Added-Value of 3DVAR Data Assimilation in The ...

Added-Value of 3DVAR Data Assimilation in The Simulation of Heavy Rainfall Events Over Western and Central Africa

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P. Moudi Igri*, 1Roméo S. Tanessong, 1D. A. Vondou, 1F. Kamga Mkankam and 3 Jagabandhu Panda

University of Yaounde I, Laboratory of Environmental Modelling and Atmospheric Physics, PO.Box: 812 Yaounde, Cameroon

Ecole Africaine de la Météorologie et de l'Aviation Civile (EAMAC). PO.Box: 746, Niamey, Niger

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Department of Earth and Atmospheric Sciences, National Institute of Technology Rourkela, Odisha-769008, India

(January, 2015)

*Corresponding Address P. Moudi Igri Ecole Africaine de la Météorologie et de l'Aviation Civile (EAMAC) PO.Box: 746, Niamey, Niger Email: [email protected]

Abstract This study aims at evaluating the ability of a Numerical Weather Prediction (NWP) model to capture the spatial distribution and the magnitude of rainfall during 3 recent intense events (15-17 June 2011, 23-25 August and 04-06 September 2012) observed over Western and Central Africa, as well as the associated atmospheric and near surface conditions. For each event, two numerical experiments are performed using the Weather Research and Forecasting (WRF) regional model without (CNTL) and with (DA) data assimilation. Simulations are initialized with the Global Forecasting System (GFS) data. The analyses are updated with the three dimensional variational (3DVAR) technique using prep-bufr and radiance observational data in a time window of ±3 hours. The potential added value of data assimilation is addressed by comparing meteorological variables such as relative humidity, zonal and meridional wind components, 2 m temperature and rainfall with the European Center for Medium Range Weather Forecasting Reanalysis (ERA-I) and the Tropical Rainfall Measuring Mission (TRMM) satellite-derived rainfall product datasets. WRF accurately simulates the spatio-temporal propagation and the zonally extended structure of rainfall, as well as of relative humidity, 2 m temperature and horizontal wind components. DA exhibits different biases, root mean square error and spatial correlation leading to mixed results in terms of outperforming CNTL. Results indicated that there is an increment in control variables implying an added value from 3DVAR to the initial and boundary conditions. Rainfall forecasts were improved by 15-25%. Uncertainties in the simulation of intense events in the study domain were noticed, but improvement resulting from DA was limited due to lack of assimilated data in this region. Key words: Africa, WRF-Var, Data assimilation, Weather Prediction, Conventional data, Radiance data

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Introduction Western and Central African regions routinely receive heavy rainfall during the

monsoon period, ranging from June to September. These rainfall events are not well forecasted in most situations. The resulting damages could be reduced if improvement was made in the forecasting of these extreme weather events. In recent years, many efforts have been made in this direction using mesoscale models. Mesoscale numerical weather models have played an important role in predicting extreme weather events (GRELL et al., 1994; DONG-KYOU et al., 2010; ROUTRAY et al., 2010, PANDA et al., 2011) and associated characteristic features (PANDA et al., 2009; PANDA and GIRI, 2012). However, predictability of heavy rainfall episodes is still associated with uncertainty (CRETAT et al., 2013). A proper assessment and establishment of an appropriate scientific framework of future trends for extreme weather would help in setting up infrastructure for disaster preparedness. This study is an effort to improve the forecasting capability of the WRF (Weather Research and Forecasting) model with respect to heavy rainfall episodes over westcentral Africa by using three dimensional variational (3DVAR) data assimilation technique. Mesoscale model forecast performance critically depends on the quality of the initial conditions (DONG-KYOU et al., 2010; MOHANTHY et al., 2011). However, the spatiotemporal variability of the model simulating rainfall is strongly modulated by the model physics (FLAOUNAS et al., 2010; POHL et al., 2011; CRETAT et al., 2012). Typically, large scale global analysis provides the initial conditions to the mesoscale models (ROUTRAY et al., 2010). These initial conditions have limitations, such as coarse resolution and inadequate representation of localized mesoscale features. Therefore, assimilation approaches that ingest local observations are important to improve the model initial conditions (DALEY, 1991). Over the last decade, high-resolution mesoscale models with 3DVAR or four dimensional variational (4DVAR) techniques have been developed to improve weather

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forecasts ( KALNAY, 2003; BARKER et al., 2004; HUANG et al., 2009). Most of the efforts have been spent in the development of variational data assimilation systems in order to replace previously used schemes, such as optimum interpolation (PARRISH and DERBER, 1992; LORENC et al., 2000). Data assimilation is known as the process of creating the best estimate of the initial state for numerical weather prediction (NWP) models by combining all available sources of information, including the first-guess and associated uncertainties from previous short-term forecasts and observations (TALAGRAND, 2003; BARKER et al., 2004; ZHANG et al., 2010; WHEATLEY, 2012). In recent years, more attention has been given to assessing model performance while simulating heavy rainfall events over different regions of Africa. Such studies primarily focused on better understanding of the associated physical mechanisms and processes involved. For example, FLAOUNAS et al. (2010) used the WRF model to study the sensitivity of 2006 West African monsoon to convection and planetary boundary layer (PBL) parameterization. They found that PBL schemes have the strongest effect on temperature, vertical distribution of humidity and rainfall amount whereas the precipitation variability is strongly influenced by convective parameterizations. Similarly, CRETAT et al. (2012) demonstrated that WRF accurately simulates seasonal large-scale rainfall patterns, as well as seasonal gradients of South African rainfall. They also quantified the seasonal biases of WRF model outputs and uncertainties associated with some physical parameterizations. Their studies indicated that the rainfall intensity and associated intra-seasonal characteristics are very sensitive to the choice of cumulus schemes. The studies by CRETAT et al. (2013) also showed that regional climate model (RCM) simulations accurately capture the spatial and temporal characteristics of intense events; while they tend to overestimate their number and underestimate their intensity over Africa. POHL et al. (2011) discussed the uncertainties in the choice of WRF physics options for the purpose of simulating the spatial variability of

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rainfall over East Africa. They found that uncertainties (defined as the differences between the experiments) are larger than the biases. Further, the physical parameterizations (and associated factors significant in numerical modeling of weather and climate) exerting largest influence on the simulated rainfall in order of decreasing importance are the shortwave radiation scheme, the land-surface model, domain size, convective schemes and land-use categories. FINK et al. (2011) studied the operational aspect of meteorology in West Africa using satellite data. They found that data assimilation using AMSU-A and AMSU-B channels improves meteorological parameters including precipitation forecasts over parts of the tropics and West Africa. Several researchers also studied heavy rainfall events and associated meteorological characteristics in other parts of the world. For example, ROUTRAY et al. (2010) studied the impact of the 3DVAR technique in the WRF model on three heavy rainfall events over the Indian monsoon region. They demonstrated that 3DVAR improved WRF model performance and better simulated the amount of rainfall over the considered region. Similar results were obtained by MOHANTHY et al. (2011). Similarly, KUMAR et al. (2008) adopted the 4DVAR to study tropical depressions over the Bay of Bengal and suggested the use of this technique in monsoon depression simulations over this region. The studies by PANDA and GIRI (2012) also showed that the use of 3DVAR in the WRF model could enhance the performance over Mumbai and Goa during a tropical storm. Another study by DONG-KYOU et al. (2010) showed that the use of the Automatic Weather System (AWS) and radar data during the assimilation process improved the temporal and spatial distribution of diurnal rainfall over southern Korea. The current study is first of its kind in view of using a combination of satellite and surface observational data as inputs in WRF data assimilation module and study the consequent impact on precipitation forecasting over West and Central

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Africa. Previous studies like the one by Fink et al. (2011) only assimilated satellite measurements over the West African region. The objective of this work is twofold: (i) evaluate the ability of WRF to simulate some basic characteristics of heavy rainfall events (i.e., location, propagation and intensity) and their physics (i.e., associated atmospheric state), and (ii) assess the potential added value of the 3DVAR technique (it is the most operationally used scheme and needs less computational power). The model simulations are performed without data assimilation (termed as CNTL) and with data assimilation (termed as DA). The model skill is evaluated based on some basic statistical calculations such as bias, spatial correlation and root mean square errors. The details of the model configuration, experimental design and the case studies are presented in section 2. Subsequently, results obtained from the CNTL and the DA experiments are discussed in section 3 and section 4 summarizes the achievements from this study. 2.

Case studies and experimental design

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Considered cases Over the last few years, the African continent has increasingly experienced severe

flooding due to the occurrence of heavy rainfall episodes. The high rainfall amounts resulting from episodic events often give rise to rain splash, surface crusting, and soil compaction. These events in turn lead to high runoff, sheet and gully erosion and finally losses to soil and lives (THIEMIG et al., 2010). Much of these losses can be attributed to some floods in the monsoon period during the years 2011 and 2012. In fact, the cases considered here were associated with intense convection leading to extreme rainfall occurrences. The three heavy rainfall episodes considered in this study are: (i) 15-17 June 2011 event (Case 1), (ii) 23-24 August 2012 event (Case 2) and (iii) 04-05 September 2012 event (Case 3). Simulations are initialized at 0000 UTC and valid for 48 hours. Case 1 was particularly set apart by its devastating effects compared to the other two events. 5

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WRF-3DVAR modeling system The WRF model is a mesoscale numerical weather prediction system designed to serve

both operational forecasting and atmospheric research needs (SKAMARAOCK et al., 2008). The effort to develop WRF has been a collaborative partnership among many USA institutions, principally the National Center for Atmospheric Research (NCAR), the National Oceanic and Atmospheric Administration (NOAA), the National Center for Environmental Prediction (NCEP) and the Forecast Systems Laboratory (FSL). The details about the modeling system can be found in SKAMAROCK et al. (2008). The model is quite robust for research and operational purpose since it contains advanced dynamics, physics and numerical schemes. It has several components including the optional 3DVAR (or WRF-Var) data assimilation system. This data assimilation technique usually improves model performance by minimizing a cost function that represents the error-weighted difference between simulated and observed weather parameters at the initial time. Based on Bayesian probabilities and Gaussian error distribution, the 3DVAR cost function J(x) is given as follows (LORENC, 1986; LORENC et al., 2000; IDE et al., 1997): (1)

where x is the analysis variables vector (n dimensional) that minimizes the cost function J(x), xb is the background variables vector (n dimensional), yo is the observation vector (m dimensional), B is the background error covariance matrix (n × n) and R is the observation error covariance matrix (m × m). The solution of the above equation represents the a posteriori maximum likelihood (minimum variance) estimate of the true state of the atmosphere given the two sources of a priori data: the first guess (or back-ground) xb and observations yo (LORENC, 1986). The fit to the considered data are weighed by estimates of their error covariance matrix represented in 6

terms of B and R. The observational error covariance R includes instrumental and representativeness error covariance matrices. The representativeness error is an estimate of inaccuracies introduced in the observation operator H, which is used to transform the gridded analysis x to observation space y = H(x) for comparison against observations. The error is model resolution dependent and also may include a contribution from approximations in H. Departures between observations and state vector ‘y’ are called innovations. In the assimilation process adopted in this study, the observations, previous forecasts, their errors and physical laws are combined to produce analysis increments that are added to the first guess analysis to provide an updated analysis (initial condition) for model simulation. Further details can be found in BOUTIER and COURTIER (1999), BARKER et al. (2004) and JIANFENG et al. (2005). The advanced research WRF modeling system version 3.3 is used to conduct this research. The study domain covers the western and central African regions and some southern parts of Atlantic Ocean with 250 x 190 grid points and a grid spacing of 25 km (fig. 1). Simulations used 41 vertical layers with the model top at 50 hPa. The physical parameterization schemes and model configuration details are summarized in Table 1. The choice of each physics scheme used in the simulations is based on literature survey and sensitivity tests (not discussed here). These efforts culminated in a WRF model configuration best suited for accurately simulating real-time weather prediction in Western and Central Africa. In this study, two types of numerical simulations were designed: (i) the control (CNTL) experiment uses WRF model only and (ii) the DA experiment uses 3DVAR within the WRF modeling system in cycling mode (6 hourly). 2.3

Data used Initial and 6-hourly boundary conditions (http://nomads.ncdc.noaa.gov/cgi-bin/ncdc-

ui/ftp4u.pl) are provided by the 0.5° resolution NCEP-GFS dataset. Additional observation 7

data is used to update initial conditions during DA experiments. Newly generated background statistics error (BE) matrix (BARKER et al., 2004) is used in DA experiments. The BE covariance is computed using the National Meteorological Center (NMC) method (PARRISH and DERBER, 1992) calculated for the month of each case selected. Radiance products used in this study are from the NCEP Global Data Assimilation System (GDAS) and include Atmospheric Infra-Red Sounder (AIRS), Advanced Microwave Sounding Unit-A (AMSU-A), Advanced Microwave Sounding Unit-B (AMSU-B), High resolution Infra-Red Sounder-3 (HIRS-3), High resolution Infra-Red Sounder-4 (HIRS-4) and Microwave Humidity Sounder (MHS) NCEP processed brightness temperatures. These datasets are supported by NCAR and available online at http://dss.ucar.edu/datasets/ds735.0/. Conventional and satellite data (Table 2) obtained from Global Data Assimilation (2.5° x 2.5°)

are

processed

through

the

NCEP

BUFRLIB

(http://www.nco.ncep.noaa.gov/sib/decoders/BUFRLIB) utility program in preparation for assimilation within WRF-Var. The observation datasets are in the World Meteorological Organization (WMO) -maintained Binary Universal Form for the Representation (BUFR) of meteorological data format. The details of the observations and retrieved number are summarized in Table 2 and Table 3. Assimilated variables from the observation network messages are given in Table 4. For the purpose of verification, Tropical Rainfall Measuring Mission (TRMM) data is considered. In this study, version 7 of TRMM 3B42 data (http://mirador.gsfc.nasa.gov/) is used as they have been widely validated in West Africa (NICHOLSON et al., 2003; HUFFMAN et al., 2007). This product version provides three hourly estimations of rainfall on a grid of 0.25° x 0.25° resolution. For comparison, 6-hourly rainfall is aggregated from 3hourly

values.

In

addition,

6-hourly

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ERA-Interim

data

(http://data-

portal.ecmwf.int/data/d/interim-daily/) of 0.75° x 0.75° resolution is used to validate relative humidity, winds and 2 m temperature (DEE et al., 2011). 2.4

Statistical scores and analysis increment The correspondence between predicted and observed rainfall can be revealed by

computing spatial correlation and errors or statistical scores such as bias and mean absolute errors. The mean error (Bias) measures the average difference between the simulated and observed values. The mean absolute error (MAE) measures the average magnitude of the error. The root mean square error (RMSE) also measures the error magnitude, but gives some greater weight to the larger errors. The correlation coefficient ‘CR’ measures the degree of correspondence between the estimated and observed distributions. It is independent of absolute or conditional bias and should be used along with other measures when validating real time forecasts. Mathematical formulations for these scores are as follows:

where

and

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In the above equations, ‘xi’ indicates the estimated value of rainfall at point ‘i’, while ‘yi’is the observed value at the same point and ‘N’ represents the total number of points. The WRF-VAR system itself has been used to monitor observations and data quality control (HOLLINGSWORTH et al., 1986) by computing statistics involving observations, such as observation increments or analysis increment (AI). The ‘AI’ is defined as the analysis 9

‘A’ minus the background ‘B’ or (A - B). In this study, the ‘AI’ is investigated for all the 41 eta levels for pressure ‘p (hPa)’, temperature ‘t (K)’, specific humidity ‘q (kg/kg)’, zonal wind ‘u (ms-1)’ and meridional wind ‘v (ms-1)’ at 0000 UTC (analysis time). The ‘AI’ statistics could be one method for quantitatively comparing assimilation impact in regions with sufficient observations (KISTLER, 2001). This is because ‘AI’ is a measure of the 6-h forecast error started from the previous analysis and it provides a quantitative assessment of the quality of the analysis to be input to the model. 3.

Results and discussion Results from both types of model simulations (i. e. CNTL and DA) are discussed.

These results are comparatively analyzed along with the 0.75°x0.75° ERA-Interim (http://data-portal.ecmwf.int/data/d/interim-daily/) global reanalysis and the 0.25°x0.25° TRMM 3B42 data (http://mirador.gsfc.nasa.gov/) in order to assess the model performance. In addition, the statistical errors and differences between simulations offer further insight into the model performance. 3.1

Near surface features In this sub-section, near surface meteorological features for Case 1 are discussed.

However, the conclusions hold true for the other two cases as well. The performance of the model is assessed in order to identify to what extent the CNTL experiment captures the spatial distribution and magnitude of the relative humidity, meridional and zonal wind and 2 m temperature. These results are compared to the DA experiment in order to reveal forecast improvements and degradations. Figures 2-3 display the spatio-temporal distribution of 6-hourly relative humidity (in %) at 1000 hPa for Case 1. The ERA-I reanalysis shows low humidity over the Sahelian regions and high humidity along the Guinean Coast. Both CNTL and DA simulations are able to capture the main observed features of the spatial distribution of relative humidity (panels d-f 10

and g-i respectively). In the coastal regions, humidity is relatively high mostly due to the advection of moist air from the Atlantic Ocean. On the other hand, both CNTL and DA simulations failed to capture low humidity in the region between 18°N and 25°N. In the Sahel belt, a relative humidity less than 30% is simulated in both of these experiments. Similarly, the sudden rise of relative humidity (from 45% to 95%) around midday, in the coastal regions is also clearly presented in both of these simulations. Figures 4-5 display the spatio-temporal distribution of 6-hourly 2 m temperature (in K) at 1000 hPa for Case 1. The ERA-I spatio-temporal distribution of 2 m temperature shows high temperature over the Sahelian regions, especially during daytime. Low temperatures are mostly observed in Central Africa and along the Guinean Coast. Highest values are simulated in the Sahelian zone located between 10°N and 25°N. The maximum value of simulated temperature is found to be ~36°C (between 1200 and 1800 UTC). High temperatures in the northern region (Sahara) indicate strong daytime surface heating (weak cloud cover) by solar radiation. The lowest values are simulated along the Guinean Coast due to marine influence and cloud cover. Thus, the near surface 2 m temperature in the southern parts of West Africa is relatively low. The CNTL analysis was noticeably warmer than the DA analysis in the Sahel belt. The CNTL simulations continued to be warmer in Ghana and the Ivory Coast during the whole simulation period, except on 15 June at 0600 UTC (figure not shown for brevity). The monsoon flow (the superimposed wind) is also evident in figures 4-5. The southwesterly monsoon flow is associated with the equatorial crossing of the southeast trade winds. This flow is further influenced by the pressure gradient set up by the surface thermal contrast between the land and sea. The pattern of wind distribution is clearly evident from ERA-I reanalysis. WRF model qualitatively reproduces the aforementioned features of the incoming flow. For example, the splitting of the incoming flow through the continent is well simulated in both CNTL and DA simulations (figures 4-5).

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Differences between CNTL and DA simulations (figures 6-9) are well marked over some countries, especially in the coastal areas bordering the Atlantic Ocean including the Congo Basin. This is mostly due to sea breeze which greatly impacts the distribution of relative humidity, and is better captured by the DA simulation. Thus, a better simulated sea breeze in WRF experiments plays a controlling factor for the distribution and amount of relative humidity over coastal regions. Although the difference between CNTL and DA results approaches zero over the major Sahel regions, the DA simulation has different patterns compared to CNTL. The difference is relevant in places where there are sufficient observations, especially over Niger, Ivory Coast and borders. An examination of the differences (set between 0º-20ºN and 16ºE-25ºE) in terms of bias for WRF surface variables indicates a tendency toward overestimation, although underestimation was also present (Tables 5-7). Despite both CNTL and DA simulations overestimate wind speed over continental areas as when compared to ERA-I, this overestimation is smaller in the DA simulation. The simulated relative humidity and 2 m temperature exhibit strong correlation (020°N, 16°E-25°E) with observations in Case 1 (figure 10). However, wind components appear to be poorly correlated with observations in this case (figure 11). The Congo Basin region displays the highest bias, either in CNTL or DA experiment. This result is consistent with the results of CRETAT et al. (2013), which revealed that the Congo Basin shows the largest differences during intense events in both regional climate models and general circulation models. The disagreements could also be due to potential uncertainties in ERA-I data. The DA experiment shows slightly improved results with weaker differences relative to the CNTL experiment. The results in the other two cases are found to be similar to that of Case 1. This demonstrates the utility of DA for improving intense event forecasts, and

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suggests that more observations are available for assimilation would help better predicting such events. 3.2

Spatial distribution of rainfall The simulated rainfall from CNTL and DA experiments are analyzed by qualitative

comparison with TRMM data. All three cases are used to understand and analyze the spatial distribution of rainfall and assess the model performance in the DA experiment. 6-hourly accumulated rainfall during Case 1 (initialized at 0000 UTC on June 15, 2011) is shown in figure 12. TRMM observations (first vertical panel) locate the main rainfall in a zonal band between the Equator and 15°N. Maximum rainfall occurred over the Cameroon Highlands, extending up to the Joss Plateau in Nigeria and along the Guinea coast. Localized precipitation fell over Mali, Central Africa and Democratic Republic of Congo. On 16 June, TRMM rainfall distribution is propagating westward from Cameroon and Nigeria to the Guinean coast. Precipitation decreased immediately north of the rain belt. The CNTL experiment for Case 1 simulates fairly fine scale features (second vertical panel in figure 12) in Central and West Africa consistent with TRMM. The CNTL is also able to reproduce the zonally extended structure of precipitation between 10°N and 20°N with a northeast-southwest tilt, but fails to replicate the desired intensity. Between 5°N and 10°N, the CNTL rainfall is underestimated and happens to be out of phase with the TRMM data. On the other hand, CNTL simulation overestimates precipitation in orographic regions and in the border areas of the Democratic Republic of Congo. The simulated precipitation in the DA experiment (third vertical panel in figure 12) is similar to that of CNTL, but differs in intensity. In fact, the DA simulation captures the precipitation maximum over the Guinea highland region to a reasonable extent, but overestimates precipitation over the Cameroon Mountains and Joss Plateau. The DA improves the spatio-temporal distribution of large scale rainfall patterns to a greater extent than the 13

location of intense convective cells. This is partly attributed to the lack of assimilated observations in this area and the considered model resolution that is still too coarse in order to capture local convection. Although both CNTL and DA simulations capture the main feature of rainfall distribution, there is still an excessive spatial spread attributable to a latitudinal shift in the monsoon system compared to the one that is usually observed. Figure 13 displays the 6-hourly accumulated rainfall for Case 2. The TRMM observations in Case 2 (the left most panel in figure 13) display the same zonal rainfall distribution, but the intensity of rainfall is more pronounced over the whole study domain. Some precipitation is also located over Mauritania. Heavy rainfall in the Cameroon Far North region and Chad moved over Nigeria from 23 August 2012 to 24 August 2012. The CNTL experiment simulates a thicker rainfall band and maxima than observed, especially during daytime between 1200 and 1800 UTC. Generally, CNTL overestimates rainfall intensity and exhibits a wide rainfall band by placing the maxima over orographic regions. Rainfall is confined between 0°N–9°N and hence showing an underestimation over the regions further north. In contrast, the DA simulation shows a well captured sharper rainfall band, but the orographic maxima locations are not well simulated. However, some peak occurrences over Central Africa Republic are still visible in the DA simulation. The rainfall distribution for Case 3 is shown in figure 14. TRMM exhibits approximately the same rainy band as in other cases, but with some precipitation over the Atlantic Ocean. The CNTL simulation appears to capture the main structures, with the maximum precipitation over Ghana, along the coast of Guinea and Sierra Leone, and in the Congo Basin. The main precipitation area was localized between the equator and 10°N. However, both CNTL and DA simulations overestimated precipitation for large areas on the Coast of Guinea.

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The WRF simulations reasonably reproduce observed features, offering further confidence that the model is capable of representing the basic characteristics of rainfall over Western and Central Africa. The CNTL experiment has the maximum averaged precipitation. A clear mode of westward phase propagation is noticed within the precipitation peak. There is some improvement in the timing, location, and the intensity of rainfall occurrences in the DA experiment, but model skill remains limited. The fine scale features of the rain belt are well captured by the model in addition to the spatio-temporal propagation and the zonally extended structure of precipitation. In all WRF simulations, the rain band associated with the ITCZ is well simulated over the Atlantic Ocean, though WRF overestimates the extent of ITCZ and the magnitude of the precipitation. Generally, precipitation decreases south and north of the maximum rain belt. Significant rainfall is reported over central Africa and Democratic Republic of Congo, even if the model does not reproduce these occurrences. DA simulations capture some features that are not captured by CNTL (figures 12-14) particularly during Case 3 (figure 14). The model satisfactorily reproduces the rainfall amount over the given domain, but fails to capture some peaks over the regions like Northern Nigeria, Sudan and the Democratic Republic of Congo. It seems that the rainfall intensity of the core of convective cells is often weaker in the simulations relative to the observations. On the other hand, WRF tends to overestimate the spatial extension of light rainfall, especially over Central Africa. Significant differences exist in TRMM and WRF simulated rainfall distributions, which could be due to model deficiencies (CRETAT et al., 2013), errors associated with satellite measurements, extraction algorithms and interpolation techniques (SYLLA et al., 2013) and domain topography (TANESSONG et al., 2012). The model skill appears to be time and region dependent as well. The regional scale modeling results over a region are usually very much dependent on input of initial and boundary conditions in addition to the choice of physical

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parameterizations (i. e. planetary boundary layer (PBL), microphysics, cumulus convection and radiative schemes). Therefore, discrepancies in the model results emphasize the uncertainties of precipitation validation over West Africa (DRUYAN et al., 2008). 3.3

Analysis of large-scale propagation of rainfall Convective propagation can be shown through Hovmöller diagrams (CARBONE et al.,

2002). Figure 15 shows the comparison of time-longitudinal rainfall between TRMM and the simulated results from CNTL and DA experiments. These diagrams are produced by averaging 48 hour accumulated rainfall over the latitude band extending from 0°N to 20°N. The most evident feature from this analysis is the abundance of precipitation episodes propagating from east to west across the study domain both in the model and observations for Cases 1, 2 and 3. Additionally, the maximum precipitation in the domain near 0000 UTC appears to propagate between 10°E-10°W. The main characteristics of the mean diurnal cycle in WRF simulations are found to be similar to that of the TRMM observations in terms of both timing and propagation. From this perspective, the WRF forecasts replicated the longevity and the propagation characteristics of the precipitation episodes. However, the latitudinal average precipitation within the WRF episodes is noticeably larger than that of the TRMM observations, offering further evidence of the previously noted positive precipitation bias (overestimation) in the WRF. Nevertheless, DA experiments for each case (figure 15) clearly depict better matches with observations compared to CNTL experiments. On the other hand, the similarity of the main characteristics of simulated large-scale mean diurnal cycle with TRMM observations was not the case at the grid point scale between 5°N and 10°N. This indicates that the model is more skillful in simulating the large-scale characteristics of rainfall than their local details. It is difficult to understand if these largescale characteristics are simulated by the regional model, or forced through the lateral boundary conditions. A comparison with the NCEP-GFS dataset may help in understanding 16

this aspect. Further, analysis of few cases may not be helpful in drawing any general conclusion in this sense. However, such comparisons would be made extensively in future works since this additional analysis would dilute the current objective and interest. 3.4

Forecast verification and analysis increment The RMSE, bias and correlation scores for 24 hour accumulated rainfall are shown in

Table 8 for all three cases. It is clearly indicated that the CNTL simulations give consistently higher error scores for the three cases studied. When verified against TRMM observations, the model errors in the DA experiments are found to be weaker. However, the correlation values appear to be random in nature with some values less than 0.5. Resulted biases may involve errors in the initial and boundary conditions due to sparse observational dataset available over the region, as well as issues resulting from physical parameterizations in Africa (FLAOUNAS et al., 2010; POHL et al., 2011; CRETAT et al., 2012). In particular, rainfall biases could be related to model deficiencies in simulating African easterly and equatorial waves, which have been shown to favor strong convective events over West and Central Africa (JANICOT, 1992; LENOUO and KAMGA, 2008). The CNTL simulations statistical scores are somewhat higher than those of DA simulations. Even if the improvement resulting from DA is moderate in absolute values (Tables 5-8), the error scores are generally 15-25% smaller than those without DA. This is in accordance with FINK et al. (2011) who found that data assimilation using AMSU-A and AMSU-B channels improves meteorological parameters including precipitation forecasts over parts of the tropics and West Africa. Thus, the result is indicative of the significance of DA and is a promising procedure to gain confidence in weather prediction over West and Central Africa. The vertical profiles of the gridded analysis increment (AI) are shown in figures 16a-b, 17a-b and 18a-b. Figures 16c, 17c and 18c display the Root Mean Square Error (RMSE) of 17

the gridded AI for the selected cases. The pressure AI profiles are presented in figure 19. Both zonal and meridional wind display similar AI at all atmospheric levels with few exceptions in the upper levels, where large values are found. The temperature AI exhibits similar behavior with that of the wind, while the specific humidity AI values are very low. For example, minimum AI is found to be nearly -6 ms-1 and -5K (figure 18) for meridional wind and temperature variables. The respective maximum AI values for temperature and meridional wind speed are approximately 4.1K (figure 17) and 6.5 ms-1 (figure 18). RMSE exhibits similar behavior to the AI for these variables. Zonal and meridional wind components have much larger RMSE values at the top of the model. However, specific humidity has the lowest RMSE at all levels. The AI is relevant in the regions where there are sufficient quality observations. In data sparse regions, the AI is small. Typically AI shows that the analysis file has been improved after the DA experiment. KISTLER (2001) interpreted the AI RMSE as a rank in the regions of sufficient quality observations. Since precipitation is not directly assimilated in WRF3DVAR, improvement in wind, temperature, pressure and specific humidity (which are the model control variables) tend to influence the rainfall field. 4.

Concluding remarks Two numerical experiments are performed during three recent intense rainfall events

occurring over West and/or Central Africa: (i) CNTL (with no data assimilation) and (ii) DA (with 3DVAR assimilation). The simulations used the WRF modeling system. The DA experiment is found to have improved the model results over Western and Central Africa. Consequently, a better simulation of rainfall amount and location is realized. The improvement of 15-25% in the model forecasts is a clear indication of the importance of the injection of additional observational data through the 3DVAR technique. The Sahel rain belt was well reproduced by the model. This result is similar to the findings by 18

MOHANTY et al. (2012). The model results could further be improved if 4DVAR or Kalman filter technique is used. The results from this study also suggest that the performance of a regional model in simulating precipitation over Western and Central Africa is very sensitive to the prevailing large-scale circulation. The model biases in large-scale circulation result in considerable differences in the amount of precipitation. In view of the earlier studies and the present findings, data assimilation remains a promising tool of reducing systematic forecast error. Although there have been remarkable improvements in recent years, quantitative precipitation forecasting is still a challenging problem for mesoscale and microscale weather prediction (TANESSONG et al., 2013). One of the fundamental reasons for this challenge is that precipitation is often concentrated in convective cells or mesoscale bands or clusters, which are difficult to reproduce in the model's initial conditions from the large-scale analysis. Data assimilation improves the spatiotemporal distribution of the large scale rainfall pattern much more than the location of intense convective cells in this study. In addition to issues related to the quality of initialization, the boundary conditions and model physics, a number of earlier studies underline the impact internal variability has on the location of such fine scale convective cells as well. The three intense events presented in this study are persistent in time and tend to propagate westward, which is reminiscent of mesoscale systems embedded in African easterly waves. However, these results are modified when local convection is considered because rainfall forecasts are very difficult due to their small spatial and temporal scale and the inherent non-continuity of the associated dynamics. Acknowledgments: WRF (www.wrf-model.org) simulations were carried out on a workstation provided by Dr Serge Janicot of LOCEAN (Paris), in the framework of the PICREVAT project, which was funded by the French government. TRMM data set used in 19

this study was acquired online from NASA. ERA-I data set was obtained from http://dataportal.ecmwf.int/data/d/interim_daily and GFS data are downloaded from http://nomads.ncdc.noaa.gov/cgi-bin/ncdc-ui/ftp4u.pl. The authors would like to thank the editor and anonymous reviewers for understanding the significance of the work and providing several chances to revise the manuscript through their valuable comments and suggestions, which helped to improve the manuscript in every direction.

20

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28

List of Tables Table 1: Model configuration for both CNTL and DA simulations. Table 2: Conventional data used in the model simulations Table 3: Observation types and total numbers Table 4: Assimilated variables u, v (m/s): zonal and meridional wind, t (K): temperature, p (hPa): pressure, q (%): specific humidity, r(%): relative humidity, tpw (mm): total precipitable water, thickness (gpm): geopotential thickness, ref (m): GPS reference height Table 5: Near surface atmospheric variables biases over West Africa for Case 1 Table 6: Near surface atmospheric variables biases over West Africa for Case 2 Table 7: Near surface atmospheric variables biases over West Africa for Case 3 Table 8: Rainfall verification

29

List of Figures Figure 1: Study domain and topography Figure 2: Spatial distribution of relative humidity (%) at 1000 hPa valid from 15 June 2011 at 0000 UTC to 15 June 2011 at 1200 UTC at a time interval of 06 hours. The first horizontal panel from top (a, b and c) represents the ERA-I distribution, the second (d, e, and f) shows results from CNTL simulations and the third one (g, h and i) displays the DA simulations. Figure 3: Same as figure 2, but valid from 16 June 2011 at 1200 UTC to 17 June 2011 at 0000 UTC. Figure 4: 2 m temperature (K) (shaded contour) superposed by wind vector distribution (m/s) at 1000 hPa valid from 0000 UTC to 1200 UTC on 15 June 2011 at a time interval of 06 hours. The first horizontal panel from top (a, b and c) represents the ERA-I distribution, the second one (d, e and f) is from the CNTL simulations and the third one (g, h and i) is the results from DA simulations. Figure 5: Same as figure 4, but valid from 1200 UTC on 16 June to 0000 UTC on 17 June 2011 Figure 6: Relative humidity difference (%) between DA and CNTL (i. e. DA - CNTL) for Case 1: (a) 0000 UTC on June 15, (b) 0600 UTC on June 15, (c) 1200 UTC on June 15, (d) 1800 UTC on June 15, (e) 0000 UTC on June 16, (f) 0600 UTC on June 16, (g) 1200 UTC on June 16, (h) 1800 UTC on June 16 and (i) 0000 UTC on June 17, 2011. Figure 7: Same as figure 6, but for 2 m temperature (K) difference. Figure 8: Same as figure 6 but for 1000 hPa U-wind (m/s) difference. 30

Figure 9: Same as figure 6 but for 1000 hPa V-wind (m/s) difference. Figure 10: Spatial correlation for relative humidity and 2 m temperature from CNTL and DA simulations. Figure 11: Spatial correlation for wind components from CNTL and DA simulations. Figure 12: 6-hourly accumulated rainfall (mm/day) initialized at 0000 UTC and valid from 0600 UTC on June 15 to 0000 UTC on June 17, 2011. The first vertical panel from left is the TRMM observation, the second is from CNTL and the third panel is from DA. The corresponding hours are indicated on the TRMM plot in the first vertical panel. Figure 13: Same as figure 12, but for Case 2. Figure 14: Same as figure 12, but for Case 3. Figure 15: Hovmöller diagrams of 6-hourly accumulated rainfall (48-h forecasts), covering the whole longitudinal band of the study domain and averaged over the region 0°N-20°N. The first horizontal panel is for Case 1, the second is for Case 2 and the third one is for Case 3. The left most vertical panel represents TRMM data, the right most one is from DA simulations and the middle one is from CNTL simulations. Figure 16: Vertical profile and RMSE of gridded analysis increment on 15 June 2011 for input atmospheric variables at considered Eta levels: (a) minimum gridded analysis increment, (b) maximum gridded analysis increment and (c) RMSE of gridded analysis increment. Figure 17: Same as figure 16, but for 23 August 2012. Figure 18: Same as figure 16, but for 04 September 2012.

31

Figure 19: Vertical profile of gridded analysis increment and RMSE of gridded analysis increment for the variable pressure at Eta levels for the three cases considered in this study: (a) minimum gridded analysis increment, (b) maximum gridded analysis increment and (c) RMSE of gridded analysis increment. The pressure has been separated from the others due to scale.

32

Table1: Model configuration for both CNTL and DA simulations.

WRF Configuration

Description / Remarks

WRF Core

Advanced Research WRF (ARW)

Horizontal resolution

25 km in both x and y directions

Sigma Levels

41 vertical levels

Integration time step

150 seconds

Spin-up-time

06 hours

Microphysics

Thompson scheme

Long-Wave Radiation

RRTMG scheme

Short-Wave Radiation

RRTMG scheme

Land surface model

Rapid Update Cycle (RUC)

Planetary boundary Layer (PBL)

Mellor Yamada Janjic (MYJ) scheme

Cumulus parameterization

Modifed Tiedtke scheme

Dynamic option

Eulerian mass

Map projection

Lambert Conformal

Initial and boundary conditions

GFS (0.5° x 0.5°)

Cloud effect

Yes

52

Table 2: Conventional data used in the model simulations

Conventional data

Description

TEMP

Upper air profiles of temperature, humidity and wind from radiosonde

PILOT

Wind profiles from optical theodolite

SYNOP

Automatic surface observations from land stations (Synoptic data )

SHIPS

Voluntary observations from sea

BUOY

Drifting and moored buoy observations

SOUND

Surface Weather Observation Stations

GEOAMV

Geo-stationary atmospheric motion vectors

AIREP

Aircraft report, colloquially air report, observations from an in-flight aircraft to a ground station

GPSRF

Reference GPS (Global Positioning System) data

METAR

METeorological Airport Report (observations from airport stations in 30 minutes interval)

SONDE SFC

Radiosonde at surface

53

Table 3: Observation types and total numbers

Serial No.

Datasets

Number of observations

1

TEMP/RADIANCE

1174

2

PILOT

6

3

SHIP

28

4

SYNOP

204

5

BUOY

2

6

SOUND

14

7

GEOAMV

7275

8

GPSRF

2740

9

METAR

101

10

SONDE FC

17

Total

11561

54

Table 4: Assimilated variables u, v (m/s): zonal and meridional wind, t (K): temperature, p (hPa): pressure, q (%): specific humidity, r (%): relative humidity, tpw (mm): total precipitable water, thickness (gpm): geopotential thickness, ref (m): GPS reference height. Type of Data Source

Variables

Synop

u, v, t, p, q

Metar

u, v, t, p, q

Ship

u, v, t, p, q

Sonde-sfc

u, v, t, p, q

Buoy

u, v, t, p, q

Sound

u, v, t, q

Geoamv

u, v

Polaramv

u, v

Pilot

u, v

Profiler

u, v

Qscat

u, v

Airep

u, v, t

Airs

t, q

Satem

thickness

Gpsref

ref

Gpspw

tpw

AMSU-A

t profile

AMSU-B

r profile

55

Table 5: Near surface atmospheric variables biases over West Africa for Case 1

Hours (UTC)

0000

Humidity (CNTL) Humidity (DA)

0600

1200

1800

0000

0600

1200

-11.219 -1.964

17.318

17.144

-9.206

0.343

-15.693 -15.745

-6.204

-9.136

1.343

17.083

16.784

-8.344

1.109

-13.916 -13.568

-4.576

2-m 1.209 Temperature (CNTL)

-0.190

1.286

1.811

0.940

0.270

1.909

2.372

0.909

2-m 0.198 Temperature (DA)

-0.551

1.277

1.683

0.689

-0.042 1.334

1.735

0.526

u-wind (CNTL)

-0.064

1.366

0.952

0.259

0.721

1.167 0.991

0.628

0.892

u-wind (DA)

0.465

1.473

0.615

-0.019

0.390

0.647

0.706

0.602

0.954

v-wind (CNTL)

-0.186

0.865

0.514

-0.011

0.647

0.602

0.540

0.463

0.414

v-wind (DA)

0.526

0.584

-0.039

-0.102

0.343

0.479

0.714

0.743

0.707

56

1800

0000

Table 6: Near surface atmospheric variables biases over West Africa for Case 2 Hours (UTC) Humidity (CNTL) Humidity (DA) 2m Temperature (CNTL) 2m Temperature (DA) u-wind (CNTL) u-wind (DA) v-wind (CNTL) v-wind (DA)

0000

0600

1200

1800

0000

0600

1200

1800

0000

-12.120

-1.180

0.563

-2.906 2.029 -5.669 3.294 -0.133 0.456

7.701 7.493 0.861

-7.545

0.439

6.756 7.425 0.630

-7.267

1.772

5.348 5.914 0.404

1.721

0.356

0.687

1.544

1.358

0.623

1.155

1.606

0.829

0.095

0.881

0.734

0.669

0.919

1.239

1.055

1.140

1.053

-0.216

0.920

0.846

0.702

1.252

1.458

1.287

1.436

1.629

0.331

0.716

0.256

0.244

0.581

0.974

0.862

0.545

0.555

0.089

0.830

0.850

0.340

0.778

1.056

0.979

1.117

1.275

-11.771

-2.356

57

-9.101

-6.937 0.456

Table 7: Near surface atmospheric variables biases over West Africa for Case 3 Hours (UTC) Humidity (CNTL) Humidity (DA) 2-m temperature (CNTL) 2-m temperature (DA) u-wind (CNTL) u-wind (DA) v-wind (CNTL) v-wind (DA)

0000

0600

1200

1800

0000

0600

1200

1800

0000

-8.250 -4.514 -1.205 -7.065 -7.333 -3.943 -2.118 -5.637 -5.648 -8.101 -4.769 -1.566 -7.186 -7.332 -4.015 -2.651 -6.117 -5.680 1.358

0.238

0.887

1.495

1.104

0.183

0.794

0.833

0.649

1.310

0.219

0.922

1.485

1.073

0.162

0.942

0.983

0.649

0.821

1.418

1.447

1.663

1.960

1.515

1.581

2.036

1.828

0.563

1.165

1.067

1.443

1.833

1.536

1.467

1.884

1.739

-0.132 0.291

0.283

0.422

0.856

0.571

0.715

0.658

0.445

-0.787 -0.161 0.050

0.443

0.704

0.428

0.608

0.743

0.597

58

Table 8: Rainfall verification

Simulation case

Correlation Bias

RMSE

Case 1 15 June: CNTL

0.195

-1.054

5.227

15 June: DA

0.184

-1.048

5.234

16 June: CNTL

0.156

-0.927

5.246

16 June: DA

0.229

-0.888

5.181

Case 2 23 August: CNTL

0.610

0.180

1.049

23 August: DA

0.514

-0.202

1.040

24 August: CNTL

0.668

0.190

1.022

24 August: DA

0.675

-0.064

1.008

Case 3 04 September: CNTL

0.564

-0.077

0.960

04 September: DA

0.561

-0.092

0.955

05 September: CNTL

0.335

0.169

1.238

05 September: DA

0.350

0.162

1.226

59

Figure 1: Study domain and topography

33

Figure 2: Spatio-temporal distribution of 6-hourly relative humidity (%) at 1000 hPa valid from 15 June 2011 at 0000 UTC to 15 June 2011 at 1200 UTC at a time interval of 06 hours. The first horizontal panel from top (a-c) represents the ERA-I distribution, the second (d-f) shows results from CNTL simulations and the third one (g-i) displays the DA simulations.

34

Figure 3: Same as figure 2, but valid from 16 June 2011 at 1200 UTC to 17 June 2011 at 0000 UTC.

35

Figure 4: Spatio-temporal distribution of 6-hourly 2 m temperature (K) distribution (shaded contour) superposed by wind vector (m/s) at 1000 hPa valid from 0000 UTC to 1200 UTC on 15 June 2011 at a time interval of 06 hours. The first horizontal panel from top (a-c) represents the ERA-I distribution, the second one (d-f) is from the CNTL simulations and the third one (g-i) is the results from DA simulations.

36

Figure 5: Same as figure 4, but valid from 1200 UTC on 16 June to 0000 UTC on 17 June 2011.

37

a)

b)

c)

d)

e)

f)

g)

h)

i)

Figure 6: Relative humidity difference (%) between DA and CNTL (i. e. DA - CNTL) for Case 1: (a) 0000 UTC on June 15, (b) 0600 UTC on June 15, (c) 1200 UTC on June 15, (d) 1800 UTC on June 15, (e) 0000 UTC on June 16, (f) 0600 UTC on June 16, (g) 1200 UTC on June 16, (h) 1800 UTC on June 16 and (i) 0000 UTC on June 17, 2011.

38

a)

b)

c)

d)

e)

f)

g)

h)

i)

Figure 7: Same as figure 6, but for 2 m temperature (K) difference.

39

a)

b)

c)

d)

e)

f)

g)

h)

i)

Figure 8: Same as figure 6 but for 1000 hPa U-wind (m/s) difference.

40

a)

b)

c)

d)

e)

f)

g)

h)

i)

Figure 9: Same as figure 6 but for 1000 hPa V-wind (m/s) difference.

41

Figure 10: Spatial correlation for relative humidity and 2 m temperature from CNTL and DA simulations for Case 1.

42

Figure 11: Spatial correlation for wind components from CNTL and DA simulations for Case 1.

43

Figure 12: Six-hourly accumulated rainfall (mm/day) initialized at 0000 UTC and valid from 0600 UTC on June 15 to 0000 UTC on June 17, 2011. The first vertical panel from left is the TRMM observation, the second is from CNTL and the third panel is from DA experiment. The corresponding hours are indicated on the TRMM plot in the first vertical panel.

44

Figure 13: Same as figure 12, but for Case 2.

45

Figure 14: Same as figure 12, but for Case 3.

46

Figure 15: Hovmöller diagrams of 6-hourly accumulated rainfall (48-h forecasts), covering the whole longitudinal band of the study domain and averaged over the region 0°N-20°N. The first horizontal panel is for Case 1, the second one is for Case 2 and the third one is for Case 3. The left most vertical panel represents TRMM data, the right most one is from DA simulations and the middle one is from CNTL simulations.

47

a)

b)

c)

Figure 16: Vertical profile and RMSE of gridded analysis increment on 15 June 2011 for input atmospheric variables at considered Eta levels: (a) minimum gridded analysis increment, (b) maximum gridded analysis increment and (c) RMSE of gridded analysis increment.

48

a)

b)

c)

Figure 17: Same as figure 16, but for 23 August 2012.

49

a)

b)

c)

Figure 18: Same as figure 16, but for 04 September 2012.

50

a)

b)

c)

Figure 19: Vertical profile of gridded analysis increment and RMSE of gridded analysis increment for the variable pressure at Eta levels for the three cases considered in this study: (a) minimum gridded analysis increment, (b) maximum gridded analysis increment and (c) RMSE of gridded analysis increment. The pressure has been separated from the others due to scale.

51