0.42356

0.176 0.179

0.028 0.004

1.165 1.181

Table 4 summarizes the adjusted semivariograms. The WTDs for October 1st and April 1st are created from the simulated data for the remaining boreholes. The WTD’s which are expected to be exceeded with 5% and 95% probability, have a spatial dependence which was modeled by semivariograms. Ancillary information was used in spatial predictions because the number of observation points in some areas was relatively low. The nugget parameter of the semivariogram reflects the measurement precision of the WTD and the short-distance spatial variation in WTD. The model with high nugget values produced maps, reflecting higher errors in the spatial model and spatial interpolation. The maps of WTDs that will be exceeded with 95% of probability were compared with maps of estimated depth of boreholes as limit for WTD. It is indicated that no problems (risk is negligible) with water levels will occur at October 1st. The same analysis was made for the map of WTDs that will be exceeded with 5% of probability with a 0.5 m limit map for shallow WTDs. 3.3.3. Cross-validation Fig. 13 shows the comparison of measured and simulated water table levels in the period from 2005 until 2007. This approach of estimating WTD has resulted in a better agreement between the simulated and measured data. The largest differences in the simulated and measured WTD of the order of 8 cm occurred during these periods. These differences may be associated with an overestimation of the evaporative losses from the surface. The results of this sensitivity analysis in terms of the seasonal mean differences and RMS (root mean square simulation error) between the simulated and measured water table levels are summarized in Table 5. Table 5 gives the results of spatial interpolation which were evaluated by crossvalidation. In conclusion, estimation is locally accurate and smooth, appropriate for visualizing trends, however, inappropriate for flow simulation where extreme values are important, and

does not assess global uncertainty. On the other hand, simulation reproduces histogram, spatial variability (variogram), is appropriate for flow simulation, allows an assessment of uncertainty with alternative realizations possible. 3.4. Predictive risk mapping of water table depths Stochastic methods enable us to characterize the water table dynamics in terms of risk, which may be valuable in taking strategic decisions on water management. The map presented reflects the risk that the water table is within a critical depth, at a critical day in a future year. Fig. 14 shows the results which detected 3 areas with potential risk of shallow water table depths. Fortunately, these areas are close to the drainages. The mapped risks may form the input of a cost function, which should inform water managers whether a decision on water management is cost-effective or not. The closer the risks to 50%, the more difficult it will be to take a decision. The risk map only shows small areas having risks near 50%, which implies that, the method can be helpful to water managers in taking strategic decisions. 3.5. Predicting water table depth using remote sensing 3.5.1. Exploratory analysis between piezometer data and satellite data Exploratory analysis between satellite data and piezometer data was carried out during the growing season at eleven locations in the study area in 2006. The average water table levels for the selected locations were collected on a monthly basis. Spectral data corresponding to the average of each location were extracted from the images. The exploratory regression analysis results are shown in Table 6. Preliminary regression analysis reveals that the blue, red, and near-infrared bands all correlate with water table levels. The visible bands have negative correlations and the

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

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E.S.E. Omran

Figure 14 Expected risk map that at April 1st (upper) in a future year WTD will be shallower than 50 cm, and areas with risk of WTDs deeper than 50 cm on October 1st (lower). Three small susceptible areas were detected with potential risk of shallow WTDs at April 1st and four areas were detected on October 1st.

Table 6 Exploratory regression analysis of water table depth (cm) and spectral data corresponding to selected locations in study area.

NDVI NIR R G B WTE * **

NDVI

NIR

R

G

B

WTE

1 .286** .069 .478** .048 .129**

.286** 1 1.000** 1.000** .568** .256**

.069 1.000** 1 1.000** .382** .177*

.478** 1.000** 1.000** 1 .103 .036

.048 .568** .382** .103 1 .040

.129** .256** .036 .177* .040 1

Correlation is significant at the 0.05 level (2-tailed). Correlation is significant at the 0.01 level (2-tailed).

near-infrared band has a positive correlation. The normalized difference vegetation index (NDVI) has a better correlation with water table level than several other linear transformation

features obtained with principal component analysis and the Kauth–Thomas transform. 3.5.2. Soil moisture retrieved from landsat data Fig. 15 shows surface temperature (Ts, Kelvin), and normalized difference vegetation index (NDVI) retrieved from Landsat data of April 1st and October 1st, 2006 in the study area. To calculate the relative soil moisture, the dry edge linear equation and wet edge linear equation of Ts/NDVI feature space were calculated first based on Eqs. (3) and (4) as follows: Dry edge : TS-max ¼ 18:36  NDVI þ 307:58 ¼ 0:4703 ð5Þ Wet edge : TS-min ¼ 0:68  NDVI þ 288:26 ¼ 0:3066

ð6Þ

The relative soil moisture of any point in output data’s Ts / NDVI feature space was calculated as:

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

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Figure 15

19

NDVI, surface temperature and SMI retrieved from Landsat 2006 image.

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E.S.E. Omran

Figure 16

Predicted of current water table depth for the 3rd of April 2015 image.

SMI ¼ 100  ðT  Tw =TD  Tw Þ  59:29

ð7Þ

where SMI is the relative soil moisture of any point, T is the surface temperature of the point, TD is the surface temperature of dry edge which is corresponding to the NDVI of the point and Tw is the one of wet edge. Then, using Eq. (7), the relative soil moisture of every pixel can be calculated. With the relative data of soil moisture content and investigation data in study area as a reference, the practical soil moisture retrieved from Landsat of April 1st and October 1st is shown in Fig. 15. According to Fig. 15, the soil moisture was relatively low in study area; most areas have soil moisture

between 5% and 15%, while few areas have soil moisture more than 20%. Contrasting the soil moisture map with the terrain and false color maps, the soil moisture has a relatively high relation with the distribution of vegetation and terrain. The point near to water has a higher soil moisture value, vice versa; the point far from water has a relatively low soil moisture value. From Fig. 15, areas with deeper in WTDs have low probability to loose water volume. Areas with higher water loss (areas with low values in the map) are areas with shallower WTD variation. This map indicates areas in which the WTDs

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are bigger and important regions for local drainage and system recharge. These areas are more sensitive to long dryness period. Areas with decreases in water table depths have high probability to loose water volume. Optimistic evaluations at areas with big variations of WTDs can incur in agricultural production crashes and errors choosing areas to install irrigation systems. Considering uncertainty contributes to preserve important areas for aquifer recharge. It allows for realistic impact evaluations of new agricultural system implementation which needs high water demand.

is relatively deep (Furley, 1999). Shallow water table fluctuates during wet and dry season causing changes in patterns of water logging. Observations are taken soon after each other is not independent, but contain almost the same information about the state of the system. Increasing sampling time frequency, the variance between observations increases and the noise model gives higher weights to the individual elements of the innovations series. The autocorrelation functions were rather smooth and the accompanying confidence interval narrow, which did not reveal seasonal patterns in the autocorrelation. It indicates that the white noise assumption holds. The noise model was effective to remove the autocorrelation in the time-series (Von Asmuth et al., 2002b). Three series of water table level observations are selected that originated from different soils and land use, and show different types of dynamic behavior. The piezometers are well observed with observations taken about the 14th and 28th of every month in the period from 2005 until 2007. As input for the time series model, observations of the precipitation and evaporation are used starting from 1-1-1984 until 31-12-2013. The use of a 30-year period representing the present day climate remains a logical choice for many applications. It is assumed that the average weather conditions during the last 30 years represent the prevailing climate. Exceedance probability, the likelihood that water levels will exceed a given elevation, is based on a statistical analysis of historic values with at least 30 years of data. When used in conjunction with real time station data, exceedance probability levels can be used to evaluate current conditions and determine whether a rare event is occurring. The maximum future high WTD level frequency curves in the next 20 years are increased from 145 cm (as shown in Fig. 8) to 100 cm (as shown in Fig. 10). The minimum future high WTD level frequency curves in the next 20 years are increased from 60 cm (Fig. 8) to 30 cm (Fig. 10). This means the future high water level frequency curves will be about 0.30–0.45 m higher than the present curves. The validation results indicate some interpolation errors. These errors can be explained from the uncertainty about the WTD parameters at the piezometer locations, the poor relationship between land use and WTD and the poor spatial correlation structure in the stochastic residual of the universal kriging model. Compared with Manzione et al. (2006, 2007b), the interpolation performed better here with the parameters of the model better adjusted. Comparing with Von Asmuth et al. (2002b), the interpolation performed better for October 1st here but the results were smoothed. Including elevation as a spatial drift into the geostatistical model caused a decrease in the semivariance as observed by Von Asmuth et al. (2002b). To enable risk management of WTDs for October 1st two levels of probability were calculated. First, a 5% probability level was considered as a measure for risk of WTD. Extremely high water levels as shown in Fig. 10 are an important factor in degradation hazard assessment and WTD management (El Baroudy and Moghanm, 2014). To summarize, surface interpolation and mathematical modeling require a high degree of site-specific knowledge and observations. Sparse and opportunistic water table information must frequently be used in regional hydrogeologic assessments. Interpolation methods do not work well in these situations because they define only general changes in water table elevation, missing the local variations in water table

3.5.3. Cokriging of soil moisture with NDVI The ability to improve the final water table prediction model by applying cokriging using NDVI was evaluated. Correlation between NDVI and soil moisture dataset was determined using Pearson correlation coefficient (r). Results indicate that the soil moisture dataset has correlation with NDVI. Fig. 16 shows the interpolated map of the systematic changes in WTD which indicate a rise of the water table in the 3rd of April 2015. The map shows a large area near the El-Salam Canal where systematic lowering occurs. These areas are covered with traditional agricultural crops, using irrigation systems that catch water directly from the river (surface water). 4. Overall discussions One of the biggest challenges in groundwater modeling is water table characterization in space and time. A simulate time-series model was developed to early predict water table depths (WTDs), in North Sinai, Egypt where only limited observations were available. GIS, simulation and stochastic methods were considered. Time-series modeling is an effective method to characterize the seasonal patterns of WTDs in the area. Stochastic methods enable us to characterize the water table dynamics in terms of risk, which may be valuable in taking strategic decisions on water management. In addition, the stochastic component in the model allows model uncertainty to be taken into account without the complexity of physical mechanistic models. Time-series modeling was efficient to model a wide range of different responses of the WTD over the study area. Stochastic simulation was performed for the 33 boreholes, which remained after inspection of the results. For seven boreholes, the simulation results indicated that the stationary conditions were not met. The distribution functions of the simulated WTD for these boreholes were bimodal. These boreholes were excluded from interpolation. Possibly the relatively short length of the water table time-series did not completely cover the response time of the hydrological system. For example, the dry years of 1999, 2012 and 2013 might have a long-term effect on water table in systems with long memory. The precipitation in these years was 18, 22 and 30 mm, which were less than the annual average (75 mm) over the last 30 years, respectively. In addition, the wet years of 1992, 2001, 2002 and 2004 have precipitation 133, 108, 108 and 115 mm, which were more than the annual, average (75 mm) over the last 30 years, respectively. This effect acts different over the basin. Continuing monitoring WTD would enable us to clarify these questions. Areas with relatively low elevation and close to drainages present relatively shallow water tables, whereas in areas with relatively high elevation and far from drainages the water table

Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001

ARTICLE IN PRESS 22 elevation with respect to land surface. Deterministic models offer explicit definition of a water table surface from physical principles. They are difficult, however, to implement reliably at regional scales and they are not straightforward to implement in a GIS. Statistical models permit direct prediction of WTD from readily measured explanatory variables without the need to characterize the physical properties or processes in the ground water system. They can take into account more of the spatial variability in water table depth on a regional scale than is generally possible with deterministic models. Statistical modeling is useful for mapping long-term averages WTD. Both deterministic and statistical models are data intensive, and generally require new data collection for model development, implementation, and calibration. The greatest limitation of statistical models, and the strength of deterministic models, is in simulating the response of the water table to short-term environmental stresses. Remote sensing and landscape classification allow water table mapping without the resources required by the deterministic and statistical approaches. It is an intuitively appealing and efficient approach, which formally characterizes conceptual models for WTD in terms of geomorphic features. Vegetation growth as manifested by the spectral properties in the blue, red, and near-infrared bands has a correlation with water table level. Use of the NDVI slightly enhances the correlation. 5. Conclusions The quality of the WTD prediction models depends on both sampling frequency and length of time-series. The quality of the output model was restricted by effects of relatively short time-series that did not satisfactorily characterize long memory systems. The use of DEM as ancillary information improved the quality of the final maps. From a time-series analysis there is no indication that the water table was rising/falling due to changes in land use, at least not during the observation period. A 5% probability level was considered as a measure for risk of WTD for October 1st. In the chosen date, April 1st, there is a negligible risk of shallow WTDs that could affect agriculture in some way. The percentage of Nash and Sutcliffe coefficient of efficiency (NSE) and variance accounted for indicate a very good fit of the model to the data. The maximum prediction of WTD level in the next 20 years will increase from 145 cm depth to 100 cm depth. However, the minimum future WTD level will increase from 60 cm depth to 30 cm depth. This means the future high water level will be about 0.30–0.45 m higher than the present level. The sensitivity analysis of WTD estimating has resulted in a better agreement between the simulated and measured data (8 cm difference) during these periods. These differences may be associated with an overestimation of the evaporative losses from the surface. Finally, the remote sensing results indicate that Landsat image was not useful for WTD prediction; however, it may useful for soil moisture prediction. This paper suggests three limitations to this research that need to be addressed in the future. First, the analysis should be extended to other dates and periods that are critical to water table. The method presented in this study enables this extension. Second, one of the future research areas is to develop and build early warning information system for water table management. Up to now, however, a little progress has been

E.S.E. Omran made in this direction. Finally, with the GRACE satellite mission the interest for ground-based gravity methods to measure the change in water table will gain new attention and potential. The ability of gravity data for monitoring annual and long term water level fluctuations at a large scale will be one of the future directions. Conflict of interest There is no conflict of interest. References Adegoke, J.O., Carleton, A.M., 2000. Warm season land surface– climate interactions in the United States Midwest from mesoscale observations. In: McLaren, S., Kniveton, D. (Eds.), Linking Climate to Land Surface Change. Kluwer Academic, pp. 83–97. Al-Khudhairy, D.H.A., Leemhuis, C., Hofhnann, V., Shepherd, I.M., Calaon, R., Thompson, J.R., Gavin, H., Gasca-Tucker, D.L., Zalldls, Q., Bilas, G.D.P., 2002. Monitoring wetland ditch water levels using Landsat TM and ground-based measurements. Photogramm. Eng. Remote Sens. 68 (8), 809–818. Al-Saifi, M.M., Qari, M.Y., 1996. Application of Landsat thematic mapper data in sabkha studies at the Red Sea coast. Int. J. Remote Sens. 17, 527–536. Angulo, J., Gonzfilez-Manteiga, W., Ferrero-Bande, M., Alonso, F., 1998. Semi-parametric statistical approaches for space–time process prediction. Environ. Ecol. Stat. 5, 297–316. Arun, P.V., 2013. A comparative analysis of different DEM interpolation methods. Egypt. J. Remote Sens. Space Sci. 16, 133–139. Arun, P.V., Katiyar, S.K., 2013. An evolutionary computing frame work toward object extraction from satellite images. Egypt. J. Remote Sens. Space Sci. 16, 163–169. Atta, E.K., 2006. Improvement and Management of Saline and Alkali Soils Under Irrigation of El-Salam Canal Project to Increase Productivity. Suez Canal University, Ismailia, Egypt. Becker, M.W., 2006. Potential for satellite remote sensing of ground water. Ground Water 44, 306–318. Beven, K., Kirkby, M., 1979. A physically based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull. 24, 43–69. Clark, I., Harper, W.V., 2000. Practical Geostatistics. Ecosse North America LLC, Columbus, OH, USA. Desbarats, A.J., Logan, C.E., Hinton, M.J., Sharpe, D.R., 2002. On the kriging of water table elevations using collateral information from a digital elevation model. J. Hydrol. 255, 25–38. Deutsch, C.V., Journel, A., 1992. GSLIB Geostatistical Software Library and User’s Guide. Oxford University Press, New York. DRC, 2006. Soils of El-Salam Canal Project. Desert Research Center, Cairo, Egypt. El Baroudy, A.A., Moghanm, F.S., 2014. Combined use of remote sensing and GIS for degradation risk assessment in some soils of the Northern Nile Delta, Egypt. Egypt. J. Remote Sens. Space Sci. http://dx.doi.org/10.1016/j.ejrs.2014.01.001. Furley, P.A., 1999. The nature and diversity of neotropical savannah vegetation with particular reference to the Brazilian Cerrados. Global Ecol. Biogeogr. 8, 223–241. Gong, P., Xin, M., Ken, T., Charles, B., Gregory, S.B., 2004. Water table level in relation to EO-1 ALI and ETM+ data over a mountainous meadow in California. Can. J. Remote Sens. 30, 691– 696. Hengl, T., Heuvelink, G.B.M., Stein, A., 2007. A generic framework for spatial prediction of soil properties based on regression-kriging. Geoderma 120, 75–93. Hipel, K., McLeod, A., 1994. Time Series Modeling of Water Resources and Environmental Systems. Elsevier, Amsterdam.

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Please cite this article in press as: Omran, E.S.E., A stochastic simulation model to early predict susceptible areas to water table level fluctuations in North Sinai, Egypt, Egypt. J. Remote Sensing Space Sci. (2016), http://dx.doi.org/10.1016/j.ejrs.2016.03.001